用物理规律指导生成模型，让数据更符合真实世界的运动规则。
Bridging the Physics-Data Gap with FNO-Guided Conditional Flow Matching: Designing Inductive Bias through Hierarchical Physical Constraints
- 将物理守恒、边界等层级约束融入生成模型，构建物理感知的先验知识。
- 在谐波振荡器等任务中，生成质量提升16.3%，物理违反减少46%。
- 适合需要高物理一致性的场景，如能源、生物信号建模。
传统时间序列生成常忽略特定领域的物理约束，导致统计与物理不一致。本文提出一种分层框架，将守恒律、动力学、边界条件和经验关系等物理规律的内在层级结构直接嵌入深度生成模型，引入一种新的物理信息归纳偏置范式。方法结合傅里叶神经算子（FNO）学习物理算子与条件流匹配（CFM）进行概率生成，通过时变分层约束与FNO引导修正实现融合。在谐波振荡器、人体活动识别及锂离子电池退化任务上的实验表明，相比基线方法，生成质量提升16.3%，物理违反减少46%，预测准确率提高18.5%。
原文摘要 · Abstract (English)
Conventional time-series generation often ignores domain-specific physical constraints, limiting statistical and physical consistency. We propose a hierarchical framework that embeds the inherent hierarchy of physical laws-conservation, dynamics, boundary, and empirical relations-directly into deep generative models, introducing a new paradigm of physics-informed inductive bias. Our method combines Fourier Neural Operators (FNOs) for learning physical operators with Conditional Flow Matching (CFM) for probabilistic generation, integrated via time-dependent hierarchical constraints and FNO-guided corrections. Experiments on harmonic oscillators, human activity recognition, and lithium-ion battery degradation show 16.3% higher generation quality, 46% fewer physics violations, and 18.5% improved predictive accuracy over baselines.
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