Learning time-varying parameters of stiff dynamical systems using physics-informed transfer neural network

Abstract

Learning the time-varying parameters of stiff dynamical systems is challenging due to their sensitivity to initial conditions and rapid dynamics. We introduce a framework based on Physics-Informed Transfer Learning Neural Networks to learn the time-varying parameters of stiff dynamic systems effectively. The framework leverages prior knowledge embedded in pre-trained models by transferring the learned model parameters to a sequential neural network architecture. This framework admits the dataset, transfers parameters from the pre-trained network, and outputs the solution to the system. Then, the system’s solution is used as input to learn the time-varying parameters. We evaluate this approach on four benchmark problems: the Robertson problem, a damped oscillator, and the High Irradiance Response problem from biochemical kinetics. Results demonstrate that the approach can accurately learn time-varying parameters and capture complex dynamics, providing a robust tool for stiff differential equations in scientific computing.