@misc{GoetschelWeiserMaierhoferetal.2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15243}, year = {2012}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @inproceedings{PetracekMaesBurgeretal.2012, author = {Petracek, Jiri and Maes, Bjorn and Burger, Sven and Luksch, Jaroslav and Kwiecien, Pavel and Richter, Ivan}, title = {Simulation of high-Q nanocavities with 1D photonic gap}, booktitle = {Transparent Optical Networks (ICTON)}, publisher = {IEEE}, doi = {10.1109/ICTON.2012.6253762}, pages = {1 -- 4}, year = {2012}, language = {en} } @inproceedings{PetracekLukschMaesetal.2012, author = {Petracek, Jiri and Luksch, Jaroslav and Maes, Bjorn and Burger, Sven and Kwiecien, Pavel and Richter, Ivan}, title = {Simulation of photonic crystal nanocavities using a bidirectional eigenmode propagation algorithm: a comparative study}, booktitle = {Micro- and nanophotonic materials and devices}, editor = {Ferrari, M. and Marciniak, M. and Righini, G. and Szoplik, T. and Varas, S.}, publisher = {IFN-CNR, Trento, Italy}, isbn = {9788377980200}, pages = {109 -- 112}, year = {2012}, language = {en} } @article{SchlosserSchothBurgeretal.2011, author = {Schlosser, Felix and Schoth, Mario and Burger, Sven and Schmidt, Frank and Knorr, Andreas and Mukamel, S. and Richter, Marten}, title = {Ultrafast nonlinear spectroscopy with spatially confined fields}, volume = {1398}, journal = {AIP Conference Proceedings}, publisher = {AIP}, doi = {10.1063/1.3644223}, pages = {94 -- 96}, year = {2011}, language = {en} } @inproceedings{SchlosserSchothBurgeretal.2012, author = {Schlosser, Felix and Schoth, Mario and Burger, Sven and Schmidt, Frank and Knorr, Andreas and Mukamel, Shaul and Richter, Marten}, title = {Coherent Nonlinear Spectroscopy with Spatiotemporally Controlled Fields}, booktitle = {CLEO/QELS}, publisher = {Optical Society of America}, doi = {10.1364/QELS.2012.QF3D.6}, pages = {QF3D.6}, year = {2012}, language = {en} } @inproceedings{SchlosserSchothHiremathetal.2012, author = {Schlosser, Felix and Schoth, Mario and Hiremath, Kirankumar and Burger, Sven and Schmidt, Frank and Knorr, Andreas and Mukamel, Shaul and Richter, Marten}, title = {Combining nanooptical fields and coherent spectroscopy on systems with delocalized excitons}, volume = {8260}, booktitle = {Proc. SPIE}, doi = {10.1117/12.906671}, pages = {82601V}, year = {2012}, language = {en} } @article{RichterSchlosserSchothetal.2012, author = {Richter, Marten and Schlosser, Felix and Schoth, Mario and Burger, Sven and Schmidt, Frank and Knorr, Andreas and Mukamel, Shaul}, title = {Reconstruction of the wave functions of coupled nanoscopic emitters using a coherent optical technique}, volume = {86}, journal = {Phys. Rev. B}, arxiv = {http://arxiv.org/abs/1201.1765}, doi = {10.1103/PhysRevB.86.085308}, pages = {085308}, year = {2012}, language = {en} } @article{ArellanoMingaleevKoltchanovetal.2013, author = {Arellano, Cristina and Mingaleev, Sergei F. and Koltchanov, Igor and Richter, Andre and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Efficient design of photonic integrated circuits (PICs) by combining device- and circuit- level simulation tools}, volume = {8627}, journal = {Proc. SPIE}, doi = {10.1117/12.2004378}, pages = {862711}, year = {2013}, language = {en} } @article{MaesPetračekBurgeretal.2013, author = {Maes, Bjorn and Petr{\´a}ček, Jiř{\´i} and Burger, Sven and Kwiecien, Pavel and Luksch, Jaroslav and Richter, Ivan}, title = {Simulations of high-Q optical nanocavities with a gradual 1D bandgap}, volume = {21}, journal = {Opt. Express}, publisher = {OSA}, doi = {10.1364/OE.21.006794}, pages = {6794 -- 6806}, year = {2013}, language = {en} } @article{GoetschelWeiserMaierhoferetal.2013, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina and R{\"o}llig, Mathias}, title = {Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography}, volume = {6}, journal = {Nondestructive Testing of Materials and Structures}, pages = {83 -- 89}, year = {2013}, language = {en} } @article{HartmannRichterSchuetteetal.2017, author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, volume = {19}, journal = {Entropy}, number = {11}, doi = {10.3390/e19110626}, pages = {626}, year = {2017}, language = {en} } @article{EgeFothBaumetal.2020, author = {Ege, Yannic and Foth, Christian and Baum, Daniel and Wirkner, Christian S. and Richter, Stefan}, title = {Making spherical-harmonics-based Geometric Morphometrics (SPHARM) approachable for 3D images containing large cavity openings using Ambient Occlusion - a study using hermit crab claw shape variability}, volume = {139}, journal = {Zoomorphology}, doi = {10.1007/s00435-020-00488-z}, pages = {421 -- 432}, year = {2020}, abstract = {An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings - between manus and "movable finger" - typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.