Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations

TL;DR

This paper introduces SDIFT, a novel diffusion-based framework that reconstructs full-field physical dynamics from sparse, irregular observations across various scientific domains, improving accuracy and efficiency.

Contribution

SDIFT leverages the functional Tucker model and a sequential diffusion process with message-passing for conditional generation from limited observations.

Findings

Achieves significant accuracy improvements over state-of-the-art methods.

Demonstrates versatility across astronomical, environmental, and molecular systems.

Enhances computational efficiency in physical dynamics reconstruction.

Abstract

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.