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PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems
KAUST DepartmentKing Abdullah Univ Sci & Technol, Thuwal, Saudi Arabia
Permanent link to this recordhttp://hdl.handle.net/10754/677982
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AbstractPhysics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differential equations, given the fact they escape the curse of dimensionality. In this paper, we present Physics Informed Neural Networks as an underdetermined point matching collocation method then expose the connection between Galerkin Least Squares (GALS) and PINNs, to develop an a priori error estimate, in the context of elliptic problems. In particular, techniques that belong to the realm of least squares finite elements and Rademacher complexity analysis are used to obtain the error estimate.
SponsorsI would like to express my deepest appreciation to Prof. G. Turkiyyah and Dr. S. Zampini without whom this paper would not have been possible.
Conference/Event name10th Vienna International Conference on Mathematical Modelling (MATHMOD)