}, language = {en} } @misc{EgeFothBaumetal.2020, author = {Ege, Yannic and Foth, Christian and Baum, Daniel and Wirkner, Christian S. and Richter, Stefan}, title = {Making spherical-harmonics-based Geometric Morphometrics (SPHARM) approachable for 3D images containing large cavity openings using Ambient Occlusion - a study using hermit crab claw shape variability}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77744}, year = {2020}, abstract = {An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings - between manus and "movable finger" - typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.}, language = {en} } @misc{RichterGebertZiegler1993, author = {Richter-Gebert, J{\"u}rgen and Ziegler, G{\"u}nter M.}, title = {Zonotopal Tilings and the Bohne-Dress Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1212}, number = {SC-93-25}, year = {1993}, abstract = {We prove a natural bijection between the polytopal tilings of a zonotope \$Z\$ by zonotopes, and the one-element-liftings of the oriented matroid \${\cal M}(Z)\$ associated with \$Z\$. This yields a simple proof and a strengthening of the Bohne-Dress Theorem on zonotopal tilings.}, language = {en} } @misc{RichterGebert1993, author = {Richter-Gebert, J{\"u}rgen}, title = {Mechanical Theorem Proving in Projective Geometry.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1013}, number = {SC-93-05}, year = {1993}, abstract = {We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this power and present a series of examples treated by the prover, including {\it Pappos' and Desargues' Theorems,} the {\it Sixteen Point Theorem, Saam's Theorem, }the {\it Bundle Condition,} the uniqueness of a harmonic Point and {\it Pascal's Theorem.}}, language = {en} } @article{KoschekDurmazKrylovaetal.2015, author = {Koschek, and Durmaz, Vedat and Krylova, and Wieczorek, and Gupta, Pooja and Richter, and Bujotzek, Alexander and Fischer, and Haag, Rainer and Freund, and Weber, Marcus and Rademann,}, title = {Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands}, volume = {11}, journal = {Beilstein J. Org. Chem.}, pages = {837 -- 847}, year = {2015}, language = {en} } @misc{GoetschelWeiserMaierhoferetal.2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, journal = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, editor = {Cardone, Gennaro}, year = {2012}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @article{BirkRaharinirinaFackeldeyetal.2021, author = {Birk, Ralph and Raharinirina, N. Alexia and Fackeldey, Konstantin and Richter, Tonio Sebastian and Weber, Marcus}, title = {Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts}, year = {2021}, abstract = {In this paper, we explore the relationship patterns between Ancient Egyptian texts of the corpus ``Synodal decrees'', which are originating between 243 and 185 BCE, during the Ptolemaic period. Particularly, we are interested in analyzing the grammatical features of the different texts. Conventional data analysis methods such as correspondence Analysis are very useful to explore the patterns of statistical interdependence between categories of variables. However, it is based on a PCA-like dimension-reduction method and turned out to be unsuitable for our dataset due to the high dimensionality of our data representations. Additionally, the similarity between pairs of texts and pairs of grammatical features is observed through the distance between their representation, but the degree of association between a particular grammatical feature and a text is not. Here, we applied a qualitative Euclidean embedding method that provides a new Euclidean representation of the categories of variables. This new representation of the categories is constructed in such a way that all the patterns of statistical interdependence, similarity, and association, are seen through the Euclidean distance between them. Nevertheless, the PCA-like dimension-reduction method also performed poorly on our new representation. Therefore, we obtained a two-dimensional visualization using non-linear methods such UMAP or t-SNE. Although these dimension-reduction methods reduced the interpretability of interpoint distances, we were still able to identify important similarity patterns between the Synodal text as well as their association patterns with the grammatical features.