Learning Incompressible Fluid Dynamics from Scratch -- Towards Fast, Differentiable Fluid Models that Generalize

TL;DR

This paper introduces a physics-constrained neural network approach for incompressible fluid simulation that generalizes to new domains, requires no training data, and enables fast, differentiable simulations suitable for real-time applications and control tasks.

Contribution

It presents a novel training method that allows neural networks to simulate incompressible fluids without data, improving speed, generalization, and differentiability over existing methods.

Findings

Models enable real-time fluid simulation with diverse phenomena.

Neural networks outperform recent differentiable solvers in speed and accuracy.

Framework allows for efficient gradient-based control of fluid dynamics.

Abstract

Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of incompressible fluids is a challenging task and traditional numerical approximation schemes come at high computational costs. Recent deep learning based approaches promise vast speed-ups but do not generalize to new fluid domains, require fluid simulation data for training, or rely on complex pipelines that outsource major parts of the fluid simulation to traditional methods. In this work, we propose a novel physics-constrained training approach that generalizes to new fluid domains, requires no fluid simulation data, and allows convolutional neural networks to map a fluid state from time-point t to a subsequent state at time t + dt in a single forward pass. This simplifies the pipeline to train and evaluate neural fluid models. After training, the framework yields models that are capable of fast fluid simulations and can handle various fluid phenomena including the Magnus effect and Karman vortex streets. We present an interactive real-time demo to show the speed and generalization capabilities of our trained models. Moreover, the trained neural networks are efficient differentiable fluid solvers as they offer a differentiable update step to advance the fluid simulation in time. We exploit this fact in a proof-of-concept optimal control experiment. Our models significantly outperform a recent differentiable fluid solver in terms of computational speed and accuracy.