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

2025-05-14

AI Summary

This work addresses the challenge of reconstructing full spatiotemporal dynamical fields from sparse, irregular, and discrete physical observations. We propose SDIFT—a Sequence Diffusion model in Functional Tucker space—that integrates Gaussian process priors with a temporally enhanced U-Net architecture and introduces a novel message-passing posterior sampling mechanism. SDIFT enables high-fidelity, continuous spatiotemporal field generation from only a few time-series observations, bypassing grid-based assumptions and supporting multi-scale modeling. Evaluated on three real-world physics tasks—supernova explosion simulation, ocean sound-speed field reconstruction, and organic liquid molecular dynamics—SDIFT achieves superior reconstruction accuracy and computational efficiency over state-of-the-art methods. The framework establishes a new paradigm for physics-informed modeling under irregular observational constraints.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Modeling physical dynamics from sparse irregular observations
• Generating full-field evolution with diffusion-based methods
• Improving reconstruction accuracy across diverse physical scales

Innovation

• Uses functional Tucker space for latent representation
• Sequential diffusion model with augmented UNet
• Message-Passing Posterior Sampling for conditional generation