Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks

TL;DR

This paper introduces CTL-PINN, a novel physics-informed neural network that combines curriculum and transfer learning to improve long-term simulation accuracy and efficiency in physical and mechanical systems.

Contribution

The paper presents a new CTL-PINN framework that decomposes long-term problems, integrating curriculum and transfer learning to enhance simulation robustness and overcome limitations of existing PINNs.

Findings

Demonstrates superior performance in nonlinear wave propagation simulations.

Achieves accurate dynamic response modeling of Kirchhoff plates.

Effectively models hydrodynamic behavior in the Three Gorges Reservoir Area.

Abstract

This paper proposes a Curriculum-Transfer-Learning based physics-informed neural network (CTL-PINN) for long-term simulation of physical and mechanical behaviors. The main innovation of CTL-PINN lies in decomposing long-term problems into a sequence of short-term subproblems. Initially, the standard PINN is employed to solve the first sub-problem. As the simulation progresses, subsequent time-domain problems are addressed using a curriculum learning approach that integrates information from previous steps. Furthermore, transfer learning techniques are incorporated, allowing the model to effectively utilize prior training data and solve sequential time domain transfer problems. CTL-PINN combines the strengths of curriculum learning and transfer learning, overcoming the limitations of standard PINNs, such as local optimization issues, and addressing the inaccuracies over extended time domains encountered in CL-PINN and the low computational efficiency of TL-PINN. The efficacy and robustness of CTL-PINN are demonstrated through applications to nonlinear wave propagation, Kirchhoff plate dynamic response, and the hydrodynamic model of the Three Gorges Reservoir Area, showcasing its superior capability in addressing long-term computational challenges.