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Found 11 papers, 7 papers with code
Fast and Unified Path Gradient Estimators for Normalizing Flows
Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training.
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) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality.
Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness
Nevertheless, it is evident that certain specifics of DL that could explain its success in applications demands systematic mathematical approaches.
Improved sampling via learned diffusions
Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes.
An optimal control perspective on diffusion-based generative modeling
In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals.
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions.
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering.
Solving high-dimensional parabolic PDEs using the tensor train format
High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering.
VarGrad: A Low-Variance Gradient Estimator for Variational Inference
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.
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 problem of solving certain Hamilton-Jacobi-Bellman equations.
Variational approach to rare event simulation using least-squares regression
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion.
Probability Optimization and Control 65C05 (primary), 65C30, 92C40 (secondary)
