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Neural networks are increasingly used to construct numerical solution methodsfor partial differential equations. In this expository review, we introduce andcontrast three important recent approaches attractive in their simplicity andtheir suitability for high-dimensional problems: physics-informed neuralnetworks, methods based on the Feynman-Kac formula and methods based on thesolution of backward stochastic differential equations. The article isaccompanied by a suite of expository software in the form of Jupyter notebooksin which each basic methodology is explained step by step, allowing for a quickassimilation and experimentation. An extensive bibliography summarizes thestate of the art.

Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review