Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions

2025-07-08

AI Summary

This work addresses the numerical solution of spatiotemporal partial differential equations (PDEs). We propose a two-stage hybrid surrogate model: in the first stage, a serialized Deep Operator Network (S-DeepONet) generates physically consistent coarse solutions; in the second stage, a conditional video diffusion model refines the solution in the residual space, incorporating physical priors directly into the diffusion process to enhance high-frequency detail recovery. By synergistically integrating deep operator learning with generative modeling, the framework achieves cross-physics generalizability. Evaluated on vortex flow simulation and elastoplastic deformation tasks, our method reduces relative L² error from 4.57% to 0.83% and from 4.42% to 2.94%, respectively—demonstrating substantial improvements in both predictive accuracy and visual fidelity.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Video-diffusion models have recently set the standard in video generation, inpainting, and domain translation thanks to their training stability and high perceptual fidelity. Building on these strengths, we repurpose conditional video diffusion as a physics surrogate for spatio-temporal fields governed by partial differential equations (PDEs). Our two-stage surrogate first applies a Sequential Deep Operator Network (S-DeepONet) to produce a coarse, physics-consistent prior from the prescribed boundary or loading conditions. The prior is then passed to a conditional video diffusion model that learns only the residual: the point-wise difference between the ground truth and the S-DeepONet prediction. By shifting the learning burden from the full solution to its much smaller residual space, diffusion can focus on sharpening high-frequency structures without sacrificing global coherence. The framework is assessed on two disparate benchmarks: (i) vortex-dominated lid-driven cavity flow and (ii) tensile plastic deformation of dogbone specimens. Across these data sets the hybrid surrogate consistently outperforms its single-stage counterpart, cutting the mean relative L2 error from 4.57% to 0.83% for the flow problem and from 4.42% to 2.94% for plasticity, a relative improvements of 81.8% and 33.5% respectively. The hybrid approach not only lowers quantitative errors but also improves visual quality, visibly recovering fine spatial details. These results show that (i) conditioning diffusion on a physics-aware prior enables faithful reconstruction of localized features, (ii) residual learning reduces the problem, accelerating convergence and enhancing accuracy, and (iii) the same architecture transfers seamlessly from incompressible flow to nonlinear elasto-plasticity without problem-specific architectural modifications, highlighting its broad applicability to nonlinear, time-dependent continua.

Problem

• Repurposing video diffusion as physics surrogate for PDEs
• Improving accuracy of spatio-temporal field predictions
• Residual learning enhances convergence and detail recovery

Innovation

• Two-stage hybrid surrogate combines S-DeepONet and diffusion
• Conditional video diffusion learns residual for high-frequency details
• Residual learning reduces problem size, enhances accuracy