Honey, I Shrunk the Domain: Frequency-aware Force Field Reduction for Efficient Fluids Optimization

Abstract

Fluid control often uses optimization of control forces that are added to a simulation at each time step, such that the final animation matches a single or multiple target density keyframes provided by an artist. The optimization problem is strongly under-constrained with a high-dimensional parameter space, and finding optimal solutions is challenging, especially for higher resolution simulations. In this paper, we propose two novel ideas that jointly tackle the lack of constraints and high dimensionality of the parameter space. We first consider the fact that optimized forces are allowed to have divergent modes during the optimization process. These divergent modes are not entirely projected out by the pressure solver step, manifesting as unphysical smoke sources that are explored by the optimizer to match a desired target. Thus, we reduce the space of the possible forces to the family of strictly divergence-free velocity fields, by optimizing directly for a vector potential. We synergistically combine this with a smoothness regularization based on a spectral decomposition of control force fields. Our method enforces lower frequencies of the force fields to be optimized first by filtering force frequencies in the Fourier domain. The mask-growing strategy is inspired by Kolmogorov's theory about scales of turbulence. We demonstrate improved results for 2D and 3D fluid control especially in higher-resolution settings, while eliminating the need for manual parameter tuning. We showcase various applications of our method, where the user effectively creates or edits smoke simulations.