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07/28/2023
From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs
The numerical approximation of partial differential equations (PDEs) pos...
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07/05/2023
Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness
The recent advances in machine learning in various fields of application...
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07/03/2023
Improved sampling via learned diffusions
Recently, a series of papers proposed deep learning-based approaches to ...
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11/02/2022
An optimal control perspective on diffusion-based generative modeling
We establish a connection between stochastic optimal control and generat...
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06/21/2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning
The combination of Monte Carlo methods and deep learning has recently le...
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12/07/2021
Interpolating between BSDEs and PINNs – deep learning for elliptic and parabolic boundary value problems
Solving high-dimensional partial differential equations is a recurrent c...
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02/23/2021
Solving high-dimensional parabolic PDEs using the tensor train format
High-dimensional partial differential equations (PDEs) are ubiquitous in...
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02/18/2021
Nonasymptotic bounds for suboptimal importance sampling
Importance sampling is a popular variance reduction method for Monte Car...
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10/20/2020
VarGrad: A Low-Variance Gradient Estimator for Variational Inference
We analyse the properties of an unbiased gradient estimator of the ELBO ...
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08/27/2020
Model Order Reduction for (Stochastic-) Delay Equations With Error Bounds
We analyze a structure-preserving model order reduction technique for de...
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05/11/2020
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Optimal control of diffusion processes is intimately connected to the pr...
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12/12/2019