Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

• Published in: Nonlinearity Vol. 35; no. 1; pp. 278 - 310
• Main Authors: E, Weinan, Han, Jiequn, Jentzen, Arnulf
• Format: Journal Article
• Language: English
• Published: IOP Publishing 06.01.2022
• Subjects: backward stochastic differential equations; deep learning; high dimension; nonlinear Monte Carlo; partial differential equations

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are potentially free of the curse of dimensionality for many differ...