Data-driven Discovery of Partial Differential Equations for Multiple-Physics Electromagnetic Problem

Abstract

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic systems, deep learning to solve these problems can achieve high efficiency and accuracy. In this paper, we propose a deep learning neutral network in combination with sparse regression to solve the hidden governing equations in multiple-physics EM problem. Pareto analysis is also adopted to preserve inversion as precise and simple as possible. This proposed network architecture can discover a set of governing partial differential equations (PDEs) based on few temporalspatial samples. The data-driven discovery method for partial differential equations (PDEs) in electromagnetic field may also contribute to solve more sophisticated problem which may not be solved by first principles.

References in corpus (5)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• PDE-Net: Learning PDEs from Data

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