TY - JOUR A1 - Sun, Jingtong A1 - Berner, Julius A1 - Richter, Lorenz A1 - Zeinhofer, Marius A1 - Müller, Johannes A1 - Azizzadenesheli, Kamyar A1 - Anandkumar, Anima T1 - Dynamical Measure Transport and Neural PDE Solvers for Sampling N2 - The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic evolutions described by partial differential equations (PDEs). This framework incorporates prior trajectory-based sampling methods, such as diffusion models or Schrödinger bridges, without relying on the concept of time-reversals. Moreover, it allows us to propose novel numerical methods for solving the transport task and thus sampling from complicated targets without the need for the normalization constant or data samples. We employ physics-informed neural networks (PINNs) to approximate the respective PDE solutions, implying both conceptional and computational advantages. In particular, PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently, leading to significantly better mode coverage in the sampling task compared to alternative methods. Moreover, they can readily be fine-tuned with Gauss-Newton methods to achieve high accuracy in sampling. Y1 - 2024 ER - TY - CHAP A1 - Winkler, Ludwig A1 - Richter, Lorenz A1 - Opper, Manfred T1 - Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models T2 - Proceedings of the 41st International Conference on Machine Learning N2 - Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this work, we study time-continuous Markov jump processes on discrete state spaces and investigate their correspondence to state-continuous diffusion processes given by SDEs. In particular, we revisit the Ehrenfest process, which converges to an Ornstein-Uhlenbeck process in the infinite state space limit. Likewise, we can show that the time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process. This observation bridges discrete and continuous state spaces and allows to carry over methods from one to the respective other setting. Additionally, we suggest an algorithm for training the time-reversal of Markov jump processes which relies on conditional expectations and can thus be directly related to denoising score matching. We demonstrate our methods in multiple convincing numerical experiments. Y1 - 2024 UR - https://raw.githubusercontent.com/mlresearch/v235/main/assets/winkler24a/winkler24a.pdf VL - 235 SP - 53017 EP - 53038 ER - TY - JOUR A1 - Hartzer, Jacob A1 - Röhrig, Olivia A1 - Wolff, Timo A1 - Yürük, Oğuzhan T1 - Initial steps in the classification of maximal mediated sets JF - Journal of Symbolic Computation Y1 - 2022 ER - TY - JOUR A1 - Kerdreux, Thomas A1 - d'Aspremont, Alexandre A1 - Pokutta, Sebastian T1 - Restarting Frank-Wolfe: Faster Rates under Hölderian Error Bounds JF - Journal of Optimization Theory and Applications Y1 - 2022 ER - TY - JOUR A1 - Combettes, Cyrille A1 - Pokutta, Sebastian T1 - Revisiting the Approximate Carathéodory Problem via the Frank-Wolfe Algorithm JF - Mathematical Programming A Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01735-x VL - 197 SP - 191 EP - 214 ER - TY - JOUR A1 - Vu‐Han, Tu‐Lan A1 - Sunkara, Vikram A1 - Bermudez‐Schettino, Rodrigo A1 - Schwechten, Jakob A1 - Runge, Robin A1 - Perka, Carsten A1 - Winkler, Tobias A1 - Pokutta, Sebastian A1 - Weiß, Claudia A1 - Pumberger, Matthias T1 - Feature Engineering for the Prediction of Scoliosis in 5q‐Spinal Muscular Atrophy JF - Journal of Cachexia, Sarcopenia and Muscle Y1 - 2025 U6 - https://doi.org/10.1002/jcsm.13599 VL - 16 IS - 1 SP - e13599 ER - TY - JOUR A1 - Jain, Toshit A1 - Singh, Upkar A1 - Singh, Varun A1 - Boda, Vijay Kumar A1 - Hotz, Ingrid A1 - Vadhiyar, Sathish S. A1 - Vinayachandran, P. N. A1 - Natarajan, Vijay T1 - A Scalable System for Visual Analysis of Ocean Data JF - Computer Graphics Forum Y1 - 2025 U6 - https://doi.org/10.1111/cgf.15279 VL - 44 IS - 1 SP - e15279 ER - TY - GEN A1 - Ragyanszki, Anita A1 - Ji, Hongchen A1 - Fournier, Rene T1 - Understanding the Origins of Life - A Machine learning approach to estimate reaction mechanisms of biotic precursors T2 - Perspectives and challenges of future HPC installations for atomistic and molecular simulations N2 - Life as we know it is the result of billions of years of evolution; yet, understanding how the very first organisms came into existence is a challenge that has yet to be solved. One theory states that components of the first biotic molecules may not have formed on Earth. Rather, they may have initially formed in the interstellar medium (ISM) and been transported to Earth, as supported by recorded instances of organic molecules detected in space. The ISM, with its low temperatures and specific collision processes, allows for molecular stability and the formation of biotic precursors that would otherwise be unlikely in Earth's prebiotic conditions. Understanding how these molecules formed in the ISM may be the key to determining how life began. The goal of this research is to develop a new model for solving astrobiophysical problems by studying the formation mechanisms of biomolecules found in the ISM. Although such pathways have been studied individually, there has not yet been a comprehensive method to understand all the formation reactions that can occur in ISM. Several quantum chemical and numerical methods are available for finding transition states (TS) and energy barriers (E) of chemical reactions but are time-consuming and can hardly be applied to systems with more than a