Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics
Asking what the right convolution is for Lagrangian particle data, and building a symmetric basis formulation to answer it.
Continuous convolutions for particle data are typically constructed ad hoc. This paper takes the basis functions seriously, studying symmetric formulations for learning Lagrangian fluid mechanics and showing what the choice of basis actually costs in accuracy and stability.
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.
@inproceedings{Winchenbach2024SFBC,author={Winchenbach, Rene and Thuerey, Nils},title={Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics},booktitle={12th International Conference on Learning Representations, {ICLR} 2024,
Vienna, Austria},year={2024},url={https://openreview.net/forum?id=HKgRwNhI9R},}
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