让机器预测物理过程时既遵守定律又会估不准，提升长期预报可靠性。
Physically consistent and uncertainty-aware learning of spatiotemporal dynamics
- 用物理约束投影层强制模型输出符合守恒定律，尤其在傅里叶空间计算质量与动量守恒。
- 在湍流、洪水和大气预报中，对复杂系统实现高保真且带不确定性估计的长期预测。
- 适合需要可靠物理一致性和不确定量化的新一代科学与工程预测任务。
长时间序列时空动态的精准预测仍是科学与工程领域的基础挑战。现有机器学习方法常忽略基本物理规律，且无法量化预测中的固有不确定性。为此，我们提出一种物理一致性神经算子（PCNO），通过将代理模型输出投影到满足预设物理定律的函数空间，强制施加物理约束。PCNO 中的物理一致性投影层可在傅里叶空间高效计算质量和动量守恒。在此确定性预测基础上，进一步提出基于扩散模型的增强型 PCNO（DiffPCNO），利用一致性模型量化并缓解不确定性，从而提升预测的准确性和可靠性。PCNO 与 DiffPCNO 在从湍流建模到真实世界洪水与大气预报等多种系统及不同空间分辨率下，均实现了高保真、物理一致且带有不确定性估计的时空预测。我们的两阶段框架为准确、物理可解释且具备不确定性感知的时空预测提供了稳健而通用的解决方案。
原文摘要 · Abstract (English)
Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent uncertainties in spatiotemporal predictions. To address these challenges, we introduce a physics-consistent neural operator (PCNO) that enforces physical constraints by projecting surrogate model outputs onto function spaces satisfying predefined laws. A physics-consistent projection layer within PCNO efficiently computes mass and momentum conservation in Fourier space. Building upon deterministic predictions, we further propose a diffusion model-enhanced PCNO (DiffPCNO), which leverages a consistency model to quantify and mitigate uncertainties, thereby improving the accuracy and reliability of forecasts. PCNO and DiffPCNO achieve high-fidelity spatiotemporal predictions while preserving physical consistency and uncertainty across diverse systems and spatial resolutions, ranging from turbulent flow modeling to real-world flood/atmospheric forecasting. Our two-stage framework provides a robust and versatile approach for accurate, physically grounded, and uncertainty-aware spatiotemporal forecasting.
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