将物理先验融入扩散模型，生成符合物理规律的动态轨迹。
Generating Physical Dynamics under Priors
- 用扩散模型结合物理先验生成动态，保持能量动量守恒。
- 在多种物理现象上生成高质量轨迹，鲁棒性强。
- 适合做物理模拟与AI4Physics研究的学者参考。
在数据驱动背景下生成符合物理规律的动态过程极具挑战性，尤其当需遵守特定方程表达的物理先验时。现有方法常忽视物理先验的整合，导致违反基本物理定律且性能不佳。本文提出一种新框架，将扩散生成模型与两类先验无缝融合：1）分布先验（如旋转平移不变性），2）物理可行性先验（包括能量与动量守恒、偏微分方程约束）。通过嵌入这些先验，方法可高效生成真实物理动态，涵盖轨迹与流场。实证评估表明，该方法在多种物理现象中均能生成高质量动态，表现出显著鲁棒性，凸显其在AI4Physics数据驱动研究中的潜力。本工作标志着生成建模领域的重要进展，提供了生成精确且物理一致动态的可靠方案。
原文摘要 · Abstract (English)
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.
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