[{"abstract":[{"text":"Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$.","lang":"eng"}],"status":"public","type":"preprint","publication":"arXiv:2304.09573","language":[{"iso":"eng"}],"external_id":{"arxiv":["2304.09573"]},"_id":"46117","user_id":"45027","department":[{"_id":"10"}],"year":"2023","citation":{"ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. <i>arXiv:230409573</i>. Published online 2023.","ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” <i>arXiv:2304.09573</i>. 2023.","chicago":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>ArXiv:2304.09573</i>, 2023.","apa":"Weich, T., &#38; Wolf, L. L. (2023). Temperedness of locally symmetric spaces: The product case. In <i>arXiv:2304.09573</i>.","short":"T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023).","bibtex":"@article{Weich_Wolf_2023, title={Temperedness of locally symmetric spaces: The product case}, journal={arXiv:2304.09573}, author={Weich, Tobias and Wolf, Lasse L.}, year={2023} }","mla":"Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>ArXiv:2304.09573</i>, 2023."},"title":"Temperedness of locally symmetric spaces: The product case","date_updated":"2023-07-24T07:53:29Z","date_created":"2023-07-24T07:52:23Z","author":[{"last_name":"Weich","full_name":"Weich, Tobias","first_name":"Tobias"},{"first_name":"Lasse L.","full_name":"Wolf, Lasse L.","last_name":"Wolf"}]},{"publication":"IEEE Transactions on Power Electronics","type":"journal_article","status":"public","_id":"46147","department":[{"_id":"52"}],"user_id":"75779","keyword":["Electrical and Electronic Engineering"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0885-8993","1941-0107"]},"publication_status":"published","year":"2023","citation":{"ama":"Brosch A, Tinazzi F, Wallscheid O, Zigliotto M, Böcker J. Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors. <i>IEEE Transactions on Power Electronics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1109/tpel.2023.3294557\">10.1109/tpel.2023.3294557</a>","chicago":"Brosch, Anian, Fabio Tinazzi, Oliver Wallscheid, Mauro Zigliotto, and Joachim Böcker. “Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors.” <i>IEEE Transactions on Power Electronics</i>, 2023. <a href=\"https://doi.org/10.1109/tpel.2023.3294557\">https://doi.org/10.1109/tpel.2023.3294557</a>.","ieee":"A. Brosch, F. Tinazzi, O. Wallscheid, M. Zigliotto, and J. Böcker, “Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors,” <i>IEEE Transactions on Power Electronics</i>, 2023, doi: <a href=\"https://doi.org/10.1109/tpel.2023.3294557\">10.1109/tpel.2023.3294557</a>.","bibtex":"@article{Brosch_Tinazzi_Wallscheid_Zigliotto_Böcker_2023, title={Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors}, DOI={<a href=\"https://doi.org/10.1109/tpel.2023.3294557\">10.1109/tpel.2023.3294557</a>}, journal={IEEE Transactions on Power Electronics}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Brosch, Anian and Tinazzi, Fabio and Wallscheid, Oliver and Zigliotto, Mauro and Böcker, Joachim}, year={2023} }","short":"A. Brosch, F. Tinazzi, O. Wallscheid, M. Zigliotto, J. Böcker, IEEE Transactions on Power Electronics (2023).","mla":"Brosch, Anian, et al. “Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors.” <i>IEEE Transactions on Power Electronics</i>, Institute of Electrical and Electronics Engineers (IEEE), 2023, doi:<a href=\"https://doi.org/10.1109/tpel.2023.3294557\">10.1109/tpel.2023.3294557</a>.","apa":"Brosch, A., Tinazzi, F., Wallscheid, O., Zigliotto, M., &#38; Böcker, J. (2023). Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors. <i>IEEE Transactions on Power Electronics</i>. <a href=\"https://doi.org/10.1109/tpel.2023.3294557\">https://doi.org/10.1109/tpel.2023.3294557</a>"},"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","date_updated":"2023-07-25T20:34:51Z","author":[{"full_name":"Brosch, Anian","id":"75779","orcid":"0000-0003-4871-1664","last_name":"Brosch","first_name":"Anian"},{"full_name":"Tinazzi, Fabio","last_name":"Tinazzi","first_name":"Fabio"},{"first_name":"Oliver","orcid":"https://orcid.org/0000-0001-9362-8777","last_name":"Wallscheid","full_name":"Wallscheid, Oliver","id":"11291"},{"full_name":"Zigliotto, Mauro","last_name":"Zigliotto","first_name":"Mauro"},{"first_name":"Joachim","orcid":"0000-0002-8480-7295","last_name":"Böcker","full_name":"Böcker, Joachim","id":"66"}],"date_created":"2023-07-25T20:33:12Z","title":"Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors","doi":"10.1109/tpel.2023.3294557"},{"abstract":[{"text":"<jats:p>While FPGA accelerator boards and their respective high-level design tools are maturing, there is still a lack of multi-FPGA applications, libraries, and not least, benchmarks and reference implementations towards sustained HPC usage of these devices. As in the early days of GPUs in HPC, for workloads that can reasonably be decoupled into loosely coupled working sets, multi-accelerator support can be achieved by using standard communication interfaces like MPI on the host side. However, for performance and productivity, some applications can profit from a tighter coupling of the accelerators. FPGAs offer unique opportunities here when extending the dataflow characteristics to their communication interfaces.</jats:p>\r\n          <jats:p>In this work, we extend the HPCC FPGA benchmark suite by multi-FPGA support and three missing benchmarks that particularly characterize or stress inter-device communication: b_eff, PTRANS, and LINPACK. With all benchmarks implemented for current boards with Intel and Xilinx FPGAs, we established a baseline for multi-FPGA performance. Additionally, for the communication-centric benchmarks, we explored the potential of direct FPGA-to-FPGA communication with a circuit-switched inter-FPGA network that is currently only available for one of the boards. The evaluation with parallel execution on up to 26 FPGA boards makes use of one of the largest academic FPGA installations.</jats:p>","lang":"eng"}],"status":"public","type":"journal_article","publication":"ACM Transactions on Reconfigurable Technology and Systems","keyword":["General Computer Science"],"language":[{"iso":"eng"}],"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"},{"_id":"4","name":"SFB 901 - C: SFB 901 - Project Area C"},{"name":"SFB 901: SFB 901","_id":"1","grant_number":"160364472"},{"_id":"14","name":"SFB 901 - C2: SFB 901 - Subproject C2","grant_number":"160364472"}],"_id":"38041","user_id":"24135","department":[{"_id":"27"},{"_id":"518"}],"year":"2023","citation":{"apa":"Meyer, M., Kenter, T., &#38; Plessl, C. (2023). Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks. <i>ACM Transactions on Reconfigurable Technology and Systems</i>. <a href=\"https://doi.org/10.1145/3576200\">https://doi.org/10.1145/3576200</a>","mla":"Meyer, Marius, et al. “Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks.” <i>ACM Transactions on Reconfigurable Technology and Systems</i>, Association for Computing Machinery (ACM), 2023, doi:<a href=\"https://doi.org/10.1145/3576200\">10.1145/3576200</a>.","bibtex":"@article{Meyer_Kenter_Plessl_2023, title={Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks}, DOI={<a href=\"https://doi.org/10.1145/3576200\">10.1145/3576200</a>}, journal={ACM Transactions on Reconfigurable Technology and Systems}, publisher={Association for Computing Machinery (ACM)}, author={Meyer, Marius and Kenter, Tobias and Plessl, Christian}, year={2023} }","short":"M. Meyer, T. Kenter, C. Plessl, ACM Transactions on Reconfigurable Technology and Systems (2023).","ama":"Meyer M, Kenter T, Plessl C. Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks. <i>ACM Transactions on Reconfigurable Technology and Systems</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1145/3576200\">10.1145/3576200</a>","chicago":"Meyer, Marius, Tobias Kenter, and Christian Plessl. “Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks.” <i>ACM Transactions on Reconfigurable Technology and Systems</i>, 2023. <a href=\"https://doi.org/10.1145/3576200\">https://doi.org/10.1145/3576200</a>.","ieee":"M. Meyer, T. Kenter, and C. Plessl, “Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks,” <i>ACM Transactions on Reconfigurable Technology and Systems</i>, 2023, doi: <a href=\"https://doi.org/10.1145/3576200\">10.1145/3576200</a>."},"publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["1936-7406","1936-7414"]},"title":"Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/3576200","open_access":"1"}],"doi":"10.1145/3576200","publisher":"Association for Computing Machinery (ACM)","date_updated":"2023-07-28T08:02:05Z","oa":"1","author":[{"full_name":"Meyer, Marius","id":"40778","last_name":"Meyer","first_name":"Marius"},{"first_name":"Tobias","last_name":"Kenter","full_name":"Kenter, Tobias","id":"3145"},{"id":"16153","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","first_name":"Christian"}],"date_created":"2023-01-23T08:40:42Z"},{"keyword":["General Engineering","General Materials Science","General Computer Science","Electrical and Electronic Engineering"],"language":[{"iso":"eng"}],"_id":"46213","department":[{"_id":"34"},{"_id":"52"}],"user_id":"24041","status":"public","publication":"IEEE Access","type":"journal_article","title":"Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems","doi":"10.1109/access.2023.3297274","date_updated":"2023-07-31T07:04:48Z","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","volume":11,"author":[{"first_name":"Daniel","full_name":"Weber, Daniel","last_name":"Weber"},{"full_name":"Schenke, Maximilian","last_name":"Schenke","first_name":"Maximilian"},{"full_name":"Wallscheid, Oliver","last_name":"Wallscheid","first_name":"Oliver"}],"date_created":"2023-07-31T07:04:27Z","year":"2023","page":"76524-76536","intvolume":"        11","citation":{"ama":"Weber D, Schenke M, Wallscheid O. Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems. <i>IEEE Access</i>. 2023;11:76524-76536. doi:<a href=\"https://doi.org/10.1109/access.2023.3297274\">10.1109/access.2023.3297274</a>","ieee":"D. Weber, M. Schenke, and O. Wallscheid, “Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems,” <i>IEEE Access</i>, vol. 11, pp. 76524–76536, 2023, doi: <a href=\"https://doi.org/10.1109/access.2023.3297274\">10.1109/access.2023.3297274</a>.","chicago":"Weber, Daniel, Maximilian Schenke, and Oliver Wallscheid. “Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems.” <i>IEEE Access</i> 11 (2023): 76524–36. <a href=\"https://doi.org/10.1109/access.2023.3297274\">https://doi.org/10.1109/access.2023.3297274</a>.","apa":"Weber, D., Schenke, M., &#38; Wallscheid, O. (2023). Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems. <i>IEEE Access</i>, <i>11</i>, 76524–76536. <a href=\"https://doi.org/10.1109/access.2023.3297274\">https://doi.org/10.1109/access.2023.3297274</a>","bibtex":"@article{Weber_Schenke_Wallscheid_2023, title={Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems}, volume={11}, DOI={<a href=\"https://doi.org/10.1109/access.2023.3297274\">10.1109/access.2023.3297274</a>}, journal={IEEE Access}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Weber, Daniel and Schenke, Maximilian and Wallscheid, Oliver}, year={2023}, pages={76524–76536} }","short":"D. Weber, M. Schenke, O. Wallscheid, IEEE Access 11 (2023) 76524–76536.","mla":"Weber, Daniel, et al. “Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems.” <i>IEEE Access</i>, vol. 11, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 76524–36, doi:<a href=\"https://doi.org/10.1109/access.2023.3297274\">10.1109/access.2023.3297274</a>."},"publication_identifier":{"issn":["2169-3536"]},"publication_status":"published"},{"citation":{"mla":"Weber, Daniel, et al. “Safe Reinforcement Learning-Based Control in Power Electronic Systems.” <i>2023 International Conference on Future Energy Solutions (FES)</i>, IEEE, 2023, doi:<a href=\"https://doi.org/10.1109/fes57669.2023.10182718\">10.1109/fes57669.2023.10182718</a>.","bibtex":"@inproceedings{Weber_Schenke_Wallscheid_2023, title={Safe Reinforcement Learning-Based Control in Power Electronic Systems}, DOI={<a href=\"https://doi.org/10.1109/fes57669.2023.10182718\">10.1109/fes57669.2023.10182718</a>}, booktitle={2023 International Conference on Future Energy Solutions (FES)}, publisher={IEEE}, author={Weber, Daniel and Schenke, Maximilian and Wallscheid, Oliver}, year={2023} }","short":"D. Weber, M. Schenke, O. Wallscheid, in: 2023 International Conference on Future Energy Solutions (FES), IEEE, 2023.","apa":"Weber, D., Schenke, M., &#38; Wallscheid, O. (2023). Safe Reinforcement Learning-Based Control in Power Electronic Systems. <i>2023 International Conference on Future Energy Solutions (FES)</i>. <a href=\"https://doi.org/10.1109/fes57669.2023.10182718\">https://doi.org/10.1109/fes57669.2023.10182718</a>","ieee":"D. Weber, M. Schenke, and O. Wallscheid, “Safe Reinforcement Learning-Based Control in Power Electronic Systems,” 2023, doi: <a href=\"https://doi.org/10.1109/fes57669.2023.10182718\">10.1109/fes57669.2023.10182718</a>.","chicago":"Weber, Daniel, Maximilian Schenke, and Oliver Wallscheid. “Safe Reinforcement Learning-Based Control in Power Electronic Systems.” In <i>2023 International Conference on Future Energy Solutions (FES)</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/fes57669.2023.10182718\">https://doi.org/10.1109/fes57669.2023.10182718</a>.","ama":"Weber D, Schenke M, Wallscheid O. Safe Reinforcement Learning-Based Control in Power Electronic Systems. In: <i>2023 International Conference on Future Energy Solutions (FES)</i>. IEEE; 2023. doi:<a href=\"https://doi.org/10.1109/fes57669.2023.10182718\">10.1109/fes57669.2023.10182718</a>"},"year":"2023","publication_status":"published","doi":"10.1109/fes57669.2023.10182718","title":"Safe Reinforcement Learning-Based Control in Power Electronic Systems","date_created":"2023-07-31T07:01:22Z","author":[{"last_name":"Weber","full_name":"Weber, Daniel","first_name":"Daniel"},{"first_name":"Maximilian","full_name":"Schenke, Maximilian","last_name":"Schenke"},{"full_name":"Wallscheid, Oliver","last_name":"Wallscheid","first_name":"Oliver"}],"date_updated":"2023-07-31T07:03:46Z","publisher":"IEEE","status":"public","publication":"2023 International Conference on Future Energy Solutions (FES)","type":"conference","language":[{"iso":"eng"}],"department":[{"_id":"34"},{"_id":"52"}],"user_id":"24041","_id":"46212"},{"language":[{"iso":"eng"}],"_id":"46221","department":[{"_id":"79"}],"user_id":"15504","status":"public","type":"mastersthesis","title":"Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering based on Neural Networks","date_updated":"2023-07-31T10:49:30Z","supervisor":[{"full_name":"Scheideler, Christian","id":"20792","last_name":"Scheideler","first_name":"Christian"}],"date_created":"2023-07-31T10:49:12Z","author":[{"last_name":"N.","full_name":"N., N.","first_name":"N."