few atoms. Our main interest is to develop a a machine learning approach to approximate TS, and E, requiring as input only estimates of geometry and energies of reactants and products. Using a complete dataset 300 reaction features are computed, and an estimate of E is obtained by fitting a Kernel Ridge Regression (KRR) model with Laplacian kernel, and a fully connected Artificial Neural Network (ANN) to estimate reaction energy barriers. Y1 - 2024 ER - TY - GEN A1 - Ragyanszki, Anita A1 - Ji, Hongchen A1 - Fournier, Rene T1 - Understanding the Origins of Life – A Machine learning approach to estimate reaction mechanisms of biotic precursors T2 - SIMPLAIX N2 - Understanding the Origins of Life - A Machine learning approach to estimate reaction mechanisms of biotic precursors. Life as we know it is the result of billions of years of evolution; however, understanding how the very first organisms came into existence is a challenge that has yet to be solved. One theory states that components of these molecules may have formed in the interstellar medium (ISM) and been transported to Earth. The ISM, with its specific conditions, allows for molecular stability and the formation of biotic precursors that would otherwise be unlikely in Earth's prebiotic conditions. Understanding how these molecules formed in the ISM may be the key to determining how life began. The goal of this research is to develop a model for solving astrobiophysical problems by studying the formation mechanisms of biomolecules found in the ISM. Although such pathways have been studied individually, there has not yet been a comprehensive method to understand the complete reactions mechanisms. Several QM methods are available for finding transition states (TS) and energy barriers (E) of chemical reactions but are time-consuming and can hardly be applied to more complex systems. Our interest is to develop a machine learning approach to approximate TS, and E, requiring as input only estimates of geometry and energies of reactants and products. Y1 - 2024 ER - TY - CHAP A1 - Christgau, Steffen A1 - Dylan, Everingham A1 - Lübke, Max A1 - De Lucia, Marco A1 - Puhan, Danny A1 - Schelten, Niklas A1 - Schnor, Bettina A1 - Signer, Hannes A1 - Spazier, Johannes A1 - Stabernack, Benno A1 - Steinert, Fritjof A1 - Yahdzhyiev, Serhii T1 - On the Usability and Energy Efficiency of High-Level Synthesis for FPGA-based Network-Attached Accelerators T2 - 2025 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) N2 - Heterogeneity in high performance computing systems is one of the most promising approaches towards more energy-efficient computing on one hand and satisfying the raising demand of global computation capacity on the other hand. Besides the well-known key components like CPUs and GPGPUs are domain-specific accelerators like TPUs, FPGAs well known for their energy efficiency. This is especially true for highly specialized use cases. Network-attached accelerators promise more scalability and flexibility for FPGA usage in HPC environments. Easy and efficient programming of those accelerators is, however, still an open issue. Based on a framework for such accelerators which enables decoupling of FPGAs from their host system, we present a workflow using High-Level Synthesis (HLS) to offload application kernels to them. We evaluate this approach against a conventional Hardware Description Language (HDL) based workflow. In addition, we introduce the energy measurement tool EMA and assess the energy efficiency of both HLS and HDL design. Y1 - 2025 U6 - https://doi.org/10.1109/IPDPSW66978.2025.00139 SP - 886 EP - 895 ER - TY - JOUR A1 - Fricke, Mackenzie S. A1 - Frometa, Magalee R. A1 - Kerkhoff, Yannic A1 - Bernhard, Samuel P. A1 - Tahir, Ramat S. A1 - Quaas, Elisa A1 - Totten, William H. A1 - Haag, Rainer A1 - Achazi, Katharina A1 - Cloninger, Mary J. T1 - The toxicity, uptake, and impact on galectin-3 mediated apoptosis of lactose functionalized PAMAM dendrimers JF - Materials Advances N2 - Poly(amidoamine) (PAMAM) dendrimers functionalized with ligands that are designed to interact with biological receptors are important macromolecules for the elucidation and mediation of biological recognition processes. Specifically, carbohydrate functionalized dendrimers are useful synthetic multivalent systems for the study of multivalent protein–carbohydrate interactions. For example, lactose functionalized glycodendrimers can be used to discern the function of galectins, galactoside-binding proteins that are often over-expressed during cancer progression. In order to effectively interpret cancer cellular assays using glycodendrimers, however, their properties in the presence of cells must first be assessed. Macromolecules that are taken up by cells would be expected to have access to many different cell signaling pathways and modes of action that solely extracellular macromolecules cannot utilize. In addition, macromolecules that display cellular toxicity could not be used as drug delivery vehicles. Here, we report fundamental studies of cellular toxicity, viability, and uptake with four generations of lactose functionalized PAMAM dendrimers. In all cases, the dendrimers are readily taken up by the cells but do not display any significant cellular toxicity. The glycodendrimers also increase cellular apoptosis, suggesting that they may abrogate the antiapoptotic protections afforded by galectin-3 to cancer cells. The results reported here indicate