Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network

Yadi Cao, Menglei Chai, Minchen Li, Chenfanfu Jiang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:3541-3558, 2023.

Abstract

Learning the long-range interactions on large-scale mesh-based physical systems with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. Therefore, there has been growing interest in the community to introduce multi-scale structures to GNNs for physics simulation. However, current state-of-the-art methods are limited by their reliance on the labor-heavy drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, bi-stride to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the Breadth-First-Search (BFS), without the need for the manual drawing of coarser meshes and, avoid wrong edges introduced by spatial proximity. Additionally, it enables a reduced number of MP times on each level and the non-parametrized pooling and unpooling by interpolations, similar to convolutional Neural Networks (CNNs), which significantly reduces computational requirements. Experiments show that the proposed framework, BSMS-GNN, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physics-based simulation scenarios.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-cao23a, title = {Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network}, author = {Cao, Yadi and Chai, Menglei and Li, Minchen and Jiang, Chenfanfu}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {3541--3558}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/cao23a/cao23a.pdf}, url = {https://proceedings.mlr.press/v202/cao23a.html}, abstract = {Learning the long-range interactions on large-scale mesh-based physical systems with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. Therefore, there has been growing interest in the community to introduce multi-scale structures to GNNs for physics simulation. However, current state-of-the-art methods are limited by their reliance on the labor-heavy drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, bi-stride to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the Breadth-First-Search (BFS), without the need for the manual drawing of coarser meshes and, avoid wrong edges introduced by spatial proximity. Additionally, it enables a reduced number of MP times on each level and the non-parametrized pooling and unpooling by interpolations, similar to convolutional Neural Networks (CNNs), which significantly reduces computational requirements. Experiments show that the proposed framework, BSMS-GNN, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physics-based simulation scenarios.} }
Endnote
%0 Conference Paper %T Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network %A Yadi Cao %A Menglei Chai %A Minchen Li %A Chenfanfu Jiang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-cao23a %I PMLR %P 3541--3558 %U https://proceedings.mlr.press/v202/cao23a.html %V 202 %X Learning the long-range interactions on large-scale mesh-based physical systems with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. Therefore, there has been growing interest in the community to introduce multi-scale structures to GNNs for physics simulation. However, current state-of-the-art methods are limited by their reliance on the labor-heavy drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, bi-stride to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the Breadth-First-Search (BFS), without the need for the manual drawing of coarser meshes and, avoid wrong edges introduced by spatial proximity. Additionally, it enables a reduced number of MP times on each level and the non-parametrized pooling and unpooling by interpolations, similar to convolutional Neural Networks (CNNs), which significantly reduces computational requirements. Experiments show that the proposed framework, BSMS-GNN, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physics-based simulation scenarios.
APA
Cao, Y., Chai, M., Li, M. & Jiang, C.. (2023). Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:3541-3558 Available from https://proceedings.mlr.press/v202/cao23a.html.

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