Learnable Stability-Aware Unstructured Grid Coarsening Using Graph Neural Networks for Accelerated Physics Simulations

Alexander Ryabov, Sergei Shumilin, Viacheslav Naumov, Nikolay Yavich, Sayan Ranu, N M Anoop Krishnan, Evgeny Burnaev, Vladimir Vanovskiy

Keywords: Graph Neural Networks, differentiable solvers, numerical modelling, grid coarsening, upscaling

TL;DR: We developed a fully differentiable framework for unstructured grid coarsening, driven by the underlying physics simulation and its stability requirements..

Abstract: Efficient simulations of complex physical systems described by partial differential equations (PDE) require computational methods that can reduce the resource demands without sacrificing the accuracy. Traditionally, this is achieved by ``upscaling'' the simulation grids or by aggregating cells based on a priori information. Here, we introduce a novel framework based on graph neural networks (GNN) for learnable self-supervised differentiable coarsening of unstructured computational grids. We leverage graph-based representation of the physical system and offer a graph coarsening method which preserves the underlying physical properties together with the stability of the chosen numerical scheme. This is achieved by minimizing the error between the output of the simulations using coarsened and original graph. We demonstrate the approach on several example differential equations, modeling sub-surface flow and wave propagation. We demonstrate that the model exhibits ability to maintain high fidelity in simulation outputs even after 95\% reduction on the nodes, significantly reducing computational overhead. We also show that the model exhibits generalizability to unseen scenarios, thereby outperforming the baselines. Thus, the developed approach demonstrates the ability to accelerate simulation without comprising accuracy and hence has potential for accelerating physical simulations in various domains.

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

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.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

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.

Submission Number: 11649