that appropriately functionalized PAMAM dendrimers can be used as nontoxic tools for the study and mediation of both extra and intracellular cancer processes. Y1 - 2025 U6 - https://doi.org/10.1039/D4MA00782D VL - 6 SP - 3171 EP - 3184 ER - TY - JOUR A1 - Khatri, Vinod A1 - Boback, Nico A1 - Abdelwahab, Hassan A1 - Niemeyer, Daniela A1 - Palmer, Tahlia M. A1 - Sahoo, Anil Kumar A1 - Kerkhoff, Yannic A1 - Ludwig, Kai A1 - Balci, Dilara A1 - Trimpert, Jakob A1 - Haag, Rainer A1 - Povolotsky, Tatyana L. A1 - Netz, Roland R. A1 - Drosten, Christian A1 - Lauster, Daniel C. A1 - Bhatia, Sumati T1 - Polysialosides outperform sulfated analogs for the inhibition of SARS-CoV-2 JF - Small N2 - Both polysialosides and polysulfates are known to interact with the receptor binding domain (RBD) of the SARS-CoV-2 spike protein. However, a comprehensive site by site analysis of their binding affinities and potential synergistic antiviral effects have not been performed. Here, we report on the synthesis of polysialosides with nanomolar binding affinities to spike proteins of SARS-CoV-2 in solution using microscale thermophoresis (MST). The dendritic polyglycerol based polysialosides dPG500(SA)0.55 and dPG500(SA)0.25, with a dissociation constant Kd of 4.78 nM and 10.85 nM, respectively, bind ~500 times stronger than the high density polysulfated analog dPG500(OSO3Na)0.55, to intact SARS-CoV-2 virus particles or isolated spike protein. In fact, the presence of sulfate groups in a heteromultivalent compound dPG500(SA)0.20(OSO3Na)0.20 weakens the binding to spike proteins. A polycarboxylated analog does not bind to SARS-CoV-2, ruling out that the interaction of polysialoside is simply driven by electrostatic interactions. Furthermore, we found potent nanomolar binding of dPG500(SA)0.55 to SARS-CoV-2 variant B.1.617 (Delta) and B.1.1.529 (Omicron) RBD. Using explicit-solvent all-atom molecular dynamics (MD) simulations and docking studies, we obtain atomistic details on the interaction of different functional groups with the SARS-CoV-2 RBD and their binding affinities. Our data support the conclusion that sialosides interact stronger with RBD than sulfates. Notably, our most affine binder dPG500(SA)0.55 inhibits SARS-CoV-2 (WT, D614G) replication up to 98.6% at low nanomolar concentrations. Y1 - 2025 UR - https://doi.org/10.26434/chemrxiv-2024-8b0gb U6 - https://doi.org/10.1002/smll.202500719 VL - 21 IS - 34 ER - TY - CHAP A1 - Ribera Borrell, Enric A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Reinforcement Learning with Random Time Horizons T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/borrell25a/borrell25a.pdf VL - 267 SP - 5101 EP - 5123 ER - TY - THES A1 - el Bahnasawy, Henry T1 - Konzeption und Entwicklung einer Plattform zur geographisch verteilten Bereitstellung von latenzkritischen Anwendungen Y1 - 2025 ER - TY - CHAP A1 - Kera, Hiroshi A1 - Ishihara, Yuki A1 - Kambe, Yuta A1 - Vaccon, Tristan A1 - Yokoyama, Kazuhiro T1 - Learning to Compute Gr\"obner Bases T2 - Proceedings of the Conference on Neural Information Processing Systems Y1 - 2024 ER - TY - CHAP A1 - Kumano, Soichiro A1 - Kera, Hiroshi A1 - Yamasaki, Toshihiko T1 - Wide Two-Layer Networks can Learn from Adversarial Perturbations T2 - Proceedings of the Conference on Neural Information Processing Systems Y1 - 2024 ER - TY - CHAP A1 - Hollender, Alexandros A1 - Maystre, Gilbert A1 - Nagarajan, Sai Ganesh T1 - The Complexity of Two-Team Polymatrix Games with Independent Adversaries T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding the limits of tractability in polymatrix games, we study the computation of Nash equilibria in such games where each pair of players plays either a zero-sum or a coordination game. We are particularly interested in the setting where players can be grouped into a small number of teams of identical interest. While the three-team version of the problem is known to be PPAD-complete, the complexity for two teams has remained open. Our main contribution is to prove that the two-team version remains hard, namely it is CLS-hard. Furthermore, we show that this lower bound is tight for the setting where one of the teams consists of multiple independent adversaries. On the way to obtaining our main result, we prove hardness of finding any stationary point in the simplest type of non-convex-concave min-max constrained optimization problem, namely for a class of bilinear polynomial objective functions. Y1 - 2025 UR - https://openreview.net/pdf?id=9VGTk2NYjF ER - TY - CHAP A1 - Besançon, Mathieu A1 - Pokutta, Sebastian A1 - Wirth, Elias T1 - The Pivoting Framework: Frank-Wolfe Algorithms with Active Set Size Control T2 - Proceedings of The 28th International Conference on Artificial Intelligence and Statistics Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v258/main/assets/besancon25a/besancon25a.pdf VL - 258 SP - 271 EP - 279 ER - TY - JOUR A1 - Wirth, Elias A1 - Pena, Javier A1 - Pokutta, Sebastian T1 - Correction: Accelerated affine-invariant convergence rates of the Frank-Wolfe algorithm with open-loop step-sizes JF - Mathematical Programming Y1 - 2025 U6 - https://doi.org/10.1007/s10107-025-02214-3 VL - 214 SP - 941 EP - 942 ER - TY - CHAP A1 - Roux, Christophe A1 - Zimmer, Max A1 - Pokutta, Sebastian T1 - On the byzantine-resilience of distillation-based federated learning T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - Federated Learning (FL) algorithms using Knowledge Distillation (KD) have received increasing attention due to their favorable properties with respect to privacy, non-i.i.d. data and communication cost. These methods depart from transmitting model parameters and instead communicate information about a learning task by sharing predictions on a public dataset. In this work, we study the performance of such approaches in the byzantine setting, where a subset of the clients act in an adversarial manner aiming to disrupt the learning process. We show that KD-based FL algorithms are remarkably resilient and analyze how byzantine clients can influence the learning process. Based on these insights, we introduce two new byzantine attacks and demonstrate their ability to break existing byzantine-resilient methods. Additionally, we propose a novel defence method which enhances the byzantine resilience of KD-based FL algorithms. Finally, we provide a general framework to obfuscate attacks, making them significantly harder to detect, thereby improving their effectiveness. Y1 - 2025 UR - https://openreview.net/pdf?id=of6EuHT7de ER - TY - CHAP A1 - Sadiku, Shpresim A1 - Wagner, Moritz A1 - Nagarajan, Sai Ganesh A1 - Pokutta, Sebastian T1 - S-CFE: Simple Counterfactual Explanations T2 - Proceedings of The 28th International Conference on Artificial Intelligence and Statistics Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v258/main/assets/sadiku25a/sadiku25a.pdf VL - 258 SP - 172 EP - 180 ER - TY - JOUR A1 - Ji, Hongchen A1 - Ragyanszki, Anita A1 - Fournier, Rene T1 - A Machine Learning and Quantum Chemistry Approach for Identifying Prebiotic Molecules in the Interstellar Medium JF - Physical Chemistry Chemical Physics N2 - The discovery of molecules in the interstellar medium (ISM) plays a key role in understanding prebiotic chemistry. Relatively few (∼250) molecules have been confirmed in the ISM, and detecting additional species is crucial for expanding our knowledge of astrochemical processes. We present a strategy for predicting possible prebiotic molecules in the ISM that combines machine learning and high-accuracy quantum chemistry calculations. Using a reaction dataset of over 153,000 possible combinations of known interstellar molecules, we applied a machine learning model to estimate reaction energy barriers and identify those with low or zero barriers that are most likely to occur in the ISM. From this screening process, 24 molecules were identified, five of which have already been observed in interstellar space. For the remaining 19 molecules, we conducted density functional theory (DFT) and coupled cluster theory calculations to determine the most stable conformers, spectroscopic parameters, and predict their detectability through spectroscopy. We present data to guide future observational searches for new interstellar species, contributing to the ongoing exploration of complex organic molecules in space and their potential role in prebiotic chemistry. Y1 - 2024 ER - TY - JOUR A1 - Zemann, Berit A1 - Le, Mai-Lee Van A1 - Sherlock, Rob E. A1 - Baum, Daniel A1 - Katija, Kakani A1 - Stach, Thomas T1 - Evolutionary traces of miniaturization in a giant – Comparative anatomy of brain and brain nerves in Bathochordaeus stygius (Tunicata, Appendicularia) JF - Journal of Morphology Y1 - 2023 U6 - https://doi.org/10.1002/jmor.21598 VL - 284 IS - 7 ER - TY - JOUR A1 - Weilandt, Frank A1 - Behling, Robert A1 - Goncalves, Romulo A1 - Madadi, Arash A1 - Richter, Lorenz A1 - Sanona, Tiago A1 - Spengler, Daniel A1 - Welsch, Jona T1 - Early Crop Classification via Multi-Modal Satellite Data Fusion and Temporal Attention JF - Remote Sensing N2 - In this article, we propose a deep learning-based algorithm for the classification of crop types from Sentinel-1 and Sentinel-2 time series data which is based on the celebrated transformer architecture. Crucially, we enable our algorithm to do early classification, i.e., predict crop types at arbitrary time points early in the year with a single trained model (progressive intra-season classification). Such early season predictions are of practical relevance for instance for yield forecasts or the modeling of agricultural water balances, therefore being important for the public as well as the private sector. Furthermore, we improve the mechanism of combining different data sources for the prediction task, allowing for both optical and radar data as inputs (multi-modal data fusion) without the need for temporal interpolation. We can demonstrate the effectiveness of our approach on an extensive data set from three federal states of Germany reaching an average F1 score of 0.92 using data of a complete growing season to predict the eight most important crop types and an F1 score above 0.8 when doing early classification at least one month before harvest time. In carefully chosen experiments, we can show that our model generalizes well in time and space. Y1 - 2023 U6 - https://doi.org/10.3390/rs15030799 VL - 15 IS - 3 SP - 799 ER - TY - CHAP A1 - Zink, Christof A1 - Ekterai, Michael A1 - Martin, Dominik A1 - Clemens, William A1 - Maennel, Angela A1 - Mundinger, Konrad A1 - Richter, Lorenz A1 - Crump, Paul A1 - Knigge, Andrea T1 - Deep-learning-based visual inspection of facets and p-sides for efficient quality control of diode lasers T2 - High-Power Diode Laser Technology XXI N2 - The optical inspection of the surfaces of diode lasers, especially the p-sides and facets, is an essential part of the quality control in the