22 citations · 61 across the 21 of their papers we have counts for
23 papers
Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling
Robert Gruhlke, Julius Berner, David Sommer +1
Diffusion models offer a powerful framework for sampling from complex probability densities by learning to reverse a noising process. A common approach involves solving for the tim…
Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference
Denis Blessing, Julius Berner, Lorenz Richter +4
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 practi…
Reinforcement Learning with Random Time Horizons
Enric Ribera Borrell, Lorenz Richter, Christof Schütte
We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of traj…
Benchmarking for Practice: Few-Shot Time-Series Crop-Type Classification on the EuroCropsML Dataset
Joana Reuss, Jan Macdonald, Simon Becker +4
Accurate crop-type classification from satellite time series is essential for agricultural monitoring. While various machine learning algorithms have been developed to enhance perf…
Underdamped Diffusion Bridges with Applications to Sampling
Denis Blessing, Julius Berner, Lorenz Richter +1
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…
From discrete-time policies to continuous-time diffusion samplers: Asymptotic equivalences and faster training
Julius Berner, Lorenz Richter, Marcin Sendera +2
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 m…
Sequential Controlled Langevin Diffusions
Junhua Chen, Lorenz Richter, Julius Berner +3
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…
Dynamical Measure Transport and Neural PDE Solvers for Sampling
Jingtong Sun, Julius Berner, Lorenz Richter +4
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…
EuroCropsML: A Time Series Benchmark Dataset For Few-Shot Crop Type Classification
Joana Reuss, Jan Macdonald, Simon Becker +2
We introduce EuroCropsML, an analysis-ready remote sensing machine learning dataset for time series crop type classification of agricultural parcels in Europe. It is the first data…
From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs
Lorenz Richter, Leon Sallandt, Nikolas Nüsken
The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called cur…
Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness
Carsten Hartmann, Lorenz Richter
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…
Improved sampling via learned diffusions
Lorenz Richter, Julius Berner
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalize…
An optimal control perspective on diffusion-based generative modeling
Julius Berner, Lorenz Richter, Karen Ullrich
We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabili…
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning
Lorenz Richter, Julius Berner
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 lear…
Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics
Enric Ribera Borrell, Jannes Quer, Lorenz Richter +1
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. Sin…
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
Nikolas Nüsken, Lorenz Richter
Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches…
Nonasymptotic bounds for suboptimal importance sampling
Carsten Hartmann, Lorenz Richter
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases…
Solving high-dimensional parabolic PDEs using the tensor train format
Lorenz Richter, Leon Sallandt, Nikolas Nüsken
High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since tr…
VarGrad: A Low-Variance Gradient Estimator for Variational Inference
Lorenz Richter, Ayman Boustati, Nikolas Nüsken +2
We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show t…
Model Order Reduction for (Stochastic-) Delay Equations With Error Bounds
Simon Becker, Lorenz Richter
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic in…
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Nikolas Nüsken, Lorenz Richter
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired app…
Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
Simon Becker, Carsten Hartmann, Martin Redmann +1
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the fi…
Variational approach to rare event simulation using least-squares regression
Carsten Hartmann, Omar Kebiri, Lara Neureither +1
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational…