Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial differential equations (ODEs/PDEs) -- largely dominate the whole process, irrespective of time or location. Physics-informed learning has recently emerged to learn physics for accurate prediction, but they often lack a mechanism to leverage localized spatial and temporal correlation or rely on hard-coded physics parameters. In this paper, we advocate a physics-coupled neural network model to learn parameters governing the physics of the system, and further couple the learned physics to assist the learning of recurring dynamics. A spatio-temporal physics-coupled neural network (ST-PCNN) model is proposed to achieve three goals: (1) learning the underlying physics parameters, (2) transition of local information between spatio-temporal regions, and (3) forecasting future values for the dynamical system. The physics-coupled learning ensures that the proposed model can be tremendously improved by using learned physics parameters, and can achieve good long-range forecasting (e.g., more than 30-steps). Experiments, using simulated and field-collected ocean current data, validate that ST-PCNN outperforms existing physics-informed models.
翻译:海洋洋流、流体力学和许多其他时空物理动态系统是宇宙的重要组成部分。这些系统的一个关键特征是某些物理法律 -- -- 以普通/局部差异方程式(ODEs/PDEs)为代表 -- -- 在很大程度上主导整个过程,而不论时间或地点。物理知识学习最近出现,学习物理,以准确预测,但它们往往缺乏利用局部空间和时间相关性或依赖硬码物理参数的机制。在本文中,我们倡导物理学组合神经网络模型,以学习系统物理参数,并进一步将学习的物理与学习的物理结合起来,以协助学习循环动态。提议采用一个空间-时空物理组合神经网络(ST-PCNN)模型,以实现三个目标:(1) 学习基本物理参数,(2) 空间-时空区域之间的本地信息转换,(3) 预测动态系统的未来价值。物理学组合学习确保了拟议的模型能够通过使用学习的物理参数而得到极大的改进,并且能够实现良好的远程预测(e.g.strod), 利用现有的模型,更多的模拟和模型。