Overcoming the Limits of Finite Difference Method; Physics-Informed Neural Network for Noisy High-Dimensional Heat Diffusion
High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable. This paper presents a Physics-Informed Neural Network (PINN) framework as a systematic solution to this problem across one, two, and three spatial dimensions, establishing clear operational regimes that redefine solver selection in noisy thermal systems. Under 20% boundary noise in 3D, PINN sustains approximately 91% accuracy while Finite Difference Method (FDM) collapses to 36%, a clear decisive advantage. This is further confirmed in a physical copper thermal system, where PINN r...
| Authors | Shreesh Bhattarai, Harish Chandra Bhandari |
|---|---|
| Primary category | cs.LG |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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