Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown external sources. In such cases, developing a purely analytical model becomes very difficult and data-driven modeling can be of assistance. In this paper, we present a hybrid framework combining physics-based numerical models with deep learning for source identification and forecasting of spatio-temporal dynamical systems with unobservable time-varying external sources. We formulate our model PhICNet as a convolutional recurrent neural network (RNN) which is end-to-end trainable for spatio-temporal evolution prediction of dynamical systems and learns the source behavior as an internal state of the RNN. Experimental results show that the proposed model can forecast the dynamics for a relatively long time and identify the sources as well.

物理过程的时空动态通常使用偏微分方程 (PDE) 进行建模。尽管核心动力学遵循一些物理学原理，但现实世界的物理过程通常由未知的外部来源驱动。在这种情况下，开发纯分析模型变得非常困难，而数据驱动的建模可能会有所帮助。在本文中，我们提出了一种将基于物理的数值模型与深度学习相结合的混合框架，用于具有不可观测的时变外部源的时空动力系统的源识别和预测。我们将我们的模型 PhICNet 制定为卷积循环神经网络 (RNN)，该网络可用于动态系统的时空演化预测的端到端训练，并将源行为作为 RNN 的内部状态进行学习。