Three ways to solve partial differential equations with neural networks — A review

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