A Pulsed Lidar System With Ultimate Quantum Range Accuracy - Kruse, Stephan; Serino, Laura; Folge, Patrick Fabian; Echeverria Oviedo, Dana; Bhattacharjee, Abhinandan; Stefszky, Michael; Scheytt, J. Christoph; Brecht, Benjamin; Silberhorn, Christine (IEEE Photonics Technology Letters)
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics; Electronic; Optical and Magnetic Materials

A parametrisation method for high-order phase reduction in coupled oscillator networks - von der Gracht, Sören; Nijholt, Eddie; Rink, Bob (arXiv:2306.03320)
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic expansion for an embedding of the perturbed invariant torus, as well as for the reduced phase dynamics in local coordinates. Both can be determined to arbitrary degrees of accuracy, and we show that the phase dynamics may directly be obtained in normal form. We apply the method to predict remote synchronisation in a chain of coupled Stuart-Landau oscillators.

Local Protocols for Contracting and Expanding Robot Formation Problems - Castenow, Jannik

Online Algorithms for Allocating Heterogeneous Resources - Knollmann, Till

Efficient Modeling and Tailoring of Nonlinear Wavefronts in Dielectric Metasurfaces - Hähnel, David; Förstner, Jens; Myroshnychenko, Viktor (ACS Photonics)
Dielectric metasurfaces provide a unique platform for efficient harmonic generation and optical wavefront manipulation at the nanoscale. Tailoring phase and amplitude of a nonlinearly generated wave with a high emission efficiency using resonance-based metasurfaces is a challenging task that often requires state-of-the-art numerical methods. Here, we propose a simple yet effective approach combining a sampling method with a Monte Carlo approach to design the third-harmonic wavefront generated by all-dielectric metasurfaces composed of elliptical silicon nanodisks. Using this approach, we theoretically demonstrate the full nonlinear 2π phase control with a uniform and highest possible amplitude in the considered parameter space, allowing us to design metasurfaces operating as third harmonic beam deflectors capable of steering light into a desired direction with high emission efficiency. The TH beam deflection with a record calculated average conversion efficiency of 1.2 × 10–1 W–2 is achieved. We anticipate that the proposed approach will be widely applied as alternative to commonly used optimization algorithms with higher complexity and implementation effort for the design of metasurfaces with other holographic functionalities.
Keywords: tet_topic_meta

Approximation Algorithms for Fair Range Clustering - Hotegni, Sedjro Salomon; Mahabadi, Sepideh; Vakilian, Ali (Proceedings of the 40th International Conference on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 2023.)
Keywords: Fair range clustering

We Really Need to Talk About Session Tickets: A Large-Scale Analysis of Cryptographic Dangers with TLS Session Tickets - Hebrok, Sven Niclas; Nachtigall, Simon; Maehren, Marcel; Erinola, Nurullah; Merget, Robert; Somorovsky, Juraj; Schwenk, Jörg (32nd USENIX Security Symposium)

Teaching Technologies: Continuous Interplay Between Educational and Industrial Advances - Jonas-Ahrend, Gabriela; Vernholz, Mats; Temmen, Katrin (Teacher Education in the Wake of Covid-19)
The field of teaching technologies is in constant interplay between educational and industrial advances. Since the beginning of the twenty-first century, digitalization and automatization have become increasingly important. In industrial and social life, we see similar fast-moving developments. These factors challenge education, specifically vocational education, greatly, and raise two very different, yet very much connected questions: how to prepare students for their vocational lives and how to prepare teachers to communicate the necessary competencies to their students? This chapter provides an overview of advances, challenges, and possible solutions, focusing on the three key fields of vocational education in Germany: Industry 4.0, Education 4.0, and innovative teacher education. Most importantly, however, the text examines the continuous interplay between and among these fields. The beginning of the chapter is dedicated to vocational teacher education, in accordance with industrial and educational advances. Specifying this, characteristics of Industry 4.0, as well as students' and teachers' perceptions of Industry 4.0, are discussed. This is followed by an introduction to the concept of so-called learning factories as a possible way of integrating aspects of Industry 4.0 in German vocational schools. The end of the chapter is dedicated to the required changes in educational settings today and in the future. Though Industry 4.0, Education 4.0, and innovative teacher education are each widely discussed in the current literature, the interplay of all three fields reveals a research gap. This chapter tries to close this gap and provide an important contribution to the research field.

Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen - Häsel-Weide, Uta (Die Grundschulzeitschrift)

Addition und Subtraktion verstehen - Graf, Lara Marie; Wienhues, Inga; Häsel-Weide, Uta (Die Grundschulzeitschrift)

Data-Driven Product Management: A Practitioner-Driven Research Agenda - Grigoryan, Khoren; Fichtler, Timm; Schreiner, Nick; Rabe, Martin; Panzner, Melina; Kühn, Arno; Dumitrescu, Roman; Koldewey, Christian (Procedia CIRP 33)
The global megatrends of digitization and sustainability lead to new challenges for the design and management of technical products in industrial companies. Product management - as the bridge between market and company - has the task to absorb and combine the manifold requirements and make the right product-related decisions. In the process, product management is confronted with heterogeneous information, rapidly changing portfolio components, as well as increasing product, and organizational complexity. Combining and utilizing data from different sources, e.g., product usage data and social media data leads to promising potentials to improve the quality of product-related decisions. In this paper, we reinforce the need for data-driven product management as an interdisciplinary field of action. The state of data-driven product management in practice was analyzed by conducting workshops with six manufacturing companies and hosting a focus group meeting with experts from different industries. We investigate the expectations and derive requirements leading us to open research questions, a vision for data-driven product management, and a research agenda to shape future research efforts.
Keywords: Product Management; Data Analytics; Data-Driven Design; Product-related data; Lifecycle Data; Tool-support

Interview Study on Strategy Options for Platform Operation in B2B Markets - Özcan, Leon; Fichtler, Timm; Kasten, Benjamin; Koldewey, Christian; Dumitrescu, Roman
Keywords: Digital Platform; Platform Strategy; Strategic Management; Platform Life Cycle; Interview Study; Business Model; Business-to-Business; Two-sided Market; Multi-sided Market

Neural Class Expression Synthesis - KOUAGOU, N'Dah Jean; Heindorf, Stefan; Demir, Caglar; Ngonga Ngomo, Axel-Cyrille (The Semantic Web - 20th Extended Semantic Web Conference (ESWC 2023))
Many applications require explainable node classification in knowledge graphs. Towards this end, a popular ``white-box'' approach is class expression learning: Given sets of positive and negative nodes, class expressions in description logics are learned that separate positive from negative nodes. Most existing approaches are search-based approaches generating many candidate class expressions and selecting the best one. However, they often take a long time to find suitable class expressions. In this paper, we cast class expression learning as a translation problem and propose a new family of class expression learning approaches which we dub neural class expression synthesizers. Training examples are ``translated'' into class expressions in a fashion akin to machine translation. Consequently, our synthesizers are not subject to the runtime limitations of search-based approaches. We study three instances of this novel family of approaches based on LSTMs, GRUs, and set transformers, respectively. An evaluation of our approach on four benchmark datasets suggests that it can effectively synthesize high-quality class expressions with respect to the input examples in approximately one second on average. Moreover, a comparison to state-of-the-art approaches suggests that we achieve better F-measures on large datasets. For reproducibility purposes, we provide our implementation as well as pretrained models in our public GitHub repository at https://github.com/dice-group/NeuralClassExpressionSynthesis
Keywords: Neural network; Concept learning; Description logics

