Neural Implicit Reduced Fluid Simulation

Yuanyuan Tao, Ivan Puhachov, Derek Nowrouzezahrai, Paul Kry

High-fidelity simulation of fluid dynamics is challenging because of the high dimensional state data needed to capture fine details and the large computational cost associated with advancing the system in time. We present neural implicit reduced fluid simulation (NIRFS), a reduced fluid simulation technique that combines an implicit neural representation of fluid shapes and a neural ordinary differential equation to model the dynamics of fluid in the reduced latent space. The latent trajectories are computed at very little cost in comparison to simulations for training, while preserving fine physical details. We show that this approach can work well, capturing the shapes and dynamics involved in a variety of scenarios with constrained initial conditions, e.g., droplet-droplet collisions, crown splashes, and fluid slosh in a container. In each scenario, we learn the latent implicit representation of fluid shapes with a deep-network signed distance function, as well as the energy function and parameters of a damped Hamiltonian system, which helps guarantee desirable properties of the latent dynamics. To ensure that latent shape representations form smooth and physically meaningful trajectories, we simultaneously learn the latent representation and dynamics. We evaluate novel simulations for conservation of volume and momentum conservation, discuss design decisions, and demonstrate an application of our method to fluid control.

Neural Implicit Reduced Fluid Simulation