}],"year":"2023","citation":{"apa":"N., N. (2023). <i>Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering based on Neural Networks</i>.","bibtex":"@book{N._2023, title={Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering based on Neural Networks}, author={N., N.}, year={2023} }","short":"N. N., Improving the End-of-Line Test of Custom-Built Geared Motors Using Clustering Based on Neural Networks, 2023.","mla":"N., N. <i>Improving the End-of-Line Test of Custom-Built Geared Motors Using Clustering Based on Neural Networks</i>. 2023.","ama":"N. N. <i>Improving the End-of-Line Test of Custom-Built Geared Motors Using Clustering Based on Neural Networks</i>.; 2023.","chicago":"N., N. <i>Improving the End-of-Line Test of Custom-Built Geared Motors Using Clustering Based on Neural Networks</i>, 2023.","ieee":"N. N., <i>Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering based on Neural Networks</i>. 2023."}},{"oa":"1","date_updated":"2023-08-01T09:44:30Z","date_created":"2023-08-01T09:30:37Z","author":[{"last_name":"Demir","full_name":"Demir, Caglar","id":"43817","first_name":"Caglar"},{"last_name":"Ngonga Ngomo","full_name":"Ngonga Ngomo, Axel-Cyrille","first_name":"Axel-Cyrille"}],"title":"Neuro-Symbolic Class Expression Learning","conference":{"name":"International Joint Conference on Artificial Intelligence IJCAI 2023","location":"Macau"},"has_accepted_license":"1","year":"2023","citation":{"ama":"Demir C, Ngonga Ngomo A-C. Neuro-Symbolic Class Expression Learning. <i>International Joint Conference on Artificial Intelligence</i>. Published online 2023.","ieee":"C. Demir and A.-C. Ngonga Ngomo, “Neuro-Symbolic Class Expression Learning,” <i>International Joint Conference on Artificial Intelligence</i>, 2023.","chicago":"Demir, Caglar, and Axel-Cyrille Ngonga Ngomo. “Neuro-Symbolic Class Expression Learning.” <i>International Joint Conference on Artificial Intelligence</i>, 2023.","apa":"Demir, C., &#38; Ngonga Ngomo, A.-C. (2023). Neuro-Symbolic Class Expression Learning. <i>International Joint Conference on Artificial Intelligence</i>. International Joint Conference on Artificial Intelligence IJCAI 2023, Macau.","mla":"Demir, Caglar, and Axel-Cyrille Ngonga Ngomo. “Neuro-Symbolic Class Expression Learning.” <i>International Joint Conference on Artificial Intelligence</i>, 2023.","short":"C. Demir, A.-C. Ngonga Ngomo, International Joint Conference on Artificial Intelligence (2023).","bibtex":"@article{Demir_Ngonga Ngomo_2023, title={Neuro-Symbolic Class Expression Learning}, journal={International Joint Conference on Artificial Intelligence}, author={Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}, year={2023} }"},"_id":"46251","project":[{"grant_number":"101070305","_id":"407","name":"ENEXA: Efficient Explainable Learning on Knowledge Graphs"},{"name":"KnowGraphs: KnowGraphs: Knowledge Graphs at Scale","_id":"410"},{"grant_number":"NW21-059D","name":"SAIL: SAIL: SustAInable Life-cycle of Intelligent Socio-Technical Systems","_id":"285"}],"department":[{"_id":"574"}],"user_id":"43817","ddc":["000"],"language":[{"iso":"eng"}],"file_date_updated":"2023-08-01T09:30:35Z","publication":"International Joint Conference on Artificial Intelligence","type":"journal_article","status":"public","file":[{"file_id":"46252","file_name":"public.pdf","access_level":"open_access","file_size":340865,"creator":"cdemir","date_created":"2023-08-01T09:30:35Z","date_updated":"2023-08-01T09:30:35Z","relation":"main_file","content_type":"application/pdf"}]},{"title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs","doi":"10.1137/22m1500654","publisher":"Society for Industrial & Applied Mathematics (SIAM)","date_updated":"2023-08-01T10:09:35Z","author":[{"first_name":"Yulai","full_name":"Ma, Yulai","id":"92748","last_name":"Ma"},{"full_name":"Mattiolo, Davide","last_name":"Mattiolo","first_name":"Davide"},{"first_name":"Eckhard","full_name":"Steffen, Eckhard","id":"15548","orcid":"0000-0002-9808-7401","last_name":"Steffen"},{"first_name":"Isaak Hieronymus","id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf"}],"date_created":"2023-08-01T10:08:32Z","volume":37,"year":"2023","citation":{"apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>, <i>37</i>(3), 1548–1565. <a href=\"https://doi.org/10.1137/22m1500654\">https://doi.org/10.1137/22m1500654</a>","mla":"Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>. 2023;37(3):1548-1565. doi:<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i> 37, no. 3 (2023): 1548–65. <a href=\"https://doi.org/10.1137/22m1500654\">https://doi.org/10.1137/22m1500654</a>.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3, pp. 1548–1565, 2023, doi: <a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>."},"page":"1548-1565","intvolume":"        37","publication_status":"published","publication_identifier":{"issn":["0895-4801","1095-7146"]},"issue":"3","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"46256","user_id":"15540","department":[{"_id":"542"}],"status":"public","type":"journal_article","publication":"SIAM Journal on Discrete Mathematics"},{"abstract":[{"lang":"eng","text":"The computation of electron repulsion integrals (ERIs) over Gaussian-type orbitals (GTOs) is a challenging problem in quantum-mechanics-based atomistic simulations. In practical simulations, several trillions of ERIs may have to be\r\ncomputed for every time step.\r\nIn this work, we investigate FPGAs as accelerators for the ERI computation. We use template parameters, here within the Intel oneAPI tool flow, to create customized designs for 256 different ERI quartet classes, based on their orbitals. To maximize data reuse, all intermediates are buffered in FPGA on-chip memory with customized layout. The pre-calculation of intermediates also helps to overcome data dependencies caused by multi-dimensional recurrence\r\nrelations. The involved loop structures are partially or even fully unrolled for high throughput of FPGA kernels. Furthermore, a lossy compression algorithm utilizing arbitrary bitwidth integers is integrated in the FPGA kernels. To our\r\nbest knowledge, this is the first work on ERI computation on FPGAs that supports more than just the single most basic quartet class. Also, the integration of ERI computation and compression it a novelty that is not even covered by CPU or GPU libraries so far.\r\nOur evaluation shows that using 16-bit integer for the ERI compression, the fastest FPGA kernels exceed the performance of 10 GERIS ($10 \\times 10^9$ ERIs per second) on one Intel Stratix 10 GX 2800 FPGA, with maximum absolute errors around $10^{-7}$ - $10^{-5}$ Hartree. The measured throughput can be accurately explained by a performance model. The FPGA kernels deployed on 2 FPGAs outperform similar computations using the widely used libint reference on a two-socket server with 40 Xeon Gold 6148 CPU cores of the same process technology by factors up to 6.0x and on a new two-socket server with 128 EPYC 7713 CPU cores by up to 1.9x."