Counterfactual Explanations for Concepts in ELH - Sieger, Leonie Nora; Heindorf, Stefan; Blübaum, Lukas; Ngonga Ngomo, Axel-Cyrille (arXiv:2301.05109)
Knowledge bases are widely used for information management on the web, enabling high-impact applications such as web search, question answering, and natural language processing. They also serve as the backbone for automatic decision systems, e.g. for medical diagnostics and credit scoring. As stakeholders affected by these decisions would like to understand their situation and verify fair decisions, a number of explanation approaches have been proposed using concepts in description logics. However, the learned concepts can become long and difficult to fathom for non-experts, even when verbalized. Moreover, long concepts do not immediately provide a clear path of action to change one's situation. Counterfactuals answering the question "How must feature values be changed to obtain a different classification?" have been proposed as short, human-friendly explanations for tabular data. In this paper, we transfer the notion of counterfactuals to description logics and propose the first algorithm for generating counterfactual explanations in the description logic $\mathcal{ELH}$. Counterfactual candidates are generated from concepts and the candidates with fewest feature changes are selected as counterfactuals. In case of multiple counterfactuals, we rank them according to the likeliness of their feature combinations. For evaluation, we conduct a user survey to investigate which of the generated counterfactual candidates are preferred for explanation by participants. In a second study, we explore possible use cases for counterfactual explanations.

Identifizierung quantifizierbarer Bewertungsinhalte und -kategorien mittels Text Mining - Kersting, Joschka
Reading between the lines has so far been reserved for humans. The present dissertation addresses this research gap using machine learning methods. Implicit expressions are not comprehensible by computers and cannot be localized in the text. However, many texts arise on interpersonal topics that, unlike commercial evaluation texts, often imply information only by means of longer phrases. Examples are the kindness and the attentiveness of a doctor, which are only paraphrased (“he didn’t even look me in the eye”). The analysis of such data, especially the identification and localization of implicit statements, is a research gap (1). This work uses so-called Aspect-based Sentiment Analysis as a method for this purpose. It remains open how the aspect categories to be extracted can be discovered and thematically delineated based on the data (2). Furthermore, it is not yet explored how a collection of tools should look like, with which implicit phrases can be identified and thus made explicit (3). Last, it is an open question how to correlate the identified phrases from the text data with other data, including the investigation of the relationship between quantitative scores (e.g., school grades) and the thematically related text (4). Based on these research gaps, the research question is posed as follows: Using text mining methods, how can implicit rating content be properly interpreted and thus made explicit before it is automatically categorized and quantified? The uniqueness of this dissertation is based on the automated recognition of implicit linguistic statements alongside explicit statements. These are identified in unstructured text data so that features expressed only in the text can later be compared across data sources, even though they were not included in rating categories such as stars or school grades. German-language physician ratings from websites in three countries serve as the sample domain. The solution approach consists of data creation, a pipeline for text processing and analyses based on this. In the data creation, aspect classes are identified and delineated across platforms and marked in text data. This results in six datasets with over 70,000 annotated sentences and detailed guidelines. The models that were created based on the training data extract and categorize the aspects. In addition, the sentiment polarity and the evaluation weight, i. e., the importance of each phrase, are determined. The models, which are combined in a pipeline, are used in a prototype in the form of a web application. The analyses built on the pipeline quantify the rating contents by linking the obtained information with further data, thus allowing new insights. As a result, a toolbox is provided to identify quantifiable rating content and categories using text mining for a sample domain. This is used to evaluate the approach, which in principle can also be adapted to any other domain.

