arXiv:2602.09708v2 Announce Type: replace Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spect
The proliferation of advanced AI models and the increasing computational power are enabling the integration of complex physical laws with generative AI, facilitating new approaches to scientific problem-solving.
This development represents a significant step towards more robust and generalizable AI for scientific discovery and engineering, enabling faster and more accurate simulations of complex systems.
The ability to generate physics-informed solutions for PDEs using diffusion models could accelerate research and development in fields reliant on complex simulations, from climate modeling to drug discovery.
- · AI researchers
- · Scientific computing sector
- · Engineering firms
- · Pharmaceutical industry
- · Traditional simulation software vendors (slow to adapt)
- · R&D teams without AI expertise
More accurate and faster predictive models across various scientific and engineering disciplines.
Reduced timelines and costs for product development and scientific discovery in areas that rely on PDE solutions.
New classes of AI-designed materials, drugs, and operational systems become feasible due to enhanced simulation capabilities.
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Read at arXiv cs.LG