Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction

2024-12-30

AI Summary

Accurate spatiotemporal dynamics prediction in complex geometric domains under few-shot settings remains challenging due to poor interpretability, physical inconsistency, heavy reliance on large-scale labeled data, and weak generalization of existing deep learning methods. Method: We propose a conservation-law-guided graph neural network (GNN) framework featuring a novel symmetric architecture that explicitly embeds conservation-law priors. It jointly integrates multi-scale graph-structured encoding with implicit latent temporal stepping and enforces physical consistency via symmetry regularization. Contribution/Results: Unlike conventional GNNs, our framework eliminates dependence on extensive labeled data and implicit physics-informed inductive biases, enabling end-to-end interpretable modeling. Extensive experiments on synthetic and real-world datasets demonstrate significant improvements over state-of-the-art baselines in prediction accuracy, cross-domain generalization, and robustness to complex boundaries—achieving both high fidelity and verifiable physical consistency.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Graph-based Machine Learning
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Responsible Web: Consent frameworks and practices on the web

Abstract

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, pure 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 generalization ability, and is readily applicable to learning for prediction of various spatiotemporal dynamics in a spatial domain with complex geometry.

Problem

• Temporal-Spatial Prediction
• Deep Learning Limitations
• Physics-based Rules

Innovation

• CiGNN
• Conservation Laws
• Multi-scale Information Propagation