Variational Monte Carlo - Bridging Concepts of Machine Learning and High Dimensional Partial Differential Equations
Numerical Analysis
2020-01-07 v1
Abstract
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range of problems. A general unified convergence analysis is derived, which takes into account the approximation and the statistical errors. By this, a combination of theoretical results from numerical analysis and statistics is obtained. Numerical experiments illustrate the performance of the method with the model class of hierarchical tensors.
Keywords
Cite
@article{arxiv.1810.01348,
title = {Variational Monte Carlo - Bridging Concepts of Machine Learning and High Dimensional Partial Differential Equations},
author = {Martin Eigel and Reinhold Schneider and Philipp Trunschke and Sebastian Wolf},
journal= {arXiv preprint arXiv:1810.01348},
year = {2020}
}