Particle-Guided Diffusion Models for Partial Differential Equations
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A new guided stochastic sampling method enhances diffusion models by integrating physics-based guidance from PDE residuals and observational data, ensuring generated outputs are physically valid. This approach is implemented within a Sequential Monte Carlo framework, demonstrating improved accuracy over existing methods in generating solution fields for various PDE systems.
New Method Enhances Diffusion Models with Physics-Based Guidance
A novel guided stochastic sampling technique has been developed to improve the accuracy of diffusion models by integrating physics-based guidance from partial differential equation (PDE) residuals. This approach ensures that generated samples remain physically admissible, marking a significant advancement in generative PDE solving.
Embedded within a new Sequential Monte Carlo (SMC) framework, the method enhances scalability and efficiency in solving complex PDEs. Researchers tested their technique across various benchmark PDE systems, demonstrating that it yields solution fields with lower numerical error compared to current generative methods.
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📰 Original Source: https://arxiv.org/abs/2601.23262v1
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