Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics

Rene Winchenbach, Nils Thuerey

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: CConv, GNN, SPH, Lagrangian Fluids, Fourier Methods

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

TL;DR: Using Fourier Terms we build a Continuous Convolution Network that outperforms prior work by leveraging even and odd symmetries.

Abstract:

Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computationally expensive and challenging to use in inverse problems, whereas Neural solvers aim to address both concerns through machine learning. We propose a general formulation for continuous convolutions using separable basis functions as a superset of existing methods and evaluate a large set of basis functions in the context of (a) a compressible 1D SPH simulation, (b) a weakly compressible 2D SPH simulation, and (c) an incompressible 2D SPH Simulation. We demonstrate that even and odd symmetries included in the basis functions are key aspects of stability and accuracy.
Our broad evaluation shows that Fourier-based continuous convolutions outperform all other architectures regarding accuracy and generalization. Finally, using these Fourier-based networks, we show that prior inductive biases, such as window functions, are no longer necessary. An implementation of our approach, as well as complete datasets and solver implementations, is available at https://github.com/orgs/tum-pbs/SFBC.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 1281