laser fabrication procedure. With reliable, fast, and flexible optical inspection processes, it is possible to identify and eliminate defects, accelerate device selection, reduce production costs, and shorten the cycle time for product development. Due to a vast range of rapidly changing designs, structures, and coatings, however, it is impossible to realize a practical inspection with conventional software. In this work, we therefore suggest a deep learning based defect detection algorithm that builds on a Faster Regional Convolutional Neural Network (Faster R-CNN) as a core component. While for related, more general object detection problems, the application of such models is straightforward, it turns out that our task exhibits some additional challenges. On the one hand, a sophisticated pre- and postprocessing of the data has to be deployed to make the application of the deep learning model feasible. On the other hand, we find that creating labeled training data is not a trivial task in our scenario, and one has to be extra careful with model evaluation. We can demonstrate in multiple empirical assessments that our algorithm can detect defects in diode lasers accurately and reliably in most cases. We analyze the results of our production-ready pipeline in detail, discuss its limitations and provide some proposals for further improvements. Y1 - 2023 U6 - https://doi.org/10.1117/12.2648691 VL - 12403 SP - 94 EP - 112 PB - SPIE ER - TY - CHAP A1 - Richter, Lorenz A1 - Berner, Julius T1 - Improved sampling via learned diffusions T2 - International Conference on Learning Representations 2024 N2 - Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schrödinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches. Y1 - 2024 UR - https://openreview.net/pdf?id=h4pNROsO06 ER - TY - CHAP A1 - Hartmann, Carsten A1 - Richter, Lorenz ED - Klimczak, Peter ED - Petersen, Christer T1 - Transgressing the Boundaries: Towards a Rigorous Understanding of Deep Learning and Its (Non )Robustness T2 - AI - Limits and Prospects of Artificial Intelligence N2 - The recent advances in machine learning in various fields of applications can be largely attributed to the rise of deep learning (DL) methods and architectures. Despite being a key technology behind autonomous cars, image processing, speech recognition, etc., a notorious problem remains the lack of theoretical understanding of DL and related interpretability and (adversarial) robustness issues. Understanding the specifics of DL, as compared to, say, other forms of nonlinear regression methods or statistical learning, is interesting from a mathematical perspective, but at the same time it is of crucial importance in practice: treating neural networks as mere black boxes might be sufficient in certain cases, but many applications require waterproof performance guarantees and a deeper understanding of what could go wrong and why it could go wrong. It is probably fair to say that, despite being mathematically well founded as a method to approximate complicated functions, DL is mostly still more like modern alchemy that is firmly in the hands of engineers and computer scientists. Nevertheless, it is evident that certain specifics of DL that could explain its success in applications demands systematic mathematical approaches. In this work, we review robustness issues of DL and particularly bridge concerns and attempts from approximation theory to statistical learning theory. Further, we review Bayesian Deep Learning as a means for uncertainty quantification and rigorous explainability. Y1 - 2023 U6 - https://doi.org/10.1515/9783839457320 VL - 4 SP - 43 EP - 82 PB - transcript Verlag ER - TY - JOUR A1 - Kevin-Martin, Aigner A1 - Bärmann, Andreas A1 - Braun, Kristin A1 - Liers, Frauke A1 - Pokutta, Sebastian A1 - Schneider, Oskar A1 - Sharma, Kartikey A1 - Tschuppik, Sebastian T1 - Data-driven Distributionally Robust Optimization over Time JF - INFORMS Journal on Optimization N2 - Stochastic optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. Because the latter is often unknown, distributionally robust optimization (DRO) provides a strong alternative that determines the best guaranteed solution over a set of distributions (ambiguity set). In this work, we present an approach for DRO over time that uses online learning and scenario observations arriving as a data stream to learn more about the uncertainty. Our robust solutions adapt over time and reduce the cost of protection with shrinking ambiguity. For various kinds of ambiguity sets, the robust solutions converge to the SO solution. Our algorithm achieves the optimization and learning goals without solving the DRO problem exactly at any step. We also provide a regret bound for the quality of the online strategy that converges at a rate of O(log T/T−−√), where T is the number of iterations. Furthermore, we illustrate the effectiveness of our procedure by numerical experiments on mixed-integer optimization instances from popular benchmark libraries and give practical examples stemming from telecommunications and routing. Our algorithm is able to solve the DRO over time problem significantly faster than standard reformulations. Y1 - 2023 U6 - https://doi.org/10.1287/ijoo.2023.0091 VL - 5 IS - 4 SP - 376 EP - 394 ER - TY - JOUR A1 - Riedel, Jerome A1 - Gelß, Patrick A1 - Klein, Rupert A1 - Schmidt, Burkhard T1 - WaveTrain: a Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains JF - The Journal of