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 - 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 - GEN A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics N2 - 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. T3 - ZIB-Report - 21-40 KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2021 SN - 1438-0064 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 - 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 -