Abstract: We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. The effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.
Bio: Maziar Raissi is an Assistant Professor of Applied Mathematics at the University of California, Riverside. After receiving his Ph.D. in Applied Mathematics & Statistics, and Scientific Computations from the University of Maryland, College Park, he carried out his postdoctoral research in the Division of Applied Mathematics at Brown University. He then worked at NVIDIA in Silicon Valley as a Senior Software Engineer before moving to Boulder, CO where he was an Assistant Professor of Applied Mathematics at the University of Colorado Boulder. Dr. Raissi's expertise lies at the intersection of Probabilistic Machine Learning, Deep Learning, and Data Driven Scientific Computing. He has been actively involved in the design of learning machines that leverage the underlying physical laws and/or governing equations to extract patterns from high-dimensional data generated from experiments.
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