Application of physics-informed neural networks in simulating heat transfer and mass diffusion
Keywords:
heat transfer, mass diffusion, physics-informed neural networks, computational physicsAbstract
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 PINNs 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.
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