}],"status":"public","type":"conference","publication":"2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)","language":[{"iso":"eng"}],"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"43228","external_id":{"arxiv":["2303.13632"]},"user_id":"75963","department":[{"_id":"27"},{"_id":"518"}],"year":"2023","citation":{"chicago":"Wu, Xin, Tobias Kenter, Robert Schade, Thomas Kühne, and Christian Plessl. “Computing and Compressing Electron Repulsion Integrals on FPGAs.” In <i>2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>, 162–73, 2023. <a href=\"https://doi.org/10.1109/FCCM57271.2023.00026\">https://doi.org/10.1109/FCCM57271.2023.00026</a>.","ieee":"X. Wu, T. Kenter, R. Schade, T. Kühne, and C. Plessl, “Computing and Compressing Electron Repulsion Integrals on FPGAs,” in <i>2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>, 2023, pp. 162–173, doi: <a href=\"https://doi.org/10.1109/FCCM57271.2023.00026\">10.1109/FCCM57271.2023.00026</a>.","mla":"Wu, Xin, et al. “Computing and Compressing Electron Repulsion Integrals on FPGAs.” <i>2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>, 2023, pp. 162–73, doi:<a href=\"https://doi.org/10.1109/FCCM57271.2023.00026\">10.1109/FCCM57271.2023.00026</a>.","short":"X. Wu, T. Kenter, R. Schade, T. Kühne, C. Plessl, in: 2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM), 2023, pp. 162–173.","bibtex":"@inproceedings{Wu_Kenter_Schade_Kühne_Plessl_2023, title={Computing and Compressing Electron Repulsion Integrals on FPGAs}, DOI={<a href=\"https://doi.org/10.1109/FCCM57271.2023.00026\">10.1109/FCCM57271.2023.00026</a>}, booktitle={2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)}, author={Wu, Xin and Kenter, Tobias and Schade, Robert and Kühne, Thomas and Plessl, Christian}, year={2023}, pages={162–173} }","ama":"Wu X, Kenter T, Schade R, Kühne T, Plessl C. Computing and Compressing Electron Repulsion Integrals on FPGAs. In: <i>2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>. ; 2023:162-173. doi:<a href=\"https://doi.org/10.1109/FCCM57271.2023.00026\">10.1109/FCCM57271.2023.00026</a>","apa":"Wu, X., Kenter, T., Schade, R., Kühne, T., &#38; Plessl, C. (2023). Computing and Compressing Electron Repulsion Integrals on FPGAs. <i>2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>, 162–173. <a href=\"https://doi.org/10.1109/FCCM57271.2023.00026\">https://doi.org/10.1109/FCCM57271.2023.00026</a>"},"page":"162-173","quality_controlled":"1","title":"Computing and Compressing Electron Repulsion Integrals on FPGAs","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/10171537"}],"doi":"10.1109/FCCM57271.2023.00026","date_updated":"2023-08-02T15:05:42Z","author":[{"id":"77439","full_name":"Wu, Xin","last_name":"Wu","first_name":"Xin"},{"first_name":"Tobias","last_name":"Kenter","id":"3145","full_name":"Kenter, Tobias"},{"first_name":"Robert","last_name":"Schade","orcid":"0000-0002-6268-539","full_name":"Schade, Robert","id":"75963"},{"first_name":"Thomas","full_name":"Kühne, Thomas","id":"49079","last_name":"Kühne"},{"first_name":"Christian","last_name":"Plessl","orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","id":"16153"}],"date_created":"2023-03-30T11:15:40Z"},{"language":[{"iso":"eng"}],"keyword":["Hardware and Architecture","Theoretical Computer Science","Software"],"publication":"The International Journal of High Performance Computing Applications","abstract":[{"lang":"eng","text":"<jats:p> The non-orthogonal local submatrix method applied to electronic structure–based molecular dynamics simulations is shown to exceed 1.1 EFLOP/s in FP16/FP32-mixed floating-point arithmetic when using 4400 NVIDIA A100 GPUs of the Perlmutter system. This is enabled by a modification of the original method that pushes the sustained fraction of the peak performance to about 80%. Example calculations are performed for SARS-CoV-2 spike proteins with up to 83 million atoms. </jats:p>"}],"date_created":"2023-05-30T09:19:09Z","publisher":"SAGE Publications","title":"Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics","quality_controlled":"1","year":"2023","user_id":"75963","department":[{"_id":"27"},{"_id":"518"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"45361","article_type":"original","article_number":"109434202311776","type":"journal_article","status":"public","author":[{"last_name":"Schade","orcid":"0000-0002-6268-539","full_name":"Schade, Robert","id":"75963","first_name":"Robert"},{"first_name":"Tobias","id":"3145","full_name":"Kenter, Tobias","last_name":"Kenter"},{"orcid":"0000-0002-4945-1481","last_name":"Elgabarty","full_name":"Elgabarty, Hossam","id":"60250","first_name":"Hossam"},{"full_name":"Lass, Michael","id":"24135","last_name":"Lass","orcid":"0000-0002-5708-7632","first_name":"Michael"},{"first_name":"Thomas","id":"49079","full_name":"Kühne, Thomas","last_name":"Kühne"},{"first_name":"Christian","full_name":"Plessl, Christian","id":"16153","last_name":"Plessl","orcid":"0000-0001-5728-9982"}],"date_updated":"2023-08-02T15:04:53Z","oa":"1","main_file_link":[{"url":"https://journals.sagepub.com/doi/10.1177/10943420231177631","open_access":"1"}],"doi":"10.1177/10943420231177631","publication_status":"published","publication_identifier":{"issn":["1094-3420","1741-2846"]},"citation":{"short":"R. Schade, T. Kenter, H. Elgabarty, M. Lass, T. Kühne, C. Plessl, The International Journal of High Performance Computing Applications (2023).","mla":"Schade, Robert, et al. “Breaking the Exascale Barrier for the Electronic Structure Problem in Ab-Initio Molecular Dynamics.” <i>The International Journal of High Performance Computing Applications</i>, 109434202311776, SAGE Publications, 2023, doi:<a href=\"https://doi.org/10.1177/10943420231177631\">10.1177/10943420231177631</a>.","bibtex":"@article{Schade_Kenter_Elgabarty_Lass_Kühne_Plessl_2023, title={Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics}, DOI={<a href=\"https://doi.org/10.1177/10943420231177631\">10.1177/10943420231177631</a>}, number={109434202311776}, journal={The International Journal of High Performance Computing Applications}, publisher={SAGE Publications}, author={Schade, Robert and Kenter, Tobias and Elgabarty, Hossam and Lass, Michael and Kühne, Thomas and Plessl, Christian}, year={2023} }","apa":"Schade, R., Kenter, T., Elgabarty, H., Lass, M., Kühne, T., &#38; Plessl, C. (2023). Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics. <i>The International Journal of High Performance Computing Applications</i>, Article 109434202311776. <a href=\"https://doi.org/10.1177/10943420231177631\">https://doi.org/10.1177/10943420231177631</a>","ama":"Schade R, Kenter T, Elgabarty H, Lass M, Kühne T, Plessl C. Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics. <i>The International Journal of High Performance Computing Applications</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1177/10943420231177631\">10.1177/10943420231177631</a>","ieee":"R. Schade, T. Kenter, H. Elgabarty, M. Lass, T. Kühne, and C. Plessl, “Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics,” <i>The International Journal of High Performance Computing Applications</i>, Art. no. 109434202311776, 2023, doi: <a href=\"https://doi.org/10.1177/10943420231177631\">10.1177/10943420231177631</a>.","chicago":"Schade, Robert, Tobias Kenter, Hossam Elgabarty, Michael Lass, Thomas Kühne, and Christian Plessl. “Breaking the Exascale Barrier for the Electronic Structure Problem in Ab-Initio Molecular Dynamics.” <i>The International Journal of High Performance Computing Applications</i>, 2023. <a href=\"https://doi.org/10.1177/10943420231177631\">https://doi.org/10.1177/10943420231177631</a>."