Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity
This work provides a physically interpretable generative reconstruction method for scientific measurements suffering from noise, incomplete coverage, or low resolution.
LatentPDE introduces a latent diffusion framework that enforces physical compliance by parameterizing latent variables as coefficients and source terms of an assumed PDE, enabling simultaneous sparse-observation reconstruction and super-resolution with high-fidelity recovery and uncertainty tracking.
Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent diffusion framework designed to simultaneously resolve sparse-observation reconstruction and super-resolution. While existing physics-guided diffusion models typically rely on soft loss penalties or uninterpretable representations, our approach enforces physical compliance by constructing an inherently interpretable latent space. Specifically, we parameterize the latent variables directly as the coefficients and source terms of an assumed governing PDE. In doing so, LatentPDE is able to reliably reconstruct dynamics across highly disparate and structured data gaps. Empirical results on diverse configurations demonstrate that our model achieves high-fidelity recovery at any desired resolution while also tracking the underlying predictive uncertainty.