nPINNs: nonlocal Physics-Informed Neural Networks, by Dr. Michael Parks скачать в хорошем качестве

nPINNs: nonlocal Physics-Informed Neural Networks, by Dr. Michael Parks

Title: nPINNs: nonlocal Physics-Informed Neural Networks Speaker: Michael L. Parks, Manager, Computational Mathematics Center for Computing Research, Sandia National Laboratories, Albuquerque NM Abstract: Physics-informed neural networks (PINNs) have proven effective in solving inverse problems based on differential equations with sparse data by incorporating governing equations (reflecting physical laws) into the loss function. In this talk, we introduce nonlocal PINNS (nPINNS), an extension of PINNs to parameter and function inference for nonlocal models. We propose a parameterized nonlocal Laplace operator for which the classical Laplacian and fractional Laplacian are special cases, and which thus has the potential to fit a broad spectrum of data sets. We demonstrate nPINNs on this nonlocal Laplace operator by estimating its model parameters and characterizing the kernel of the operator, showing that nPINNs can correctly infer classical, fractional, and general nonlocal Laplacians from data. Lastly, we propose another nonlocal operator with spatially variable order which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as the nonlocal interaction distance. These parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence. This is a joint work with G. Pang, M. D’Elia, and G. E. Karniadakis. For more information, please visit https://sites.google.com/view/onenonl...