}},{"status":"public","file":[{"relation":"main_file","content_type":"application/pdf","file_id":"46118","file_name":"dissertation_alexander_tornede_final_publishing_compressed.pdf","access_level":"open_access","file_size":4300633,"title":" Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions","date_created":"2023-07-24T08:40:35Z","creator":"ahetzer","date_updated":"2023-07-24T08:42:01Z"}],"type":"dissertation","ddc":["006"],"file_date_updated":"2023-07-24T08:42:01Z","language":[{"iso":"eng"}],"_id":"45780","project":[{"name":"SFB 901 - B2: Konfiguration und Bewertung (B02)","_id":"10","grant_number":"160364472"},{"_id":"3","name":"SFB 901 - B: SFB 901 - Project Area B"},{"name":"SFB 901: SFB 901: On-The-Fly Computing - Individualisierte IT-Dienstleistungen in dynamischen Märkten ","_id":"1","grant_number":"160364472"}],"department":[{"_id":"355"}],"user_id":"15504","year":"2023","citation":{"ama":"Tornede A. <i>Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>.; 2023. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1780 \">10.17619/UNIPB/1-1780 </a>","apa":"Tornede, A. (2023). <i>Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1780 \">https://doi.org/10.17619/UNIPB/1-1780 </a>","mla":"Tornede, Alexander. <i>Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>. 2023, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1780 \">10.17619/UNIPB/1-1780 </a>.","short":"A. Tornede, Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions, 2023.","bibtex":"@book{Tornede_2023, title={Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1780 \">10.17619/UNIPB/1-1780 </a>}, author={Tornede, Alexander}, year={2023} }","chicago":"Tornede, Alexander. <i>Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>, 2023. <a href=\"https://doi.org/10.17619/UNIPB/1-1780 \">https://doi.org/10.17619/UNIPB/1-1780 </a>.","ieee":"A. Tornede, <i>Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>. 2023."},"has_accepted_license":"1","title":"Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions","doi":"10.17619/UNIPB/1-1780 ","oa":"1","date_updated":"2023-08-04T06:01:49Z","date_created":"2023-06-27T05:20:14Z","author":[{"last_name":"Tornede","full_name":"Tornede, Alexander","id":"38209","first_name":"Alexander"}],"supervisor":[{"last_name":"Hüllermeier","full_name":"Hüllermeier, Eyke","first_name":"Eyke"}]},{"file":[{"description":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions\nconnecting two points in a phase space, the system will exhibit those motions which extremise an action functional.\nMany qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-\ntions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms\nfor dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features\nwith the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-\ntions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position\ndata of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no\nprior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward\nerror analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the\nlearned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of\nvariational backward error analysis. (3) Finally, we introduce a method to perform system identification from position\nobservations only, based on variational backward error analysis.","title":"Variational Learning of Euler–Lagrange Dynamics from Data","access_level":"open_access","file_id":"32274","date_updated":"2022-06-28T15:25:50Z","date_created":"2022-06-28T15:25:50Z","relation":"main_file","file_size":3640770,"file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","creator":"coffen","content_type":"application/pdf"}],"abstract":[{"text":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\r\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.","lang":"eng"}],"publication":"Journal of Computational and Applied Mathematics","language":[{"iso":"eng"}],"ddc":["510"],"keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"external_id":{"arxiv":["2112.12619"]},"year":"2023","quality_controlled":"1","title":"Variational Learning of Euler–Lagrange Dynamics from Data","date_created":"2022-01-11T13:24:00Z","publisher":"Elsevier","status":"public","type":"journal_article","file_date_updated":"2022-06-28T15:25:50Z","article_type":"original","user_id":"85279","department":[{"_id":"636"}],"_id":"29240","citation":{"ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>. 2023;421:114780. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, p. 114780, 2023, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i> 421 (2023): 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>.","bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, Elsevier, 2023, p. 114780, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","apa":"Ober-Blöbaum, S., &#38; Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>, <i>421</i>, 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>"},"page":"114780","intvolume":"       421","related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianShadowIntegration","relation":"software"}]},"publication_status":"epub_ahead","publication_identifier":{"issn":["0377-0427"]},"has_accepted_license":"1","doi":"10.1016/j.cam.2022.114780","author":[{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279","full_name":"Offen, Christian"}],"volume":421,"oa":"1","date_updated":"2023-08-10T08:42:39Z"},{"publication":"Journal of Geometric Mechanics","abstract":[{"text":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","lang":"eng"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_name":"BEA_MultiStep_Matrix.pdf","access_level":"open_access","file_id":"32801","title":"Backward error analysis for conjugate symplectic methods","file_size":827030,"description":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","creator":"coffen","date_created":"2022-08-12T16:48:59Z","date_updated":"2022-08-12T16:48:59Z"}],"external_id":{"arxiv":["2201.03911"]},"ddc":["510"],"keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"language":[{"iso":"eng"}],"quality_controlled":"1","issue":"1","year":"2023","publisher":"AIMS Press","date_created":"2022-01-11T12:48:39Z","title":"Backward error analysis for conjugate symplectic methods","type":"journal_article","status":"public","_id":"29236","user_id":"85279","department":[{"_id":"636"}],"article_type":"original","file_date_updated":"2022-08-12T16:48:59Z","publication_status":"published","has_accepted_license":"1","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/BEAConjugateSymplectic"}]},"citation":{"apa":"McLachlan, R., &#38; Offen, C. (2023). Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>, <i>15</i>(1), 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>","bibtex":"@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }","mla":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","short":"R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.","ieee":"R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, pp. 98–115, 2023, doi: <a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i> 15, no. 1 (2023): 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>.","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>. 2023;15(1):98-115. doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>"},"page":"98-115","intvolume":"        15","oa":"1","date_updated":"2023-08-10T08:40:30Z","author":[{"full_name":"McLachlan, Robert","last_name":"McLachlan","first_name":"Robert"},{"last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279","first_name":"Christian"}],"volume":15,"doi":"10.3934/jgm.2023005"},{"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","publisher":"AIP Publishing","date_created":"2023-01-20T09:10:06Z","year":"2023","issue":"6","ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2301.07928"]},"abstract":[{"lang":"eng","text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered."