Pioneer: Physics-informed Riemannian Graph ODE for Entropy-increasing Dynamics
Li Sun, Ziheng Zhang, Zixi Wang, Yujie Wang, Qiqi Wan, Hao Li, Hao Peng, Philip S. Yu
Abstract
Dynamic interacting system modeling is important for understanding and simulating real world systems, e.g., meteorology and the spread of COVID. The system is typically described as a graph, where multiple objects dynamically interact with each other and evolve over time. In recent years, graph Ordinary Differential Equations (ODE) receive increasing research attentions. While achieving encouraging results, existing solutions prioritize the traditional Euclidean space, and neglect the intrinsic geometry of the system and physics laws, e.g., the principle of entropy increasing. The aforementioned limitations motivate us to rethink the system dynamics from a fresh perspective of Riemannian geometry, and pose a more realistic problem of physics-informed dynamic system modeling, considering the underlying geometry and physics law for the first time. In this paper, we present a novel physics-informed Riemannian graph ODE for a wide range of entropy-increasing dynamic systems (termed as Pioneer). In particular, we formulate a differential system on the Riemannian manifold, where a manifold-valued graph ODE is governed by the proposed constrained Ricci flow, and a manifold preserving Gyro-transform aware of system geometry. Theoretically, we report the provable entropy non-decreasing of our formulation, obeying the physics laws. Empirical results show the superiority of Pioneer on real datasets.
BibTeX
@article{Sun_Zhang_Wang_Wang_Wan_Li_Peng_Yu_2025, title={Pioneer: Physics-informed Riemannian Graph ODE for Entropy-increasing Dynamics}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/33372}, DOI={10.1609/aaai.v39i12.33372}, abstractNote={Dynamic interacting system modeling is important for understanding and simulating real world systems, e.g., meteorology and the spread of COVID. The system is typically described as a graph, where multiple objects dynamically interact with each other and evolve over time. In recent years, graph Ordinary Differential Equations (ODE) receive increasing research attentions. While achieving encouraging results, existing solutions prioritize the traditional Euclidean space, and neglect the intrinsic geometry of the system and physics laws, e.g., the principle of entropy increasing. The aforementioned limitations motivate us to rethink the system dynamics from a fresh perspective of Riemannian geometry, and pose a more realistic problem of physics-informed dynamic system modeling, considering the underlying geometry and physics law for the first time. In this paper, we present a novel physics-informed Riemannian graph ODE for a wide range of entropy-increasing dynamic systems (termed as Pioneer). In particular, we formulate a differential system on the Riemannian manifold, where a manifold-valued graph ODE is governed by the proposed constrained Ricci flow, and a manifold preserving Gyro-transform aware of system geometry. Theoretically, we report the provable entropy non-decreasing of our formulation, obeying the physics laws. Empirical results show the superiority of Pioneer on real datasets.}, number={12}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Sun, Li and Zhang, Ziheng and Wang, Zixi and Wang, Yujie and Wan, Qiqi and Li, Hao and Peng, Hao and Yu, Philip S.}, year={2025}, month={Apr.}, pages={12586-12594} }