Topology-aware Neural Flux Prediction Guided by Physics

Haoyang Jiang, Jindong Wang, Xingquan Zhu, Yi He
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:27670-27684, 2025.

Abstract

Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a graph with forward and reverse topologies equal. To make GNNs sensitive to those high-frequency components thereby being capable to capture detailed topological differences, this paper proposes a novel framework that combines 1) explicit difference matrices that model directional gradients and 2) implicit physical constraints that enforce messages passing within GNNs to be consistent with natural laws. Evaluations on two real-world directed graph data, namely, water flux network and urban traffic flow network, demonstrate the effectiveness of our proposal.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-jiang25i, title = {Topology-aware Neural Flux Prediction Guided by Physics}, author = {Jiang, Haoyang and Wang, Jindong and Zhu, Xingquan and He, Yi}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {27670--27684}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/jiang25i/jiang25i.pdf}, url = {https://proceedings.mlr.press/v267/jiang25i.html}, abstract = {Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a graph with forward and reverse topologies equal. To make GNNs sensitive to those high-frequency components thereby being capable to capture detailed topological differences, this paper proposes a novel framework that combines 1) explicit difference matrices that model directional gradients and 2) implicit physical constraints that enforce messages passing within GNNs to be consistent with natural laws. Evaluations on two real-world directed graph data, namely, water flux network and urban traffic flow network, demonstrate the effectiveness of our proposal.} }
Endnote
%0 Conference Paper %T Topology-aware Neural Flux Prediction Guided by Physics %A Haoyang Jiang %A Jindong Wang %A Xingquan Zhu %A Yi He %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-jiang25i %I PMLR %P 27670--27684 %U https://proceedings.mlr.press/v267/jiang25i.html %V 267 %X Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a graph with forward and reverse topologies equal. To make GNNs sensitive to those high-frequency components thereby being capable to capture detailed topological differences, this paper proposes a novel framework that combines 1) explicit difference matrices that model directional gradients and 2) implicit physical constraints that enforce messages passing within GNNs to be consistent with natural laws. Evaluations on two real-world directed graph data, namely, water flux network and urban traffic flow network, demonstrate the effectiveness of our proposal.
APA
Jiang, H., Wang, J., Zhu, X. & He, Y.. (2025). Topology-aware Neural Flux Prediction Guided by Physics. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:27670-27684 Available from https://proceedings.mlr.press/v267/jiang25i.html.

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