NeuralPDE: Modelling Dynamical Systems from Data

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling dynamical systems using Neural Networks is an active research field. However, current methods still very limited, they do not exploit the knowledge about nature of system, require extensive prior governing limited to linear first-order equations. In this work we make observation that Method Lines used solve PDEs can be represented convolutions which makes convolutional neural networks (CNNs) natural choice parametrize arbitrary PDE dynamics. We combine parametrization with differentiable ODE solvers form NeuralPDE Model, explicitly takes into account fact data show in several experiments on toy and real-world our model consistently outperforms state-of-the-art models learn systems.