Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics

Lukas Prantl, Benjamin Ummenhofer, Vladlen Koltun, Nils Thuerey

Keywords: particle-based fluids, conservation of momentum, symmetry, antisymmetry, physical simulation

TL;DR: We use conservation of momentum as an inductive bias in the form of a hard constraint for learning particle-based fluid dynamics.

Abstract: We present a novel method for guaranteeing linear momentum in learned physics simulations. Unlike existing methods, we enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional layers. We combine these strict constraints with a hierarchical network architecture, a carefully constructed resampling scheme, and a training approach for temporal coherence. In combination, the proposed method allows us to increase the physical accuracy of the learned simulator substantially. In addition, the induced physical bias leads to significantly better generalization performance and makes our method more reliable in unseen test cases. We evaluate our method on a range of different, challenging fluid scenarios. Among others, we demonstrate that our approach generalizes to new scenarios with up to one million particles. Our results show that the proposed algorithm can learn complex dynamics while outperforming existing approaches in generalization and training performance. An implementation of our approach is available at https://github.com/tum-pbs/DMCF.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2210.06036/code)