Overcoming the Limits of Finite Difference Method; Physics-Informed Neural Network for Noisy High-Dimensional Heat Diffusion
arXiv:2606.07982v1 Announce Type: new Abstract: 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
The increasing complexity of physical systems and the prevalence of noisy real-world data necessitate advancements in computational modeling, pushing the integration of AI methods like PINNs.
This development represents a significant step towards more accurate and robust simulation of complex physical phenomena, crucial for engineering, scientific discovery, and industrial applications.
The ability to accurately model high-dimensional heat diffusion under noisy conditions using PINNs redefines how challenging thermal systems can be simulated and optimized, especially where classical methods fail.
- · AI/ML researchers
- · Engineering simulation software providers
- · Industries relying on thermal management (e.g., aerospace, electronics)
- · PINN developers
- · Traditional numerical methods (in specific applications)
- · Organizations slow to adopt AI in simulations
Improved design and operational efficiency for systems involving complex heat transfer.
Acceleration of materials science and climate modeling through better understanding of thermal dynamics.
New avenues for autonomous design systems that can leverage robust physics-informed AI models.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG