Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction

TL;DR

CiGNN introduces a conservation-informed graph neural network that enforces a general conservation law via symmetry, placing physics priors at the core of graph-based spatiotemporal learning. The architecture combines a space block with a multi-mesh graph, a SymMPNN processor that handles symmetric and asymmetric flux updates, and a latent time integrator to stabilize long-term predictions. Across four synthetic and real datasets (2D Burgers, 3D Gray-Scott RD, flow past a cylinder, and Black Sea hydrology), CiGNN achieves superior accuracy and generalization compared with state-of-the-art baselines, while remaining data-efficient. The approach offers an explainable framework for learning dynamics on irregular geometries with potential applications in complex physics-driven systems.

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.

Figures (4)

• Figure 1: Schematic of the CiGNN model. a, The main network architecture. b, The space block that defines a multi-mesh graph to account for different scales and transforms the physical state to a low-dimensional representation. c, The SymMPNN block that is designed for learning high-dimensional representation. d, The Flux update component that passes symmetric and asymmetric information on edges. e, The time block that marches the sequenced high-dimensional features.
• Figure 2: Diagrams of irregular domains. a, Schematic diagram of the CF example setup with the fluid flowing in from the inflow to the outflow. b, The geographic and sensor information of the BS Real-world dataset.
• Figure 3: Error distributions and the system state snapshots predicted by CiGNN and other baselines. a, The 2D viscous Burgers equation example. b, The 3D Gray-Scott equation example. c, The 2D CF example setup with the fluid flowing in from the inflow to the outflow.
• Figure 4: Prediction results of CiGNN on real-world BS hydrological dataset. a--b, Snapshots of the predicted flow velocity and water temperature at day 1, day 69, and day 137. c--d, Pearson correlation of the corresponding predicted flow velocity and water temperature. The above three time points represent the sampling moments during the early, middle, and late stages of prediction, respectively. The blue line represents the mean value of the correlation, and the light blue area the deviation (e.g., $\pm\sigma$).