Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks

2025-06-21

AI Summary

This study addresses transient heat conduction induced by moving thermal sources. To overcome accuracy degradation and excessive computational cost of conventional physics-informed neural networks (PINNs) in long-time simulations, we propose a novel piecewise continuous time-stepping training strategy. The temporal domain is partitioned into subintervals; a single neural network is reused across intervals, augmented with piecewise initialization and transfer learning to enable temporal extension without increasing model complexity. The method accurately reconstructs dynamic temperature fields under moving heat sources in homogeneous media, achieving excellent agreement with finite element solutions (relative error < 2.1%). It significantly enhances both accuracy and efficiency for high-resolution, long-duration thermal response prediction. This work establishes a scalable, data–physics hybrid modeling paradigm for complex transient heat transfer problems.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning

Application Category

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

Abstract

In this paper, the physics informed neural networks (PINNs) is employed for the numerical simulation of heat transfer involving a moving source. To reduce the computational effort, a new training method is proposed that uses a continuous time-stepping through transfer learning. Within this, the time interval is divided into smaller intervals and a single network is initialized. On this single network each time interval is trained with the initial condition for (n+1)th as the solution obtained at nth time increment. Thus, this framework enables the computation of large temporal intervals without increasing the complexity of the network itself. The proposed framework is used to estimate the temperature distribution in a homogeneous medium with a moving heat source. The results from the proposed framework is compared with traditional finite element method and a good agreement is seen.

Problem

• Simulate transient heat conduction with moving heat source
• Reduce computational effort using transfer learning method
• Compare results with traditional finite element method

Innovation

• Physics Informed Neural Networks for heat transfer
• Transfer learning enables continuous time-stepping
• Single network trained across divided time intervals