@unpublished{46117, abstract = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the asymptotic growth of $\Gamma$ in the two direction defined by the two factors. We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of $\Gamma$.}}, author = {{Weich, Tobias and Wolf, Lasse L.}}, booktitle = {{arXiv:2304.09573}}, title = {{{Temperedness of locally symmetric spaces: The product case}}}, year = {{2023}}, } @article{46147, author = {{Brosch, Anian and Tinazzi, Fabio and Wallscheid, Oliver and Zigliotto, Mauro and Böcker, Joachim}}, issn = {{0885-8993}}, journal = {{IEEE Transactions on Power Electronics}}, keywords = {{Electrical and Electronic Engineering}}, publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}}, 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}}, year = {{2023}}, } @article{38041, abstract = {{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. 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.}}, author = {{Meyer, Marius and Kenter, Tobias and Plessl, Christian}}, issn = {{1936-7406}}, journal = {{ACM Transactions on Reconfigurable Technology and Systems}}, keywords = {{General Computer Science}}, publisher = {{Association for Computing Machinery (ACM)}}, title = {{{Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks}}}, doi = {{10.1145/3576200}}, year = {{2023}}, } @article{46213, author = {{Weber, Daniel and Schenke, Maximilian and Wallscheid, Oliver}}, issn = {{2169-3536}}, journal = {{IEEE Access}}, keywords = {{General Engineering, General Materials Science, General Computer Science, Electrical and Electronic Engineering}}, pages = {{76524--76536}}, publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}}, title = {{{Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems}}}, doi = {{10.1109/access.2023.3297274}}, volume = {{11}}, year = {{2023}}, } @inproceedings{46212, author = {{Weber, Daniel and Schenke, Maximilian and Wallscheid, Oliver}}, booktitle = {{2023 International Conference on Future Energy Solutions (FES)}}, publisher = {{IEEE}}, title = {{{Safe Reinforcement Learning-Based Control in Power Electronic Systems}}}, doi = {{10.1109/fes57669.2023.10182718}}, year = {{2023}}, } @misc{46221, author = {{N., N.}}, title = {{{Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering based on Neural Networks}}}, year = {{2023}}, } @article{46251, author = {{Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}}, journal = {{International Joint Conference on Artificial Intelligence}}, location = {{Macau}}, title = {{{Neuro-Symbolic Class Expression Learning}}}, year = {{2023}}, } @article{46256, author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0895-4801}}, journal = {{SIAM Journal on Discrete Mathematics}}, keywords = {{General Mathematics}}, number = {{3}}, pages = {{1548--1565}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}}}, doi = {{10.1137/22m1500654}}, volume = {{37}}, year = {{2023}}, } @inproceedings{43228, abstract = {{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 computed for every time step. In 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 relations. 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 best 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. Our 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.}}, author = {{Wu, Xin and Kenter, Tobias and Schade, Robert and Kühne, Thomas and Plessl, Christian}}, booktitle = {{2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM)}}, pages = {{162--173}}, title = {{{Computing and Compressing Electron Repulsion Integrals on FPGAs}}}, doi = {{10.1109/FCCM57271.2023.00026}}, year = {{2023}}, } @article{45361, abstract = {{ 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. }}, author = {{Schade, Robert and Kenter, Tobias and Elgabarty, Hossam and Lass, Michael and Kühne, Thomas and Plessl, Christian}}, issn = {{1094-3420}}, journal = {{The International Journal of High Performance Computing Applications}}, keywords = {{Hardware and Architecture, Theoretical Computer Science, Software}}, publisher = {{SAGE Publications}}, title = {{{Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics}}}, doi = {{10.1177/10943420231177631}}, year = {{2023}}, } @phdthesis{45780, author = {{Tornede, Alexander}}, 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 }}, year = {{2023}}, } @article{29240, abstract = {{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, we 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.}}, author = {{Ober-Blöbaum, Sina and Offen, Christian}}, issn = {{0377-0427}}, journal = {{Journal of Computational and Applied Mathematics}}, keywords = {{Lagrangian learning, variational backward error analysis, modified Lagrangian, variational integrators, physics informed learning}}, pages = {{114780}}, publisher = {{Elsevier}}, title = {{{Variational Learning of Euler–Lagrange Dynamics from Data}}}, doi = {{10.1016/j.cam.2022.114780}}, volume = {{421}}, year = {{2023}}, } @article{29236, abstract = {{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.}}, author = {{McLachlan, Robert and Offen, Christian}}, journal = {{Journal of Geometric Mechanics}}, keywords = {{variational integrators, backward error analysis, Euler--Lagrange equations, multistep methods, conjugate symplectic methods}}, number = {{1}}, pages = {{98--115}}, publisher = {{AIMS Press}}, title = {{{Backward error analysis for conjugate symplectic methods}}}, doi = {{10.3934/jgm.2023005}}, volume = {{15}}, year = {{2023}}, } @article{37654, abstract = {{Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.}}, author = {{Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}}, issn = {{1054-1500}}, journal = {{Chaos}}, number = {{6}}, publisher = {{AIP Publishing}}, title = {{{Hamiltonian Neural Networks with Automatic Symmetry Detection}}}, doi = {{10.1063/5.0142969}}, volume = {{33}}, year = {{2023}}, } @phdthesis{46482, abstract = {{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. With 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. To 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.}}, author = {{Sprenger, Alexander}}, keywords = {{Testantwortkompaktierung, Prozessvariation, Silicon Lifecycle Management}}, pages = {{xi, 160}}, publisher = {{Universität Paderborn}}, title = {{{Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen}}}, doi = {{10.17619/UNIPB/1-1787}}, year = {{2023}}, } @misc{45558, abstract = {{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.}}, 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}}, publisher = {{LibreCat University}}, title = {{{IngridKG: A FAIR Knowledge Graph of Graffiti}}}, doi = {{10.5281/ZENODO.7560242}}, year = {{2023}}, } @unpublished{46579, abstract = {{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 dynamics 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 graining (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.}}, author = {{Peitz, Sebastian and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}}, booktitle = {{arXiv:2307.15325}}, title = {{{Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems}}}, year = {{2023}}, } @article{23428, abstract = {{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. samples. 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 best 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 = {{Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}}, journal = {{Journal of Nonlinear Science}}, title = {{{Finite-data error bounds for Koopman-based prediction and control}}}, doi = {{10.1007/s00332-022-09862-1}}, volume = {{33}}, year = {{2023}}, } @article{21600, abstract = {{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.}}, author = {{Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}}, journal = {{SIAM Journal on Scientific Computing}}, number = {{2}}, pages = {{A579--A595}}, title = {{{Efficient time stepping for numerical integration using reinforcement learning}}}, doi = {{10.1137/21M1412682}}, volume = {{45}}, year = {{2023}}, } @inproceedings{46739, author = {{Sadeghi-Kohan, Somayeh and Hellebrand, Sybille and Wunderlich, Hans-Joachim}}, booktitle = {{2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)}}, publisher = {{IEEE}}, title = {{{Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication}}}, doi = {{10.1109/dsn-w58399.2023.00056}}, year = {{2023}}, }