🤖 AI Summary
This work addresses the challenge of high-fidelity reconstruction of physical fields under suboptimal observational conditions—such as noise, incomplete spatial coverage, or limited resolution—by introducing LatentPDE, a novel framework that explicitly parameterizes the latent variables of a diffusion model as the coefficients and source terms of governing partial differential equations (PDEs). This approach constructs a physically interpretable latent space by integrating structured sparsity modeling with PDE priors, enabling simultaneous field reconstruction and super-resolution at arbitrary resolutions. Moreover, it incorporates a mechanism for uncertainty quantification. Experimental results demonstrate that LatentPDE significantly outperforms existing physics-informed diffusion methods across diverse missing-data scenarios, achieving both high reconstruction accuracy and reliable uncertainty estimates.
📝 Abstract
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.