Physics-Informed Neural Networks for Solving Forward and Inverse PDEs with Limited and Noisy Data: Application to Solar Corona Modeling

TL;DR

This paper demonstrates how Physics-Informed Neural Networks (PINNs) effectively solve PDEs with limited or noisy data and can identify unknown parameters, with applications to modeling solar corona magnetohydrodynamics.

Contribution

It introduces the application of PINNs to solve forward and inverse PDE problems in plasma physics with scarce or noisy data, specifically in solar corona modeling.

Findings

PINNs successfully solve PDEs with limited/noisy data.

PINNs can identify unknown coefficients in PDEs.

Application to solar corona demonstrates practical relevance.

Abstract

I will demonstrate the effectiveness of Physics-Informed Neural Networks (PINNs) in solving partial differential equations (PDEs) when training data are scarce or noisy. The training data can be located either at the boundaries or within the domain. Additionally, PINNs can be used as an inverse method to determine unknown coefficients in the equations. This study will highlight the application of PINNs in modeling magnetohydrodynamic processes relevant to strongly magnetized plasmas, such as those found in the solar corona.