}],"file":[{"title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","file_size":5200111,"description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously.","access_level":"open_access","file_name":"JournalPaper_main.pdf","file_id":"44205","date_updated":"2023-04-26T16:20:56Z","creator":"coffen","date_created":"2023-04-26T16:20:56Z","relation":"main_file","content_type":"application/pdf"}],"publication":"Chaos","doi":"10.1063/5.0142969","oa":"1","date_updated":"2023-08-10T08:37:01Z","author":[{"full_name":"Dierkes, Eva","last_name":"Dierkes","first_name":"Eva"},{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp","first_name":"Kathrin"}],"volume":33,"citation":{"ieee":"E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” <i>Chaos</i>, vol. 33, no. 6, Art. no. 063115, 2023, doi: <a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i> 33, no. 6 (2023). <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>.","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>. 2023;33(6). doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>","short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","mla":"Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i>, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","bibtex":"@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }","apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., &#38; Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>, <i>33</i>(6), Article 063115. <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>"},"intvolume":"        33","publication_status":"published","publication_identifier":{"issn":["1054-1500"]},"has_accepted_license":"1","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"article_type":"original","article_number":"063115","file_date_updated":"2023-04-26T16:20:56Z","_id":"37654","user_id":"85279","department":[{"_id":"636"}],"status":"public","type":"journal_article"},{"date_created":"2023-08-12T09:10:38Z","publisher":"Universität Paderborn","title":"Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen","year":"2023","language":[{"iso":"ger"}],"keyword":["Testantwortkompaktierung","Prozessvariation","Silicon Lifecycle Management"],"abstract":[{"text":"Ever increasing demands on the performance of microchips are leading to ever more complex semiconductor technologies with ever shrinking feature sizes. Complex applications with high demands on safety and reliability, such as autonomous driving, are simultaneously driving the requirements for test and diagnosis of VLSI circuits. Throughout the life cycle of a microchip, uncertainties occur that affect its timing behavior. For example, weak circuit structures, aging effects, or process variations can lead to a change in the timing behavior of the circuit. While these uncertainties do not necessarily lead to a change of the functional behavior, they can lead to a reliability problem.\r\nWith modular and hybrid compaction two test instruments are presented in this work that can be used for X-tolerant test response compaction in the built-in Faster-than-At-Speed Test (FAST) which is used to detect uncertainties in VLSI circuits. One challenge for test response compaction during FAST is the high and varying X-rate at the outputs of the circuit under test. By dividing the circuit outputs into test groups and separately compacting these test groups using stochastic compactors, the modular compaction is able to handle these high and varying X-rates.\r\nTo deal with uncertainties on logic interconnects, a method for distinguishing crosstalk and process variation is presented. In current semiconductor technologies, the number of parasitic coupling capacitances between logic interconnects is growing. These coupling capacitances can lead to crosstalk, which causes increased current flow in the logic interconnects, which in turn can lead to increased electromigration. In the presented method, delay maps describing the timing behavior of the circuit outputs at different operating points are used to train artificial neural networks which classify the tested circuits into fault-free and faulty.","lang":"eng"},{"text":"Immer größere Anforderungen an die Leistungsfähigkeit von Mikrochips führen zu Halbleitertechnologien mit immer kleiner werdenden Strukturgrößen. Anwendungen mit hohen Ansprüchen an Sicherheit und Zuverlässigkeit, wie z.B. das autonome Fahren, treiben gleichzeitig die Anforderungen an den Test hochintegrierter Schaltungen an. Während des gesamten Lebenszyklus eines Mikrochips kommt es zu Unsicherheiten im Zeitverhalten. So können z.B. schwache Schaltungsstrukturen, Alterungseffekte oder Prozessvariationen zu einer Veränderung des Zeitverhaltens führen. Während diese Unsicherheiten nicht zu einer Veränderung des funktionalen Verhaltens führen müssen, können sie jedoch zu einem Zuverlässigkeitsproblem führen.\r\nMit der modularen und der hybriden Kompaktierung werden in dieser Arbeit zwei Testinstrumente vorgestellt, die für die X-tolerante Testantwortkompaktierung im eingebauten Hochgeschwindigkeitstest verwendet werden können. Eine Herausforderung für die Testantwortkompaktierung während des Hochgeschwindigkeitstests ist die hohe und variierende X-Rate an den Ausgängen der zu testenden Schaltung. Durch die Einteilung der Schaltungsausgänge in Prüfgruppen und die separierte Kompaktierung der Prüfgruppen mithilfe von stochastischen Kompaktierern, können die vorgestellten Verfahren diese hohen und variierenden X-Raten verarbeiten.\r\nFür den Umgang mit Unsicherheiten auf Verbindungsleitungen der Logik-Schaltung wird ein Verfahren zur Unterscheidung von Übersprechen und Prozessvariation vorgestellt. In aktuellen Halbleitertechnologien kommt es vermehrt zu parasitären Koppelkapazitäten zwischen den Verbindungsleitungen. In dem vorgestellten Verfahren werden künstliche neuronale Netze trainiert, um die Schaltungen in fehlerfrei und fehlerhaft zu klassifizieren.","lang":"ger"}],"author":[{"first_name":"Alexander","id":"22707","full_name":"Sprenger, Alexander","orcid":"0000-0002-0775-7677","last_name":"Sprenger"}],"supervisor":[{"id":"209","full_name":"Hellebrand, Sybille","last_name":"Hellebrand","orcid":"0000-0002-3717-3939","first_name":"Sybille"},{"last_name":"Platzner","id":"398","full_name":"Platzner, Marco","first_name":"Marco"}],"date_updated":"2023-08-12T09:13:18Z","oa":"1","main_file_link":[{"url":"https://nbn-resolving.org/urn:nbn:de:hbz:466:2-45493","open_access":"1"}],"doi":"10.17619/UNIPB/1-1787","publication_status":"published","citation":{"bibtex":"@book{Sprenger_2023, place={Paderborn}, title={Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1787\">10.17619/UNIPB/1-1787</a>}, publisher={Universität Paderborn}, author={Sprenger, Alexander}, year={2023} }","short":"A. Sprenger, Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen, Universität Paderborn, Paderborn, 2023.","mla":"Sprenger, Alexander. <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Universität Paderborn, 2023, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1787\">10.17619/UNIPB/1-1787</a>.","apa":"Sprenger, A. (2023). <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Universität Paderborn. <a href=\"https://doi.org/10.17619/UNIPB/1-1787\">https://doi.org/10.17619/UNIPB/1-1787</a>","ieee":"A. Sprenger, <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Paderborn: Universität Paderborn, 2023.","chicago":"Sprenger, Alexander. <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Paderborn: Universität Paderborn, 2023. <a href=\"https://doi.org/10.17619/UNIPB/1-1787\">https://doi.org/10.17619/UNIPB/1-1787</a>.","ama":"Sprenger A. <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Universität Paderborn; 2023. