An overview on deep learning-based approximation methods for partial differential equations

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem have been proposed and tested numerically on a number examples PDEs. This has given rise lively field research which methods related Monte Carlo are In article we offer an introduction by revisiting selected mathematical results learning PDEs reviewing main ideas their proofs. We also provide short overview recent literature area research.