Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction

• URL: http://arxiv.org/abs/2412.20962v3
• Date: Mon, 06 Jan 2025 14:36:13 GMT
• Title: Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction
• Authors: Yuan Mi, Pu Ren, Hongteng Xu, Hongsheng Liu, Zidong Wang, Yike Guo, Ji-Rong Wen, Hao Sun, Yang Liu,
• Abstract summary: In this paper, we introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework. The network is designed to conform to the general symmetry conservation law via symmetry where conservative and non-conservative information passes over a multiscale space by a latent temporal marching strategy. Results demonstrate that CiGNN exhibits remarkable baseline accuracy and generalizability, and is readily applicable to learning for prediction of varioustemporal dynamics.
• Score: 84.26340606752763
• License:
• Abstract: Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey intrinsic physics, and struggle to cope with the various domains. While geometry-based methods, e.g., graph neural networks (GNNs), have been proposed to further tackle these challenges, they still need to find the implicit physical laws from large datasets and rely excessively on rich labeled data. In this paper, we herein introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework, to learn spatiotemporal dynamics based on limited training data. The network is designed to conform to the general conservation law via symmetry, where conservative and non-conservative information passes over a multiscale space enhanced by a latent temporal marching strategy. The efficacy of our model has been verified in various spatiotemporal systems based on synthetic and real-world datasets, showing superiority over baseline models. Results demonstrate that CiGNN exhibits remarkable accuracy and generalizability, and is readily applicable to learning for prediction of various spatiotemporal dynamics in a spatial domain with complex geometry.

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