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

arXiv: https://arxiv.org/abs/2506.17726 · HTML: https://mlsanity.com/paper/2506.17726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 21 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations](https://mlsanity.com/paper/1907.03507/) (2019)
- [SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs](https://mlsanity.com/paper/2102.13037/) (2021)
- [Distributed physics informed neural network for data-efficient solution to partial differential equations](https://mlsanity.com/paper/1907.08967/) (2019)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates](https://mlsanity.com/paper/2010.05698/) (2020)
- [Artificial intelligence for partial differential equations in computational mechanics: A review](https://mlsanity.com/paper/2410.19843/) (2024)
- [Burgers' pinns with implicit euler transfer learning](https://mlsanity.com/paper/2310.15343/) (2023)

## Abstract (arXiv)

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.