Physics-Informed Neural Networks for Solving Forward and Inverse PDEs with Limited and Noisy Data: Application to Solar Corona Modeling (2502.19843v1)

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.