Chemical Physics N2 - WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum–classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics “on the fly,” with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available. Y1 - 2023 U6 - https://doi.org/10.1063/5.0147314 VL - 158 IS - 16 SP - 164801 ER - TY - JOUR A1 - Combettes, Cyrille A1 - Pokutta, Sebastian T1 - Revisiting the Approximate Carathéodory Problem via the Frank-Wolfe Algorithm JF - Mathematical Programming Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01735-x VL - 197 SP - 191 EP - 214 ER - TY - JOUR A1 - Rozsa, Zsofia Borbala A1 - Ragyanszki, Anita A1 - Viskolcz, Bela A1 - Szori, Milan T1 - Chemical space of the singlet C4H8O2 species. A systematic theoretical analysis on their structural and thermochemical properties JF - Computational and Theoretical Chemistry N2 - The goal of this study was to explore and define the thermodynamic properties of one of the subspaces of ‘chemical space’ using a mixture of graph theory and theoretical chemistry tools. Therefore, all possible mo- lecular structures with C4H8O2 stoichiometry were generated, considering constitutional isomers and molecular complexes. The thermodynamic properties of the obtained isomers have been obtained by G3MP2B3 protocol. The classification of the obtained isomers was simplified by using thermodynamic maps, which is an effective method for the comparison of thermodynamic stability for entities of complex molecular systems. Modern computational methods can be used to understand larger systems, which has made it possible to characterize a chemical subspace not only by selecting individual entities, but also as a whole. With this pro- cedure one can catch a glimpse into the diversity of a molecular system and predict further uses of newly discovered molecules or design molecules with predefined properties. Y1 - 2023 U6 - https://doi.org/10.1016/j.comptc.2023.114162 VL - 1225 SP - 114162 ER - TY - JOUR A1 - Ragyanszki, Anita A1 - Fiser, Bela A1 - Lee-Ruff, Edward A1 - Liebman, Joel F. T1 - Strained Small Nitrogen Heterocycles-Azabicyclobutanes and Azirines JF - ChemistrySelect N2 - Small ring nitrogen heterocycles, azabicyclobutanes and azirines, were investigated by computational methods in order to address the discrepancy between their regioisomers 1- and 2-azabicyclobutane and 1H- and 2H-azirines. Both 1-azabicyclobutane and 2H-azirine are well known synthetic starting points to larger nitrogen heterocycles whereas 2-azabicyclobutane and 1H-azirine and their derivatives have yet to be reported as isolable compounds. Calculated parameters such as structure, base strength (proton affinities), NICS values and enthalpies of formation from which strain energies are derived are reported. The destabilization of the less stable regioisomers is attributed to homoantiaromaticity in 2-azabicyclobutane and antiaromaticity in 1H-azirine. Two stereoisomers exist for 2-azabicyclobutane with the endo- stereoisomer being more stable. This phenomenon is indicative of the hydrogen bond acceptor properties of the neighboring cyclpropane and the π-bond character of the central bond in 2-azabicyclobutane. Y1 - 2023 U6 - https://doi.org/10.1002/slct.202301405 VL - 8 IS - 26 ER - TY - CHAP A1 - Chaukair, Mustafa A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - On the Activation Space of ReLU Equipped Deep Neural Networks T2 - Procedia Computer Science N2 - Modern Deep Neural Networks are getting wider and deeper in their architecture design. However, with an increasing number of parameters the decision mechanisms becomes more opaque. Therefore, there is a need for understanding the structures arising in the hidden layers of deep neural networks. In this work, we present a new mathematical framework for describing the canonical polyhedral decomposition in the input space, and in addition, we introduce the notions of collapsing- and preserving patches, pertinent to understanding the forward map and the activation space they induce. The activation space can be seen as the output of a layer and, in the particular case of ReLU activations, we prove that this output has the structure of a polyhedral complex. Y1 - 2023 U6 - https://doi.org/10.1016/j.procs.2023.08.200 VL - 222 SP - 624 EP - 635 ER - TY - CHAP A1 - Yousefian, Maryam A1 - Donati, Luca A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Röblitz, Susanna T1 - Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN T2 - Computational Methods in Systems Biology. CMSB 2025 N2 - Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system’s long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs. Y1 - 2026 U6 - https://doi.org/10.1007/978-3-032-01436-8_8 VL - 15959 SP - 126 EP - 149 ER - TY - JOUR A1 - Kourov, Mikhail N. A1 - Samoilova, Anna E. A1 - Straube, Arthur T1 - Dynamics of a chain of interacting magnetic particles in a one-dimensional periodic energy landscape JF - Bull. Russ. Acad. Sci. Phys. N2 - We explore the dynamics of a one-dimensional chain of paramagnetic colloidal particles in a periodic potential. The model accounts for a constant external force, along with magnetic dipolar attraction and hard-core repulsive interactions between particles. Numerical simulations reveal the emergence of a traveling kink – a chain defect propagating along the chain. We show that the kink emerges beyond a critical force threshold and identify parameter regimes corresponding to distinct dynamic modes such as a pinned kink, a running kink, a cluster kink, and chain drift. Y1 - 2025 U6 - https://doi.org/10.1134/S1062873825711742 SN - 1062-8738 VL - 89 IS - 7 SP - 1086 EP - 1092 ER - TY - JOUR A1 - Reuss, Joana A1 - Macdonald, Jan A1 - Becker, Simon A1 - Richter, Lorenz A1 - Körner, Marco T1 - The EuroCropsML time series benchmark dataset for few-shot crop type classification in Europe JF - Scientific Data N2 - We introduce EuroCropsML, an analysis-ready remote sensing dataset based on the open-source EuroCrops collection, for machine learning (ML) benchmarking of time series crop type classification in Europe. It is the first time-resolved remote sensing dataset designed to benchmark transnational few-shot crop type classification algorithms that supports advancements in algorithmic development and research comparability. It comprises 706683 multi-class labeled data points across 176 crop classes. Each data point features a time series of per-parcel median pixel values extracted from Sentinel-2 L1C data and precise geospatial coordinates. EuroCropsML is publicly available on Zenodo. Y1 - 2025 U6 - https://doi.org/10.1038/s41597-025-04952-7 VL - 12 ER - TY - JOUR A1 - Blessing, Denis A1 - Berner, Julius A1 - Richter, Lorenz A1 - Domingo-Enrich, Carles A1 - Du, Yuanqi A1 - Vahdat, Arash A1 - Neumann, Gerhard T1 - Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference N2 - Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular if the target measure differs substantially from the prior. In this work, we therefore approach the problem by iteratively solving constrained problems incorporating trust regions that aim for approaching the target measure gradually in a systematic way. It turns out that this trust region based strategy can be understood as a geometric annealing from the prior to the target measure, where, however, the incorporated trust regions lead to a principled and educated way of choosing the time steps in the annealing path. We demonstrate in multiple optimal control applications that our novel method can improve performance significantly, including tasks in diffusion-based sampling, transition path sampling, and fine-tuning of diffusion models. Y1 - 2025 ER - TY - CHAP A1 - Blessing, Denis A1 - Berner, Julius A1 - Richter, Lorenz A1 - Neumann, Gerhard T1 - Underdamped Diffusion Bridges with Applications to Sampling T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices, where the noise only acts in certain dimensions. Extending previous findings, our framework allows to rigorously show that score matching in the underdamped case is indeed equivalent to maximizing a lower bound on the likelihood. Motivated by superior convergence properties and compatibility with sophisticated numerical integration schemes of underdamped stochastic processes, we propose \emph{underdamped diffusion bridges}, where a general density evolution is learned rather than prescribed by a fixed noising process. We apply our method to the challenging task of sampling from unnormalized densities without access to samples from the target distribution. Across a diverse range of sampling problems, our approach demonstrates state-of-the-art performance, notably outperforming alternative methods, while requiring significantly fewer discretization steps and no hyperparameter tuning. Y1 - 2025 UR - https://openreview.net/attachment?id=Q1QTxFm0Is&name=pdf ER - TY - JOUR A1 - Berner, Julius A1 - Richter, Lorenz A1 - Sendera, Marcin A1 - Rector-Brooks, Jarrid A1 - Malkin, Nikolay T1 - From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster training N2 - We study the problem of training neural stochastic differential equations, or diffusion models, to sample from a Boltzmann distribution without access to target samples. Existing methods for training such models enforce time-reversal of the generative and noising processes, using either differentiable simulation or off-policy reinforcement learning (RL). We prove equivalences between families of objectives in the limit of infinitesimal discretization steps, linking entropic RL methods (GFlowNets) with continuous-time objects (partial differential equations and path space measures). We further show that an appropriate choice of coarse time discretization during training allows greatly improved sample efficiency and the use of time-local objectives, achieving competitive performance on standard sampling benchmarks with reduced computational cost. Y1 - 2025 ER - TY - CHAP A1 - Chen, Junhua A1 - Richter, Lorenz A1 - Berner, Julius A1 - Blessing, Denis A1 - Neumann, Gerhard A1 - Anandkumar, Anima T1 - Sequential Controlled Langevin Diffusions T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers. Y1 - 2025 UR - https://openreview.net/pdf?id=dImD2sgy86 ER - TY - JOUR A1 - Reuss, Joana A1 - Macdonald, Jan A1 - Becker, Simon A1 - Schultka, Konrad A1 - Richter, Lorenz A1 - Körner, Marco T1 - Meta-learning For Few-Shot Time Series Crop Type Classification: A Benchmark On The EuroCropsML Dataset N2 - Spatial imbalances in crop type data pose significant challenges for accurate classification in remote sensing applications. Algorithms aiming at transferring knowledge from data-rich to data-scarce tasks have thus surged in popularity. However, despite their effectiveness in previous evaluations, their performance in challenging real-world applications is unclear and needs to be evaluated. This study benchmarks transfer learning and several meta-learning