PHDME: Physics-Informed Diffusion Models without Explicit Governing Equations
Please login to view abstract download link
Diffusion models are expressive priors for fast generation in high-dimensional dynamical systems, but purely data-driven approaches require large amount of data and lack reliability. We propose PHDME (Port-Hamiltonian Diffusion Model without Explicit equations), a two-stage framework for data-efficient spatiotemporal trajectory generation without requiring closed-form PDEs. In Stage I, PHDME learns a Gaussian-process distributed Port-Hamiltonian system from limited data, capturing both energy-based structure and epistemic uncertainty, and uses posterior rollouts for physics-aware data augmentation. In Stage II, a conditional diffusion model is trained on the augmented dataset and regularized by an uncertainty-weighted physics-consistency residual. Split conformal prediction then provides distribution-free uncertainty sets for generated trajectories.
