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

2025-02-11

AI Summary

To address the local optimization traps and low computational efficiency of Physics-Informed Neural Networks (PINNs) in long-term physical/mechanical system simulation, this paper proposes a Curriculum Transfer Learning-driven PINN (CTL-PINN). CTL-PINN decomposes long-time modeling into a sequence of progressively increasing short-term subtasks, regulates training difficulty via curriculum learning, and enables parameter inheritance and fine-tuning across temporal segments through transfer learning. Compared with standard PINNs, curriculum-learning-only PINNs (CL-PINNs), and transfer-learning-only PINNs (TL-PINNs), CTL-PINN substantially alleviates both accuracy degradation over time and excessive computational cost. Evaluated on three canonical benchmarks—nonlinear wave propagation, dynamic response of Kirchhoff plates, and hydrodynamic simulation of the Three Gorges Reservoir—the method achieves 23–41% higher prediction accuracy and reduces training time by 35–58%, demonstrating superior generalizability and engineering applicability.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Long-term simulation of physical behaviors
• Overcoming local optimization in neural networks
• Enhancing computational efficiency in time-domain problems

Innovation

• Curriculum-Transfer-Learning based PINN
• Decomposes long-term into short-term
• Integrates prior training data effectively