Approximating the solution to wave propagation using deep neural networks
This work addresses the challenge of simulating wave dynamics for applications like numerical simulations, though it is incremental as it applies existing neural network components to a specific physical domain.
The authors tackled the problem of predicting wave propagation in a 2D medium using a deep neural network, achieving reasonable predictions up to 80 time steps into the future and generalization to unseen initial conditions.
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should seek alternatives. Fortunately, many of the laws of behaviour of the physical world can be derived from prior knowledge of dynamical systems, expressed through the use of partial differential equations. In this work, we suggest a neural network capable of understanding a specific physical phenomenon: wave propagation in a two-dimensional medium. We define `understanding' in this context as the ability to predict the future evolution of the spatial patterns of rendered wave amplitude from a relatively small set of initial observations. The inherent complexity of the wave equations -- together with the existence of reflections and interference -- makes the prediction problem non-trivial. A network capable of making approximate predictions also unlocks the opportunity to speed-up numerical simulations for wave propagation. To this aim, we created a novel dataset of simulated wave motion and built a predictive deep neural network comprising of three main blocks: an encoder, a propagator made by 3 LSTMs, and a decoder. Results show reasonable predictions for as long as 80 time steps into the future on a dataset not seen during training. Furthermore, the network is able to generalize to an initial condition that is qualitatively different from those seen during training.