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

Ebenezer O. Oluwasakin, Abdul Q.M. Khaliq and Khaled M. Furati

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 82-102

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.

Keywords: Stiff dynamical systems; Physics-informed transfer learning neural networks; Time-varying parameters; Deep learning (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:82-102

DOI: 10.1016/j.matcom.2025.04.038

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