SimPINNs: Simulation-Driven Physics-Informed Neural Networks for
  Enhanced Performance in Nonlinear Inverse Problems
Sidney Besnard Frédéric Jurie Jalal M. Fadili
This paper introduces a novel approach to solve inverse problems by
leveraging deep learning techniques. The objective is to infer unknown
parameters that govern a physical system based on observed data. We focus on
scenarios where the underlying forward model demonstrates pronounced nonlinear
behaviour, and where the dimensionality of the unknown parameter space is
substantially smaller than that of the observations. Our proposed method builds
upon physics-informed neural networks (PINNs) trained with a hybrid loss
function that combines observed data with simulated data generated by a known
(approximate) physical model. Experimental results on an orbit restitution
problem demonstrate that our approach surpasses the performance of standard
PINNs, providing improved accuracy and robustness.