}, language = {en} } @article{RichterSallandtNuesken2024, author = {Richter, Lorenz and Sallandt, Leon and N{\"u}sken, Nikolas}, title = {From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs}, volume = {25}, journal = {Journal of Machine Learning Research}, arxiv = {http://arxiv.org/abs/2307.15496}, pages = {248}, year = {2024}, abstract = {The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination of Monte Carlo methods and variational formulations, using neural networks for function approximation. Extending previous work (Richter et al., 2021), we argue that tensor trains provide an appealing framework for parabolic PDEs: The combination of reformulations in terms of backward stochastic differential equations and regression-type methods holds the romise of leveraging latent low-rank structures, enabling both compression and efficient computation. Emphasizing a continuous-time viewpoint, we develop iterative schemes, which differ in terms of computational efficiency and robustness. We demonstrate both theoretically and numerically that our methods can achieve a favorable trade-off between accuracy and computational efficiency. While previous methods have been either accurate or fast, we have identified a novel numerical strategy that can often combine both of these aspects.}, language = {en} } @inproceedings{VaitlWinklerRichteretal.2024, author = {Vaitl, Lorenz and Winkler, Ludwig and Richter, Lorenz and Kessel, Pan}, title = {Fast and unified path gradient estimators for normalizing flows}, booktitle = {International Conference on Learning Representations 2024}, arxiv = {http://arxiv.org/abs/2403.15881}, year = {2024}, abstract = {Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood train- ing in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy func- tion into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.}, language = {en} } @article{SunBernerRichteretal.2024, author = {Sun, Jingtong and Berner, Julius and Richter, Lorenz and Zeinhofer, Marius and M{\"u}ller, Johannes and Azizzadenesheli, Kamyar and Anandkumar, Anima}, title = {Dynamical Measure Transport and Neural PDE Solvers for Sampling}, arxiv = {http://arxiv.org/abs/2407.07873}, year = {2024}, abstract = {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 Schr{\"o}dinger 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.}, language = {en} } @inproceedings{WinklerRichterOpper2024, author = {Winkler, Ludwig and Richter, Lorenz and Opper, Manfred}, title = {Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models}, volume = {235}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, arxiv = {http://arxiv.org/abs/2405.03549}, pages = {53017 -- 53038}, year = {2024}, abstract = {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.}, language = {en} } @inproceedings{RiberaBorrellRichterSchuette2025, author = {Ribera Borrell, Enric and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Reinforcement Learning with Random Time Horizons}, volume = {267}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, arxiv = {http://arxiv.org/abs/2506.00962}, pages = {5101 -- 5123}, year = {2025}, language = {en} } @misc{RiberaBorrellQuerRichteretal.2021, author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, issn = {1438-0064}, year = {2021}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @article{WeilandtBehlingGoncalvesetal.2023, author = {Weilandt, Frank and Behling, Robert and Goncalves, Romulo and Madadi, Arash and Richter, Lorenz and Sanona, Tiago and Spengler, Daniel and Welsch, Jona}, title = {Early Crop Classification via Multi-Modal Satellite Data Fusion and Temporal Attention}, volume = {15}, journal = {Remote Sensing}, number = {3}, doi = {10.3390/rs15030799}, pages = {799}, year = {2023}, abstract = {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.}, language = {en} } @inproceedings{ZinkEkteraiMartinetal.2023, author = {Zink, Christof and Ekterai, Michael and Martin, Dominik and Clemens, William and Maennel, Angela and Mundinger, Konrad and Richter, Lorenz and Crump, Paul and Knigge, Andrea}, title = {Deep-learning-based visual inspection of facets and p-sides for efficient quality control of diode lasers}, volume = {12403}, booktitle = {High-Power Diode Laser Technology XXI}, publisher = {SPIE}, doi = {10.1117/12.2648691}, pages = {94 -- 112}, year = {2023}, abstract = {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.}, language = {en} } @inproceedings{RichterBerner2024, author = {Richter, Lorenz and Berner, Julius}, title = {Improved sampling via learned diffusions}, booktitle = {International Conference on Learning Representations 2024}, arxiv = {http://arxiv.org/abs/2307.01198}, year = {2024}, abstract = {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 Schr{\"o}dinger 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.