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Variational Monte Carlo - Bridging Concepts of Machine Learning and High Dimensional Partial Differential Equations

Martin EigelPhilipp TrunschkeReinhold SchneiderSebastian Wolf

出版	Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018
URL	http://books.google.com.hk/books?id=UuYBzwEACAAJ&hl=&source=gbs_api

註釋

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.