Physics-Informed Learning via Diffusion Framework for System State Estimation

We propose PILD (Physics-Informed Learning via Diffusion), a novel state estimation framework that combines a diffusion method with physical information. PILD introduces a physics-informed conditional embedding module in diffusion process, ensuring that physical observations stably guide the network's parameter updates. Moreover, we propose a first-principle-based joint loss, achieving an elegant mathematical unification between the diffusion denoising loss and physical loss to ensure the training consistency with physical laws. Experimental results on different systems demonstrate that our PILD achieves superior accuracy, and exhibits strong generalization capability. This framework offers a promising direction for the development of more accurate and more robust engineering systems.