arXiv:2601.23262v2 Announce Type: replace Abstract: We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical er
The convergence of advanced diffusion models in AI and the growing need for scalable, accurate PDE solvers is driving innovation in scientific computing.
This development allows for more accurate and efficient simulation of complex physical systems, which is critical for scientific discovery, engineering, and climate modeling.
The ability to generate physically admissible solutions to PDEs using AI fundamentally changes how complex systems can be understood and predicted.
- · Scientific research institutions
- · Engineering sectors
- · Climate modeling agencies
- · AI compute providers
- · Traditional numerical simulation methods
- · Simulation software reliant on older algorithms
Improved accuracy and speed in simulating complex physical phenomena across various domains.
Accelerated development of new materials, drugs, and resilient infrastructure due to enhanced predictive capabilities.
Potential for new scientific discoveries previously hindered by computational limitations, leading to breakthroughs in areas like fusion energy or quantum materials.
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Read at arXiv cs.LG