algorithms, including (First-Order) Model-Agnostic Meta-Learning ((FO)-MAML), Almost No Inner Loop (ANIL), and Task-Informed Meta-Learning (TIML), on the real-world EuroCropsML time series dataset, which combines farmer-reported crop data with Sentinel-2 satellite observations from Estonia, Latvia, and Portugal. Our findings indicate that MAML-based meta-learning algorithms achieve slightly higher accuracy compared to simpler transfer learning methods when applied to crop type classification tasks in Estonia after pre-training on data from Latvia. However, this improvement comes at the cost of increased computational demands and training time. Moreover, we find that the transfer of knowledge between geographically disparate regions, such as Estonia and Portugal, poses significant challenges to all investigated algorithms. These insights underscore the trade-offs between accuracy and computational resource requirements in selecting machine learning methods for real-world crop type classification tasks and highlight the difficulties of transferring knowledge between different regions of the Earth. To facilitate future research in this domain, we present the first comprehensive benchmark for evaluating transfer and meta-learning methods for crop type classification under real-world conditions. The corresponding code is publicly available at this https URL. Y1 - 2025 ER - TY - GEN ED - Fackeldey, Konstantin ED - Kannan, Aswin ED - Pokutta, Sebastian ED - Sharma, Kartikey ED - Walter, Daniel ED - Walter, Andrea ED - Weiser, Martin T1 - Mathematical Optimization for Machine Learning N2 - Mathematical optimization and machine learning are closely related. This proceedings volume of the Thematic Einstein Semester 2023 of the Berlin Mathematics Research Center MATH+ collects recent progress on their interplay in topics such as discrete optimization, nonlinear programming, optimal control, first-order methods, multilevel optimization, machine learning in optimization, physics-informed learning, and fairness in machine learning. Y1 - 2025 SN - 9783111376776 U6 - https://doi.org/10.1515/9783111376776 PB - De Gruyter ER - TY - JOUR A1 - Ramos, Alejandro A1 - Kühn, Oliver T1 - Manipulating the dynamics of a Fermi resonance with light. A direct optimal control theory approach JF - Chemical Physics Y1 - 2022 ER - TY - CHAP A1 - Zimmer, Max A1 - Spiegel, Christoph A1 - Pokutta, Sebastian ED - Fackeldey, K. T1 - Compression-aware training of neural networks using Frank-Wolfe T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 Y1 - 2025 U6 - https://doi.org/10.1515/9783111376776-010 SP - 137 EP - 168 PB - De Gruyter ER - TY - CHAP A1 - Urbano, Alonso A1 - Romero, David W. T1 - Self-Supervised Detection of Perfect and Partial Input-Dependent Symmetries T2 - Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) at ICML 2024 Y1 - 2024 ER - TY - JOUR A1 - Ramos, Alejandro A1 - Fischer, Eric W. A1 - Saalfrank, Peter A1 - Kühn, Oliver T1 - Shaping the laser control landscape of a hydrogen transfer reaction by vibrational strong coupling. A direct optimal control approach JF - The Journal of Chemical Physics Y1 - 2024 ER - TY - CHAP A1 - Clausecker, Robert A1 - Schintke, Florian T1 - A Measure of Quality for IDA* Heuristics T2 - Proceedings of the Fourteenth International Symposium on Combinatorial Search (SoCS 2021) Y1 - 2021 N1 - Best SoCS21 paper award SP - 55 EP - 63 ER - TY - JOUR A1 - Nitzke, Isabel A1 - Fackeldey, Konstantin A1 - Vrabec, Jadran T1 - Long range corrections for inhomogeneous fluids containing a droplet or a bubble JF - Molecular Simulation N2 - Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monatomic Lennard–Jones fluid. The method is generalised to the Mie potential and arbitrary molecular structures, employing a numerically efficient centre of mass cut-off scheme. The results are validated by a series of droplet simulations for one-centre and two-centre Lennard–Jones fluids with different cut-off radii rc. Systems with rc=8σ provide a check of self-consistence. Further, a system containing a bubble is investigated for the one-centre Lennard–Jones fluid. The equilibrium properties are almost completely independent on the cut-off radius. In comparison with vapour–liquid equilibrium data for systems without a curved interface, all properties show the expected behaviour. Simulation data are used to approximate the surface tension, which is in good agreement with the findings for planar interfaces, thus verifying the present corrections. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1080/08927022.2021.1954639 SP - 1 EP - 14 ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Γ-convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems JF - Inverse Problems Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac3f81 VL - 38 IS - 2 ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces JF - Inverse Problems Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac3f82 VL - 38 IS - 2 ER - TY - JOUR A1 - Wang, Junyang A1 - Cockayne, Jon A1 - Chkrebtii, Oksana A1 - Sullivan, T. J. A1 - Oates, Chris T1 - Bayesian numerical methods for nonlinear partial differential equations JF - Statistics and Computing Y1 - 2021 U6 - https://doi.org/10.1007/s11222-021-10030-w VL - 31 IS - 5 ER - TY - CHAP A1 - Kaiser, Benjamin A1 - Clausecker, Robert T1 - CleanMaple T2 - Proceedings of SAT Competition 2021 : Solver and Benchmark Descriptions Y1 - 2021 UR - http://hdl.handle.net/10138/333647 SP - 24 ER -