Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity

arXiv:2604.23867v1 Announce Type: new 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.

Related

• In Situ Training of Implicit Neural Compressors for Scientific Simulations via Sketch-Based Regularization
• Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
• Smoothing the Edges: Smooth Optimization for Sparse Regularization using Hadamard Overparametrization
• Sparse Concept Anchoring for Interpretable and Controllable Neural Representations
• SLE-FNO: Single-Layer Extensions for Task-Agnostic Continual Learning in Fourier Neural Operators

Source: arXiv cs.LG | 2026-04-28