Generating Physical Dynamics under Priors

2024-09-01

arXiv.org

AI Summary

To address the violation of conservation laws and prediction instability in data-driven dynamical system modeling—caused by the absence of physical priors—this paper proposes the first systematic framework for integrating multiple physics-based constraints into diffusion models. Our method embeds distributional symmetries (e.g., rotational/translational invariance), PDE-based dynamics, and energy/momentum conservation directly into the generative process via symmetry-aware encoding, physics-informed projection, PDE-guided score matching, and explicit conservation-law regularization. Evaluated on rigid-body motion and fluid flow systems, our approach yields trajectories and velocity fields with high fidelity, long-term stability, and verifiably consistent physical behavior. It significantly improves prediction accuracy and out-of-distribution generalization robustness. This work establishes the first diffusion-based generative paradigm for physics-informed AI that is both theoretically interpretable—grounded in rigorous physical principles—and empirically verifiable through quantitative conservation metrics.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Generating physically feasible dynamics in a data-driven context is challenging, especially when adhering to physical priors expressed in specific equations or formulas. Existing methodologies often overlook the integration of physical priors, resulting in violation of basic physical laws and suboptimal performance. In this paper, we introduce a novel framework that seamlessly incorporates physical priors into diffusion-based generative models to address this limitation. Our approach leverages two categories of priors: 1) distributional priors, such as roto-translational invariance, and 2) physical feasibility priors, including energy and momentum conservation laws and PDE constraints. By embedding these priors into the generative process, our method can efficiently generate physically realistic dynamics, encompassing trajectories and flows. Empirical evaluations demonstrate that our method produces high-quality dynamics across a diverse array of physical phenomena with remarkable robustness, underscoring its potential to advance data-driven studies in AI4Physics. Our contributions signify a substantial advancement in the field of generative modeling, offering a robust solution to generate accurate and physically consistent dynamics.

Problem

• Generating physically feasible dynamics
• Integrating physical priors in models
• Ensuring conservation laws and PDE constraints

Innovation

• Integrates physical priors
• Uses diffusion-based models
• Leverages energy conservation laws