}, language = {en} } @incollection{HartmannRichter2023, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Transgressing the Boundaries: Towards a Rigorous Understanding of Deep Learning and Its (Non )Robustness}, volume = {4}, booktitle = {AI - Limits and Prospects of Artificial Intelligence}, editor = {Klimczak, Peter and Petersen, Christer}, publisher = {transcript Verlag}, arxiv = {http://arxiv.org/abs/2307.02454}, doi = {10.1515/9783839457320}, pages = {43 -- 82}, year = {2023}, abstract = {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.}, language = {en} } @article{ReussMacdonaldBeckeretal.2025, author = {Reuss, Joana and Macdonald, Jan and Becker, Simon and Richter, Lorenz and K{\"o}rner, Marco}, title = {The EuroCropsML time series benchmark dataset for few-shot crop type classification in Europe}, volume = {12}, journal = {Scientific Data}, doi = {10.1038/s41597-025-04952-7}, year = {2025}, abstract = {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.}, language = {en} } @article{BlessingBernerRichteretal.2025, author = {Blessing, Denis and Berner, Julius and Richter, Lorenz and Domingo-Enrich, Carles and Du, Yuanqi and Vahdat, Arash and Neumann, Gerhard}, title = {Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference}, arxiv = {http://arxiv.org/abs/2508.12511}, year = {2025}, abstract = {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.}, language = {en} } @inproceedings{BlessingBernerRichteretal.2025, author = {Blessing, Denis and Berner, Julius and Richter, Lorenz and Neumann, Gerhard}, title = {Underdamped Diffusion Bridges with Applications to Sampling}, booktitle = {13th International Conference on Learning Representations (ICLR 2025)}, arxiv = {http://arxiv.org/abs/2503.01006}, year = {2025}, abstract = {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.}, language = {en} } @article{BernerRichterSenderaetal.2025, author = {Berner, Julius and Richter, Lorenz and Sendera, Marcin and Rector-Brooks, Jarrid and Malkin, Nikolay}, title = {From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster training}, arxiv = {http://arxiv.org/abs/2501.06148}, year = {2025}, abstract = {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.}, language = {en} } @inproceedings{ChenRichterBerneretal.2025, author = {Chen, Junhua and Richter, Lorenz and Berner, Julius and Blessing, Denis and Neumann, Gerhard and Anandkumar, Anima}, title = {Sequential Controlled Langevin Diffusions}, booktitle = {13th International Conference on Learning Representations (ICLR 2025)}, arxiv = {http://arxiv.org/abs/2412.07081}, year = {2025}, abstract = {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.}, language = {en} } @article{ReussMacdonaldBeckeretal.2025, author = {Reuss, Joana and Macdonald, Jan and Becker, Simon and Schultka, Konrad and Richter, Lorenz and K{\"o}rner, Marco}, title = {Meta-learning For Few-Shot Time Series Crop Type Classification: A Benchmark On The EuroCropsML Dataset}, arxiv = {http://arxiv.org/abs/2504.11022}, year = {2025}, abstract = {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.}, language = {en} } @misc{RaharinirinaWeberBirketal.2021, author = {Raharinirina, N. Alexia and Weber, Marcus and Birk, Ralph and Fackeldey, Konstantin and Klasse, Sarah M. and Richter, Tonio Sebastian}, title = {Different Tools and Results for Correspondence Analysis}, doi = {10.12752/8257}, year = {2021}, abstract = {This is a list of codes generated from ancient egyptian texts. The codes are used for a correspondence analysis (CA). Codes and CA software are available from the linked webpage.}, language = {en} } @article{RiberaBorrellQuerRichteretal.2023, author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, volume = {89}, journal = {SIAM Journal on Scientific Computing (SISC)}, number = {1}, doi = {10.1137/22M1503464}, year = {2023}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @inproceedings{BernerRichterUllrich2024, author = {Berner, Julius and Richter, Lorenz and Ullrich, Karen}, title = {An optimal control perspective on diffusion-based generative modeling}, booktitle = {Transactions on Machine Learning Research}, year = {2024}, abstract = {We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs) such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences.