用物理规律生成新数据，让模型在少样本和分布外情况下仍能准确预测动态系统。
Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation
- 通过物理约束的编码器构建物理状态字典，实现可解释的数据增强。
- 在少样本和分布外测试中，性能超越现有方法，尤其在长时序预测上表现优异。
- 适合需要高可靠性、低数据依赖的物理建模场景，如气候与流体模拟。
在动力系统建模中，传统数值方法受限于高计算成本，而现代数据驱动方法则面临数据稀缺和分布偏移问题。为此，我们提出SPARK——一种基于物理规律的定量数据增强插件。SPARK利用重建自编码器将物理参数融入丰富的离散状态字典，该字典作为物理状态的结构化表示，通过潜空间中的合理插值生成新的、符合物理规律的训练样本。此外，在下游预测任务中，这些增强表示与傅里叶增强图微分方程（Fourier-enhanced Graph ODE）无缝结合，以稳健建模扩展后的数据分布并捕捉长期时间依赖性。在多个基准测试上的大量实验表明，SPARK显著优于现有最先进方法，尤其在挑战性的分布外场景和数据稀缺条件下表现突出，验证了物理引导增强范式的有效性。
原文摘要 · Abstract (English)
In dynamical system modeling, traditional numerical methods are limited by high computational costs, while modern data-driven approaches struggle with data scarcity and distribution shifts. To address these fundamental limitations, we first propose SPARK, a physics-guided quantitative augmentation plugin. Specifically, SPARK utilizes a reconstruction autoencoder to integrate physical parameters into a physics-rich discrete state dictionary. This state dictionary then acts as a structured dictionary of physical states, enabling the creation of new, physically-plausible training samples via principled interpolation in the latent space. Further, for downstream prediction, these augmented representations are seamlessly integrated with a Fourier-enhanced Graph ODE, a combination designed to robustly model the enriched data distribution while capturing long-term temporal dependencies. Extensive experiments on diverse benchmarks demonstrate that SPARK significantly outperforms state-of-the-art baselines, particularly in challenging out-of-distribution scenarios and data-scarce regimes, proving the efficacy of our physics-guided augmentation paradigm.
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