Condition-Aware Graph Flow Matching for Modeling the Distributions of Complex Fluid Systems

Xiaochao Deng, Jie Chen, Xiaogang Deng
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:23830-23852, 2026.

Abstract

Accurately modeling the full distributions of possible states is crucial for understanding statistical properties and enabling reliable predictions in complex fluid systems. Recently, diffusion models and flow matching have shown promise in these tasks. However, they remain limited in uncovering the general principles of systems from multiple short trajectories across the condition space. In addition, they exhibit inferior adaptability to large irregular geometries, particularly in regions with sharp gradients. In this paper, we propose a condition-aware graph flow matching (CGFM) method that combines condition-aware flow matching with a hierarchical graph structure to learn the full distributions of fluid systems from incomplete training data. Specifically, CGFM constructs a flow enabling smooth interpolation across physical conditions and parameterizes the graph-conditioned vector field through HieraGraphNet. HieraGraphNet performs message passing across multilevel graphs to capture multi-scale dynamics and facilitate long-range information interactions in fluid systems. Moreover, we introduce a topology- and geometry-aware graph coarsening scheme that incorporates topological connectivity and local geometric density to construct reliable coarse graphs. We validate the effectiveness of CGFM on three canonical scenarios across both 2D and 3D dynamics, which demonstrate its superior performance compared with that of state-of-the-art baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-deng26c, title = {Condition-Aware Graph Flow Matching for Modeling the Distributions of Complex Fluid Systems}, author = {Deng, Xiaochao and Chen, Jie and Deng, Xiaogang}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {23830--23852}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/deng26c/deng26c.pdf}, url = {https://proceedings.mlr.press/v306/deng26c.html}, abstract = {Accurately modeling the full distributions of possible states is crucial for understanding statistical properties and enabling reliable predictions in complex fluid systems. Recently, diffusion models and flow matching have shown promise in these tasks. However, they remain limited in uncovering the general principles of systems from multiple short trajectories across the condition space. In addition, they exhibit inferior adaptability to large irregular geometries, particularly in regions with sharp gradients. In this paper, we propose a condition-aware graph flow matching (CGFM) method that combines condition-aware flow matching with a hierarchical graph structure to learn the full distributions of fluid systems from incomplete training data. Specifically, CGFM constructs a flow enabling smooth interpolation across physical conditions and parameterizes the graph-conditioned vector field through HieraGraphNet. HieraGraphNet performs message passing across multilevel graphs to capture multi-scale dynamics and facilitate long-range information interactions in fluid systems. Moreover, we introduce a topology- and geometry-aware graph coarsening scheme that incorporates topological connectivity and local geometric density to construct reliable coarse graphs. We validate the effectiveness of CGFM on three canonical scenarios across both 2D and 3D dynamics, which demonstrate its superior performance compared with that of state-of-the-art baselines.} }
Endnote
%0 Conference Paper %T Condition-Aware Graph Flow Matching for Modeling the Distributions of Complex Fluid Systems %A Xiaochao Deng %A Jie Chen %A Xiaogang Deng %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-deng26c %I PMLR %P 23830--23852 %U https://proceedings.mlr.press/v306/deng26c.html %V 306 %X Accurately modeling the full distributions of possible states is crucial for understanding statistical properties and enabling reliable predictions in complex fluid systems. Recently, diffusion models and flow matching have shown promise in these tasks. However, they remain limited in uncovering the general principles of systems from multiple short trajectories across the condition space. In addition, they exhibit inferior adaptability to large irregular geometries, particularly in regions with sharp gradients. In this paper, we propose a condition-aware graph flow matching (CGFM) method that combines condition-aware flow matching with a hierarchical graph structure to learn the full distributions of fluid systems from incomplete training data. Specifically, CGFM constructs a flow enabling smooth interpolation across physical conditions and parameterizes the graph-conditioned vector field through HieraGraphNet. HieraGraphNet performs message passing across multilevel graphs to capture multi-scale dynamics and facilitate long-range information interactions in fluid systems. Moreover, we introduce a topology- and geometry-aware graph coarsening scheme that incorporates topological connectivity and local geometric density to construct reliable coarse graphs. We validate the effectiveness of CGFM on three canonical scenarios across both 2D and 3D dynamics, which demonstrate its superior performance compared with that of state-of-the-art baselines.
APA
Deng, X., Chen, J. & Deng, X.. (2026). Condition-Aware Graph Flow Matching for Modeling the Distributions of Complex Fluid Systems. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:23830-23852 Available from https://proceedings.mlr.press/v306/deng26c.html.

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