}, language = {en} } @article{NueskenRichter2023, author = {N{\"u}sken, Nikolas and Richter, Lorenz}, title = {Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems}, volume = {2}, journal = {Journal of Machine Learning}, number = {1}, arxiv = {http://arxiv.org/abs/2112.03749}, doi = {0.4208/jml.220416}, pages = {31 -- 64}, year = {2023}, abstract = {Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination of Monte Carlo sampling and deep learning based approximation. For elliptic and parabolic problems, existing methods can broadly be classified into those resting on reformulations in terms of backward stochastic differential equations (BSDEs) and those aiming to minimize a regression-type L2-error (physics-informed neural networks, PINNs). In this paper, we review the literature and suggest a methodology based on the novel diffusion loss that interpolates between BSDEs and PINNs. Our contribution opens the door towards a unified understanding of numerical approaches for high-dimensional PDEs, as well as for implementations that combine the strengths of BSDEs and PINNs. The diffusion loss furthermore bears close similarities to (least squares) temporal difference objectives found in reinforcement learning. We also discuss eigenvalue problems and perform extensive numerical studies, including calculations of the ground state for nonlinear Schr ¨odinger operators and committor functions relevant in molecular dynamics.}, language = {en} } @article{HartmannRichter2024, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Nonasymptotic bounds for suboptimal importance sampling}, volume = {12}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {2}, arxiv = {http://arxiv.org/abs/2102.09606}, doi = {10.1137/21M1427760}, pages = {309 -- 346}, year = {2024}, abstract = {Importance sampling is a popular variance reduction method for Monte Carlo estimation, where an evident question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. Previous analysis on importance sampling has often focused on asymptotic arguments that work well in a large deviations regime. In this article, we provide lower and upper bounds on the relative error in a nonasymptotic setting. They depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We particularly focus on path sampling problems for diffusion processes with nonvanishing noise, for which generating good proposals comes with additional technical challenges. We provide numerous numerical examples that support our findings and demonstrate the applicability of the derived bounds.}, language = {en} } @inproceedings{RichterBerner2022, author = {Richter, Lorenz and Berner, Julius}, title = {Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning}, volume = {162}, booktitle = {Proceedings of the 39th International Conference on Machine Learning, PMLR}, pages = {18649 -- 18666}, year = {2022}, abstract = {The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs), which allow the minimization of corresponding losses using gradient-based optimization methods. In respective numerical implementations it is therefore crucial to rely on adequate gradient estimators that exhibit low variance in order to reach convergence accurately and swiftly. In this article, we rigorously investigate corresponding numerical aspects that appear in the context of linear Kolmogorov PDEs. In particular, we systematically compare existing deep learning approaches and provide theoretical explanations for their performances. Subsequently, we suggest novel methods that can be shown to be more robust both theoretically and numerically, leading to substantial performance improvements.}, language = {en} } @masterthesis{Richter2013, type = {Bachelor Thesis}, author = {Richter, Stephanie}, title = {Mathematische Behandlung von Dienstreihenfolgeregeln in der Wochenschemaoptimierung}, year = {2013}, language = {de} } @misc{HartmannRichterSchuetteetal.2017, author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: Theory and algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65045}, year = {2017}, abstract = {The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.}, language = {en} } @article{RayaMorenoDaschFarahanietal.2026, author = {Raya-Moreno, Mart{\´i} and Dasch, Noah Alexy and Farahani, Nasrin and Gonzalez Oliva, Ignacio and Gulans, Andris and Hossain, Manoar and Kleine, Hannah and Kuban, Martin and Lubeck, Sven and Maurer, Benedikt and Pavone, Pasquale and Peschel, Fabian and Popova-Gorelova, Daria and Qiao, Lu and Richter, Elias and Rigamonti, Santiago and Rodrigues Pel{\´a}, Ronaldo and Sinha, Kshitij and Speckhard, Daniel T. and Tillack, Sebastian and Tumakov, Dmitry and Hong, Seokhyun and Uzulis, Janis and Voiculescu, Mara and Vona, Cecilia and Yang, Mao and Draxl, Claudia}, title = {An exciting approach to theoretical spectroscopy}, arxiv = {http://arxiv.org/abs/2601.11388}, year = {2026}, language = {en} }