Accelerating fluid simulations

Simulating how fluids move is accurate but slow. A single high-resolution flow can take hours to compute, which rules it out of any setting where you need many simulations quickly: exploring designs, reacting in real time, or running an outer optimization loop. A machine-learned surrogate can be orders of magnitude faster, but a surrogate is only useful if it stays accurate on flows it was not trained on.

The way in is a symmetry. Rotate or translate a flow field and the underlying physics does not change, so a good surrogate should behave the same way. Most networks have to learn this invariance from data, wasting capacity and examples on something we already know. Instead, we build it in.

We designed a graph neural network that is equivariant to 2D rotations and translations and works directly on irregular, non-gridded domains. The key idea is to align the internal representations with the principal axis of the local flow, which lets the architecture stay flexible while still guaranteeing SE(2) equivariance (Bånkestad et al., 2024). Because the symmetry is built in rather than learned, the model needs less data and produces more stable long rollouts than non-equivariant baselines.

Rollout predictions of our SE(2) equivariant GNN (middle), its non-equivariant counterpart (right), and the true simulation (left). The models have only seen the first two seconds of the simulation.

Publications

2024

Flexible SE(2) graph neural networks with applications to PDE surrogates

Maria Bånkestad, Olof Mogren, and Aleksis Pirinen

arXiv preprint arXiv:2405.20287, 2024

Abs arXiv Bib Code

This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy.
@article{bankestad2024flexible, title = {Flexible SE(2) graph neural networks with applications to PDE surrogates}, author = {B{\aa}nkestad, Maria and Mogren, Olof and Pirinen, Aleksis}, journal = {arXiv preprint arXiv:2405.20287}, year = {2024}, }