11. Application of physics-informed neural networks in simulating heat transfer and mass diffusion

Tóm tắt

This paper presents a novel approach to simulating classical physical phenomena-specifically heat transfer and mass diffusion-using Physics-Informed Neural Networks (PINNs), a class of deep neural networks that incorporate physical constraints. Unlike conventional machine learning models, PINNs allow the integration of empirical data with partial differential equations (PDEs) governing the underlying physical systems. This results in models capable of making accurate predictions even in the presence of incomplete or noisy data. The study constructs and trains PINN models for two canonical problems: heat conduction in a one-dimensional (1D) rod and concentration diffusion in a closed medium. Simulation results demonstrate that the PINNs achieve significantly lower prediction errors compared to standard neural networks without physical constraints, while also exhibiting strong generalization capabilities and numerical stability. This method offers a promising new direction for simulating physical processes, particularly in scenarios where real-world data are limited-making it well-suited for applications in education, engineering, and scientific research.