  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.
