用部分观测数据学习未知物理系统的动态规律
Learning Physics Informed Neural ODEs With Partial Measurements
- 基于状态估计与物理约束神经ODE的顺序优化框架
- 在仿真和真实电机械系统数据上实现更优建模精度
- 适合处理状态不完整且动力学未知的物理系统建模
学习支配物理与时空过程的动力学规律是一项挑战，尤其在系统状态部分不可测的情况下。本文针对非测量状态的动力学未知场景，结合状态估计理论与物理信息神经微分方程（Physics Informed Neural ODEs），提出一种序列优化框架，可有效学习未观测过程的动力学。通过数值模拟和来自电机械定位系统的实测数据验证了方法的有效性。结果表明，所提方法能准确拟合底层物理方程，并在性能上优于基线模型。
原文摘要 · Abstract (English)
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.
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