The dataset used for our ICLR 2024 paper on symmetric basis convolutions.
The dataset behind our ICLR 2024 paper on symmetric basis convolutions for learning Lagrangian fluid mechanics. It consists of weakly compressible SPH trajectories in periodic domains, generated so that a learned model can be trained and evaluated against a consistent ground truth.
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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