Regularized physics-informed neural networks for numerical solving of inverse problems in dynamical systems

Shcherbina Yakov, Olga Krivorotko, Neverov Andrei

Keywords: Physics-Informed Neural Networks, regularization, inverse problems, epidemic modeling, SIR model, parameter identification.

Abstract:

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for
solving forward and inverse problems governed by differential equations by embedding physical laws directly into the learning process, see Raissi et al. (2019) for
more information. In epidemiological modeling, PINNs offer a promising framework for reconstructing hidden state trajectories and identifying key epidemiological parameters from sparse and noisy data. However, training PINNs for inverse
problems remains challenging due to strong imbalance between loss components
associated with governing equations, initial conditions, and observational data. In
this work, we propose a regularized PINN approach for inverse epidemic modeling based on the classical SIR model. The method incorporates normalization of
time and state variables, weighted loss balancing, and hybrid optimization strategies. Numerical experiments demonstrate improved training stability, enhanced
physical consistency, and more accurate parameter identification under limited
data availability.

Submission Number: 135