PILD: Physics-Informed Learning via Diffusion
This work addresses the problem of ensuring physical consistency in generative models for engineering and scientific applications, representing an incremental advancement by combining existing techniques.
The paper tackles the limitation of diffusion models in adhering to physical laws by proposing PILD, a framework that integrates physical constraints into diffusion modeling, resulting in improved accuracy, stability, and generalization across various engineering and scientific tasks.
Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be followed. This paper proposes Physics-Informed Learning via Diffusion (PILD), a framework that unifies diffusion modeling and first-principles physical constraints by introducing a virtual residual observation sampled from a Laplace distribution to supervise generation during training. To further integrate physical laws, a conditional embedding module is incorporated to inject physical information into the denoising network at multiple layers, ensuring consistent guidance throughout the diffusion process. The proposed PILD framework is concise, modular, and broadly applicable to problems governed by ordinary differential equations, partial differential equations, as well as algebraic equations or inequality constraints. Extensive experiments across engineering and scientific tasks including estimating vehicle trajectories, tire forces, Darcy flow and plasma dynamics, demonstrate that our PILD substantially improves accuracy, stability, and generalization over existing physics-informed and diffusion-based baselines.