VortexNet: Learning Complex Dynamic Systems with Physics-Embedded Networks

In this paper, we present a novel physics-rooted network structure that dramatically facilitates the learning of complex dynamic systems. Our method is inspired by the Vortex Method in fluid dynamics, whose key idea lies in that, given the observed flow field, instead of describing it with a function of space and time, one can equivalently understand the observation as being caused by a number of Lagrangian particles ----- vortices, flowing with the field. Since the number of such vortices are much smaller than that of the Eulerian, grid discretization, this Lagrangian discretization in essence encodes the system dynamics on a compact physics-based latent space. Our method enforces such Lagrangian discretization with a Encoder---Dynamics---Decode network structure, and trains it with a novel three-stage curriculum learning algorithm. With data generated from the high precision Eulerian DNS method, our alorithm takes advantage of the simplifying power of the Lagrangian method while persisting the physical integrity. This method fundamentally differs from the current approaches in the field of physics-informed learning, and provides superior results for being more versatile, yielding more physical-correctness with less data sample, and faster to compute at high precision. Beyond providing a viable way of simulating complex fluid at high-precision, our method opens up a brand new horizon for embedding knowledge prior via constructing physically-valid latent spaces, which can be applied to further research areas beyond physical simulation.