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Spatio-temporal dynamics of physical processes are generally modeled usingpartial differential equations (PDEs). Though the core dynamics follows someprinciples of physics, real-world physical processes are often driven byunknown external sources. In such cases, developing a purely analytical modelbecomes very difficult and data-driven modeling can be of assistance. In thispaper, we present a hybrid framework combining physics-based numerical modelswith deep learning for source identification and forecasting of spatio-temporaldynamical systems with unobservable time-varying external sources. We formulateour model PhICNet as a convolutional recurrent neural network (RNN) which isend-to-end trainable for spatio-temporal evolution prediction of dynamicalsystems and learns the source behavior as an internal state of the RNN.Experimental results show that the proposed model can forecast the dynamics fora relatively long time and identify the sources as well.

Physics-Incorporated Convolutional Recurrent Neural Networks for Source Identification and Forecasting of Dynamical Systems