融合物理模型与数据，提升混沌系统预测精度。
Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics
- 用自编码器找到不变流形，将物理模型投影其上
- 在数据充足、稀缺及物理模型错误时均显著提升预测
- 适合需要高精度长期预测的复杂系统研究者
尽管数据驱动方法在混沌系统降阶建模中表现强大，但结合已知物理规律（即全阶模型，FOM）仍具巨大潜力。本文构建一种融合数据与FOM的混合降阶模型（ROM），用于演化定义在不变流形上的时空混沌动力学，该流形通过自编码器获得。该方法将FOM的向量场投影至不变流形，并以动态数据校正或作为贝叶斯先验进行更新，均采用神经微分方程实现。实验基于Kuramoto-Sivashinsky和复Ginzburg-Landau方程的模拟数据。相较于纯数据方法，在数据丰富、稀缺甚至使用错误参数的不准确FOM情形下，混合方法均显著提升时间序列预测性能。
原文摘要 · Abstract (English)
While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a hybrid reduced order model (ROM), informed by both data and FOM, for evolving spatiotemporal chaotic dynamics on an invariant manifold whose coordinates are found using an autoencoder. This approach projects the vector field of the FOM onto the invariant manifold; then, this physics-derived vector field is either corrected using dynamic data, or used as a Bayesian prior that is updated with data. In both cases, the neural ordinary differential equation approach is used. We consider simulated data from the Kuramoto-Sivashinsky and complex Ginzburg-Landau equations. Relative to the data-only approach, for scenarios of abundant data, scarce data, and even an incorrect FOM (i.e. erroneous parameter values), the hybrid approach yields substantially improved time-series predictions.
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