An Unconditionally Stable Real-time Physics Solver

Water Simulation

ACM SIGGRAPH Asia 2015

Data-Driven Fluid Simulations

using Regression Forests

Ľubor Ladický, SoHyeon Jeong, Barbara Solenthaler, Marc Pollefeys and Markus Gross

Traditional fluid simulations require large computational resources even for an average sized scene with the main bottleneck being a very small time step size, required to guarantee the stability of the solution. Despite a large progress in parallel computing and efficient algorithms for pressure computation in the recent years, realtime fluid simulations have been possible only under very restricted conditions. In this paper we propose a novel **machine learning based approach**, that formulates **physics-based fluid simulation as a regression problem**, estimating the acceleration of every particle for each frame. We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a **large time step** setting on yet unseen test videos. We used a regression forest to approximate the behaviour of particles observed in the large training set of simulations obtained using a traditional solver. Our **GPU implementation** led to a speed-up of one to three orders of magnitude compared to the state-of-the-art position-based fluid solver and runs **in real-time** for systems with **up to 2 million particles.**

The Features

Water particles flows along the velocity field learned from the water simulation examples instead of resolving expensive Navier-Stokes equations.

A diversity of materials can be represented by changing material properties such as viscosity, surface tension, adhesion, static friction and vorticity confinement using the same trained model of water.

Simulations with up to 2M particles, a 1/32 time-step and interactive user controls can run in real-time.