# Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics

arXiv: https://arxiv.org/abs/2403.16680 · HTML: https://mlsanity.com/paper/2403.16680/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2024.

## Built on by (most cited first, 4 of 4)

- [A Neural Material Point Method for Particle-based Emulation](https://mlsanity.com/paper/2408.15753/) (2024)
- [A Pioneering Neural Network Method for Efficient and Robust Fluid Simulation](https://mlsanity.com/paper/2412.10748/) (2024)
- [CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation](https://mlsanity.com/paper/2511.22938/) (2025)
- [Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence](https://mlsanity.com/paper/2403.17993/) (2024)

## Abstract (arXiv)

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/tum-pbs/SFBC.