Capabilities and Limitations of Local Strategies in Dynamic Networks - Götte, Thorsten; Knollmann, Till; Meyer auf der Heide, Friedhelm; Scheideler, Christian; Werthmann, Julian (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

On-The-Fly Compute Centers II: Execution of Composed Services in Configurable Compute Centers - Karl, Holger; Maack, Marten; Meyer auf der Heide, Friedhelm; Pukrop, Simon; Redder, Adrian (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Practical Cryptograhic Techniques for Secure and Privacy-Preserving Customer Loyalty Systems - Blömer, Johannes; Bobolz, Jan; Eidens, Fabian; Jager, Tibor; Kramer, Paul (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Architectural Management of OTF Computing Markets - Gottschalk, Sebastian; Vorbohle, Christian; Kundisch, Dennis; Engels, Gregor; Wünderlich, Nacy V. (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Robustness and Security - Blömer, Johannes; Eidens, Fabian; Jager, Tibor; Niehues, David; Scheideler, Christian (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Dialogue-based Requirement Compensation and Style-adjusted Data-to-text Generation - Bäumer, Frederik Simon; Chen, Wei-Fan; Geierhos, Michaela; Kersting, Joschka; Wachsmuth, Henning (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Configuration and Evaluation - Hanselle, Jonas Manuel; Hüllermeier, Eyke; Mohr, Felix; Ngonga Ngomo, Axel-Cyrille; Sherif, Mohamed; Tornede, Alexander; Wever, Marcel Dominik (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

The Market for Services: Incentives, Algorithms, Implementation - Haake, Claus-Jochen; Hehenkamp, Burkhard; Polevoy, Gleb (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Composition Analysis in Unknown Contexts - Wehrheim, Heike; Hüllermeier, Eyke; Becker, Steffen; Becker, Matthias; Richter, Cedric; Sharma, Arnab (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Reconfigurable Random Forest Implementation on FPGA - Raeisi Nafchi, Masood

Data Analytics for Predictive Maintenance of Time Series Data - Yadalam Murali Kumar, Nihal

The Optimal Depth of Variational Quantum Algorithms Is QCMA-Hard to Approximate - Bittel, Lennart; Gharibian, Sevag; Kliesch, Martin (Proceedings of the 38th Computational Complexity Conference (CCC))
Variational Quantum Algorithms (VQAs), such as the Quantum Approximate Optimization Algorithm (QAOA) of [Farhi, Goldstone, Gutmann, 2014], have seen intense study towards near-term applications on quantum hardware. A crucial parameter for VQAs is the depth of the variational ansatz used - the smaller the depth, the more amenable the ansatz is to near-term quantum hardware in that it gives the circuit a chance to be fully executed before the system decoheres. This potential for depth reduction has made VQAs a staple of Noisy Intermediate-Scale Quantum (NISQ)-era research. In this work, we show that approximating the optimal depth for a given VQA ansatz is intractable. Formally, we show that for any constant $ε>0$, it is QCMA-hard to approximate the optimal depth of a VQA ansatz within multiplicative factor $N^{1-ε}$, for $N$ denoting the encoding size of the VQA instance. (Here, Quantum Classical Merlin-Arthur (QCMA) is a quantum generalization of NP.) We then show that this hardness persists even in the "simpler" setting of QAOAs. To our knowledge, this yields the first natural QCMA-hard-to-approximate problems. To achieve these results, we bypass the need for a PCP theorem for QCMA by appealing to the disperser-based NP-hardness of approximation construction of [Umans, FOCS 1999].

On Cloud Assisted, Restricted, and Reosurce Constrained Scheduling - Pukrop, Simon

Utilizing Redundancy in Distributed Heterogeneous Storage - Schneider, Fabian

Graph Neural Network-based Anomaly Detection in Smart Grid Energy Consumption - Ranade, Amruta

Highly accurate deep compressed facial recognition - Ali, Osama

Super-Gaussian decay of exponentials: A sufficient condition - Hinrichs, Benjamin; Janssen, Daan W.; Ziebell, Jobst (Journal of Mathematical Analysis and Applications)
Keywords: Applied Mathematics; Analysis

Virtual On-Demand Volunteer System Based on Delaunay Triangulation - Ashri, Nivedita

Temperedness of locally symmetric spaces: The product case - Weich, Tobias; Wolf, Lasse L. (arXiv:2304.09573)
Let $X=X_1× X_2$ be a product of two rank one symmetric spaces of non-compact type and $Γ$ a torsion-free discrete subgroup in $G_1× G_2$. We show that the spectrum of $Γ \backslash X$ is related to the asymptotic growth of $Γ$ in the two direction defined by the two factors. We obtain that $L^2(Γ \backslash G)$ is tempered for large class of $Γ$.

Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors - Brosch, Anian; Tinazzi, Fabio; Wallscheid, Oliver; Zigliotto, Mauro; Böcker, Joachim (IEEE Transactions on Power Electronics)
Keywords: Electrical and Electronic Engineering

Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks - Meyer, Marius; Kenter, Tobias; Plessl, Christian (ACM Transactions on Reconfigurable Technology and Systems)
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.
Keywords: General Computer Science

Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems - Weber, Daniel; Schenke, Maximilian; Wallscheid, Oliver (IEEE Access)
Keywords: General Engineering; General Materials Science; General Computer Science; Electrical and Electronic Engineering

Safe Reinforcement Learning-Based Control in Power Electronic Systems - Weber, Daniel; Schenke, Maximilian; Wallscheid, Oliver (2023 International Conference on Future Energy Solutions (FES))

Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering based on Neural Networks - N., N.

Neuro-Symbolic Class Expression Learning - Demir, Caglar; Ngonga Ngomo, Axel-Cyrille (International Joint Conference on Artificial Intelligence)

Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs - Ma, Yulai; Mattiolo, Davide; Steffen, Eckhard; Wolf, Isaak Hieronymus (SIAM Journal on Discrete Mathematics)
Keywords: General Mathematics

Computing and Compressing Electron Repulsion Integrals on FPGAs - Wu, Xin; Kenter, Tobias; Schade, Robert; Kühne, Thomas; Plessl, Christian (2023 IEEE 31st Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM))
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 ($10 × 10^9$ 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.

Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics - Schade, Robert; Kenter, Tobias; Elgabarty, Hossam; Lass, Michael; Kühne, Thomas; Plessl, Christian (The International Journal of High Performance Computing Applications)
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.
Keywords: Hardware and Architecture; Theoretical Computer Science; Software

Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions - Tornede, Alexander

Generation of 100 GHz Periodic Nyquist Pulses using Cascaded Mach-Zehnder Modulators in a Silicon Electronic-Photonic Platform - Kress, Christian; Schwabe, Tobias; Silberhorn, Christine; Scheytt, J. Christoph (Conference on Lasers and Electro-Optics (CLEO) 2023)
A frequency-flexible Nyquist pulse synthesizer is presented with optical pulse bandwidths up to fopt=100 GHz and repetition rates equal to fopt/9, fabricated in an electronic-photonic co-integrated platform utilizing linear on-chip drivers.

Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves - Offen, Christian; Ober-Blöbaum, Sina (Geometric Science of Information)
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.
Keywords: System identification; discrete Lagrangians; travelling waves

Variational Learning of Euler–Lagrange Dynamics from Data - Ober-Blöbaum, Sina; Offen, Christian (Journal of Computational and Applied Mathematics)
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.
Keywords: Lagrangian learning; variational backward error analysis; modified Lagrangian; variational integrators; physics informed learning

Backward error analysis for conjugate symplectic methods - McLachlan, Robert; Offen, Christian (Journal of Geometric Mechanics)
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.
Keywords: variational integrators; backward error analysis; Euler--Lagrange equations; multistep methods; conjugate symplectic methods

Hamiltonian Neural Networks with Automatic Symmetry Detection - Dierkes, Eva; Offen, Christian; Ober-Blöbaum, Sina; Flaßkamp, Kathrin (Chaos)
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.

Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen - Sprenger, Alexander
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.
Keywords: Testantwortkompaktierung; Prozessvariation; Silicon Lifecycle Management