Point-wise Diffusion Models for Physical Systems with Shape Variations: Application to Spatio-temporal and Large-scale system

2025-08-02

AI Summary

Modeling complex physical systems with dynamically evolving geometries—such as fluid flow, collisions, and aerodynamics—remains challenging due to the difficulty of efficiently representing unstructured spatiotemporal data (e.g., meshes or point clouds) while preserving geometric fidelity. To address this, we propose the Pointwise Diffusion Model (PDM), the first diffusion framework that decouples forward and reverse diffusion processes to individual spatiotemporal points, eliminating reliance on regular grids. PDM integrates a pointwise diffusion Transformer architecture, DDIM-based accelerated sampling, and an incremental prediction mechanism. We systematically analyze the impact of sampling strategies and prediction objectives. Experiments demonstrate that PDM achieves 100–200× faster inference (requiring only 5–10 sampling steps), reduces training time by 94.4%, decreases parameter count by 89.0%, and improves prediction accuracy by over 28%. It significantly outperforms DeepONet and MeshGraphNet across diverse multiphysics tasks.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward and backward diffusion processes at individual spatio-temporal points, coupled with a point-wise diffusion transformer architecture for denoising. Unlike conventional image-based diffusion models that operate on structured data representations, this framework enables direct processing of any data formats including meshes and point clouds while preserving geometric fidelity. We validate our approach across three distinct physical domains with complex geometric configurations: 2D spatio-temporal systems including cylinder fluid flow and OLED drop impact test, and 3D large-scale system for road-car external aerodynamics. To justify the necessity of our point-wise approach for real-time prediction applications, we employ denoising diffusion implicit models (DDIM) for efficient deterministic sampling, requiring only 5-10 steps compared to traditional 1000-step and providing computational speedup of 100 to 200 times during inference without compromising accuracy. In addition, our proposed model achieves superior performance compared to image-based diffusion model: reducing training time by 94.4% and requiring 89.0% fewer parameters while achieving over 28% improvement in prediction accuracy. Comprehensive comparisons against data-flexible surrogate models including DeepONet and Meshgraphnet demonstrate consistent superiority of our approach across all three physical systems. To further refine the proposed model, we investigate two key aspects: 1) comparison of final physical states prediction or incremental change prediction, and 2) computational efficiency evaluation across varying subsampling ratios (10%-100%).

Problem

• Predicts complex physical systems with shape variations efficiently
• Processes spatio-temporal points independently for geometric fidelity
• Achieves real-time prediction with significant computational speedup

Innovation

• Point-wise diffusion for shape-varying systems
• Independent spatio-temporal point processing
• Efficient deterministic sampling with DDIM