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1787\">10.17619/UNIPB/1-1787</a>"},"page":"xi, 160","place":"Paderborn","user_id":"22707","department":[{"_id":"48"}],"_id":"46482","extern":"1","type":"dissertation","status":"public"},{"department":[{"_id":"34"}],"user_id":"67234","_id":"45558","project":[{"name":"INGRID: INGRID: Informationssystem Graffiti in Deutschland","_id":"104","grant_number":"289287267"}],"type":"research_data","status":"public","abstract":[{"text":"Graffiti is an urban phenomenon that is increasingly attracting the interest of the sciences. To the best of our knowledge, no suitable data corpora are available for systematic research until now. The Information System Graffiti in Germany project (Ingrid) closes this gap by dealing with graffiti image collections that have been made available to the project for public use. Within Ingrid, the graffiti images are collected, digitized and annotated. With this work, we aim to support the rapid access to a comprehensive data source on Ingrid targeted especially by researchers. In particular, we present IngridKG, an RDF knowledge graph of annotated graffiti, abides by the Linked Data and FAIR principles. We weekly update IngridKG by augmenting the new annotated graffiti to our knowledge graph. Our generation pipeline applies RDF data conversion, link discovery and data fusion approaches to the original data. The current version of IngridKG contains 460,640,154 triples and is linked to 3 other knowledge graphs by over 200,000 links. In our use case studies, we demonstrate the usefulness of our knowledge graph for different applications.","lang":"eng"}],"author":[{"first_name":"Mohamed","orcid":"https://orcid.org/0000-0002-9927-2203","last_name":"Sherif","id":"67234","full_name":"Sherif, Mohamed"},{"full_name":"Morim da Silva, Ana Alexandra","last_name":"Morim da Silva","first_name":"Ana Alexandra"},{"full_name":"Pestryakova, Svetlana","last_name":"Pestryakova","first_name":"Svetlana"},{"full_name":"Ahmed, Abdullah Fathi Ahmed","id":"29670","last_name":"Ahmed","first_name":"Abdullah Fathi Ahmed"},{"first_name":"Sven","last_name":"Niemann","full_name":"Niemann, Sven","id":"6593"},{"first_name":"Axel-Cyrille","id":"65716","full_name":"Ngonga Ngomo, Axel-Cyrille","last_name":"Ngonga Ngomo"}],"date_created":"2023-06-09T10:09:34Z","publisher":"LibreCat University","date_updated":"2023-08-16T10:23:55Z","doi":"10.5281/ZENODO.7560242","title":"IngridKG: A FAIR Knowledge Graph of Graffiti","citation":{"short":"M. Sherif, A.A. Morim da Silva, S. Pestryakova, A.F.A. Ahmed, S. Niemann, A.-C. Ngonga Ngomo, IngridKG: A FAIR Knowledge Graph of Graffiti, LibreCat University, 2023.","bibtex":"@book{Sherif_Morim da Silva_Pestryakova_Ahmed_Niemann_Ngonga Ngomo_2023, title={IngridKG: A FAIR Knowledge Graph of Graffiti}, DOI={<a href=\"https://doi.org/10.5281/ZENODO.7560242\">10.5281/ZENODO.7560242</a>}, publisher={LibreCat University}, author={Sherif, Mohamed and Morim da Silva, Ana Alexandra and Pestryakova, Svetlana and Ahmed, Abdullah Fathi Ahmed and Niemann, Sven and Ngonga Ngomo, Axel-Cyrille}, year={2023} }","mla":"Sherif, Mohamed, et al. <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat University, 2023, doi:<a href=\"https://doi.org/10.5281/ZENODO.7560242\">10.5281/ZENODO.7560242</a>.","apa":"Sherif, M., Morim da Silva, A. A., Pestryakova, S., Ahmed, A. F. A., Niemann, S., &#38; Ngonga Ngomo, A.-C. (2023). <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat University. <a href=\"https://doi.org/10.5281/ZENODO.7560242\">https://doi.org/10.5281/ZENODO.7560242</a>","chicago":"Sherif, Mohamed, Ana Alexandra Morim da Silva, Svetlana Pestryakova, Abdullah Fathi Ahmed Ahmed, Sven Niemann, and Axel-Cyrille Ngonga Ngomo. <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat University, 2023. <a href=\"https://doi.org/10.5281/ZENODO.7560242\">https://doi.org/10.5281/ZENODO.7560242</a>.","ieee":"M. Sherif, A. A. Morim da Silva, S. Pestryakova, A. F. A. Ahmed, S. Niemann, and A.-C. Ngonga Ngomo, <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat University, 2023.","ama":"Sherif M, Morim da Silva AA, Pestryakova S, Ahmed AFA, Niemann S, Ngonga Ngomo A-C. <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat University; 2023. doi:<a href=\"https://doi.org/10.5281/ZENODO.7560242\">10.5281/ZENODO.7560242</a>"},"year":"2023"},{"title":"Partial observations, coarse graining and equivariance in Koopman  operator theory for large-scale dynamical systems","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2307.15325"}],"oa":"1","date_updated":"2023-08-21T05:53:35Z","author":[{"orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"id":"98879","full_name":"Harder, Hans","last_name":"Harder","first_name":"Hans"},{"first_name":"Feliks","full_name":"Nüske, Feliks","last_name":"Nüske"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"}],"date_created":"2023-08-21T05:52:24Z","year":"2023","citation":{"ieee":"S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, and K. Worthmann, “Partial observations, coarse graining and equivariance in Koopman  operator theory for large-scale dynamical systems,” <i>arXiv:2307.15325</i>. 2023.","chicago":"Peitz, Sebastian, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Partial Observations, Coarse Graining and Equivariance in Koopman  Operator Theory for Large-Scale Dynamical Systems.” <i>ArXiv:2307.15325</i>, 2023.","ama":"Peitz S, Harder H, Nüske F, Philipp F, Schaller M, Worthmann K. Partial observations, coarse graining and equivariance in Koopman  operator theory for large-scale dynamical systems. <i>arXiv:230715325</i>. Published online 2023.","apa":"Peitz, S., Harder, H., Nüske, F., Philipp, F., Schaller, M., &#38; Worthmann, K. (2023). Partial observations, coarse graining and equivariance in Koopman  operator theory for large-scale dynamical systems. In <i>arXiv:2307.15325</i>.","short":"S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, K. Worthmann, ArXiv:2307.15325 (2023).","mla":"Peitz, Sebastian, et al. “Partial Observations, Coarse Graining and Equivariance in Koopman  Operator Theory for Large-Scale Dynamical Systems.” <i>ArXiv:2307.15325</i>, 2023.","bibtex":"@article{Peitz_Harder_Nüske_Philipp_Schaller_Worthmann_2023, title={Partial observations, coarse graining and equivariance in Koopman  operator theory for large-scale dynamical systems}, journal={arXiv:2307.15325}, author={Peitz, Sebastian and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }"},"language":[{"iso":"eng"}],"_id":"46579","external_id":{"arxiv":["2307.15325"]},"department":[{"_id":"655"}],"user_id":"47427","abstract":[{"text":"The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems, the main reason being the enormous potential of identifying linear function space representations of nonlinear\r\ndynamics from measurements. Until now, the situation where for large-scale systems, we (i) only have access to partial observations (i.e., measurements, as is very common for experimental data) or (ii) deliberately perform coarse\r\ngraining (for efficiency reasons) has not been treated to its full extent. In this paper, we address the pitfall associated with this situation, that the classical EDMD algorithm does not automatically provide a Koopman operator approximation for the underlying system if we do not carefully select the number of observables. Moreover, we show that symmetries in the system dynamics can be carried over to the Koopman operator, which allows us to massively increase the model efficiency. We also briefly draw a connection to domain decomposition techniques for partial differential equations and present numerical evidence using the Kuramoto--Sivashinsky equation.","lang":"eng"}],"status":"public","publication":"arXiv:2307.15325","type":"preprint"},{"user_id":"47427","department":[{"_id":"101"},{"_id":"655"}],"_id":"23428","language":[{"iso":"eng"}],"article_number":"14","type":"journal_article","publication":"Journal of Nonlinear Science","status":"public","abstract":[{"lang":"eng","text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled."}],"author":[{"last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","id":"81513","first_name":"Feliks"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"}],"date_created":"2021-08-17T12:25:09Z","volume":33,"oa":"1","date_updated":"2023-08-24T07:50:12Z","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"doi":"10.1007/s00332-022-09862-1","title":"Finite-data error bounds for Koopman-based prediction and control","publication_status":"published","citation":{"bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={<a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","short":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023).","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” <i>Journal of Nonlinear Science</i>, vol. 33, 14, 2023, doi:<a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>.","apa":"Nüske, F., Peitz, S., Philipp, F., Schaller, M., &#38; Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. <i>Journal of Nonlinear Science</i>, <i>33</i>, Article 14. <a href=\"https://doi.org/10.1007/s00332-022-09862-1\">https://doi.org/10.1007/s00332-022-09862-1</a>","ama":"Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. <i>Journal of Nonlinear Science</i>. 2023;33. doi:<a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>","ieee":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” <i>Journal of Nonlinear Science</i>, vol. 33, Art. no. 14, 2023, doi: <a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>.","chicago":"Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” <i>Journal of Nonlinear Science</i> 33 (2023). <a href=\"https://doi.org/10.1007/s00332-022-09862-1\">https://doi.org/10.1007/s00332-022-09862-1</a>."},"intvolume":"        33","year":"2023"},{"abstract":[{"lang":"eng","text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML."}],"publication":"SIAM Journal on Scientific Computing","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["arXiv:2104.03562"]},"year":"2023","issue":"2","title":"Efficient time stepping for numerical integration using reinforcement  learning","date_created":"2021-04-09T07:59:19Z","status":"public","type":"journal_article","user_id":"47427","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"_id":"21600","citation":{"apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., &#38; Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>, <i>45</i>(2), A579–A595. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement  learning}, volume={45}, DOI={<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.","mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, 2023, pp. A579–95, doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>.","ieee":"M. Dellnitz <i>et al.</i>, “Efficient time stepping for numerical integration using reinforcement  learning,” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, pp. A579–A595, 2023, doi: <a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>.","chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i> 45, no. 2 (2023): A579–95. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>.","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>. 2023;45(2):A579-A595. doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>"},"intvolume":"        45","page":"A579-A595","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/lueckem/quadrature-ML"}]},"publication_status":"published","has_accepted_license":"1","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"doi":"10.1137/21M1412682","author":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"first_name":"Eyke","full_name":"Hüllermeier, Eyke","id":"48129","last_name":"Hüllermeier"},{"first_name":"Marvin","last_name":"Lücke","full_name":"Lücke, Marvin"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"full_name":"Offen, Christian","id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X"},{"id":"13472","full_name":"Pfannschmidt, Karlson","orcid":"0000-0001-9407-7903","last_name":"Pfannschmidt","first_name":"Karlson"}],"volume":45,"date_updated":"2023-08-25T09:24:50Z"},{"publisher":"IEEE","date_updated":"2023-08-26T10:49:07Z","date_created":"2023-08-26T10:48:31Z","author":[{"id":"78614","full_name":"Sadeghi-Kohan, Somayeh","last_name":"Sadeghi-Kohan","orcid":"https://orcid.org/0000-0001-7246-0610","first_name":"Somayeh"},{"full_name":"Hellebrand, Sybille","id":"209","last_name":"Hellebrand","orcid":"0000-0002-3717-3939","first_name":"Sybille"},{"first_name":"Hans-Joachim","last_name":"Wunderlich","full_name":"Wunderlich, Hans-Joachim"}],"title":"Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication","doi":"10.1109/dsn-w58399.2023.00056","publication_status":"published","year":"2023","citation":{"ama":"Sadeghi-Kohan S, Hellebrand S, Wunderlich H-J. Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication. In: <i>2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)</i>. IEEE; 2023. doi:<a href=\"https://doi.org/10.1109/dsn-w58399.2023.00056\">10.1109/dsn-w58399.2023.00056</a>","chicago":"Sadeghi-Kohan, Somayeh, Sybille Hellebrand, and Hans-Joachim Wunderlich. “Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication.” In <i>2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/dsn-w58399.2023.00056\">https://doi.org/10.1109/dsn-w58399.2023.00056</a>.","ieee":"S. Sadeghi-Kohan, S. Hellebrand, and H.-J. Wunderlich, “Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication,” 2023, doi: <a href=\"https://doi.org/10.1109/dsn-w58399.2023.00056\">10.1109/dsn-w58399.2023.00056</a>.","mla":"Sadeghi-Kohan, Somayeh, et al. “Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication.” <i>2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)</i>, IEEE, 2023, doi:<a href=\"https://doi.org/10.1109/dsn-w58399.2023.00056\">10.1109/dsn-w58399.2023.00056</a>.","short":"S. Sadeghi-Kohan, S. Hellebrand, H.-J. Wunderlich, in: 2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W), IEEE, 2023.","bibtex":"@inproceedings{Sadeghi-Kohan_Hellebrand_Wunderlich_2023, title={Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication}, DOI={<a href=\"https://doi.org/10.1109/dsn-w58399.2023.00056\">10.1109/dsn-w58399.2023.00056</a>}, booktitle={2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)}, publisher={IEEE}, author={Sadeghi-Kohan, Somayeh and Hellebrand, Sybille and Wunderlich, Hans-Joachim}, year={2023} }","apa":"Sadeghi-Kohan, S., Hellebrand, S., &#38; Wunderlich, H.-J. (2023). Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication. <i>2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)</i>. <a href=\"https://doi.org/10.1109/dsn-w58399.2023.00056\">https://doi.org/10.1109/dsn-w58399.2023.00056</a>"},"_id":"46739","user_id":"78614","department":[{"_id":"48"}],"language":[{"iso":"eng"}],"type":"conference","publication":"2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)","status":"public"}]