PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty

2026-04-29

AI Summary

This work addresses the challenge of online state estimation for complex nonlinear dynamical systems under model-form uncertainty and sparse sensor observations. The authors propose PiGGO, a novel framework that integrates physics-informed Graph Neural Ordinary Differential Equations (GNODEs) into an extended Kalman filter, thereby unifying continuous-time dynamics modeling, graph-structured representation, and physical inductive biases within a Bayesian filtering paradigm. PiGGO enables uncertainty-aware virtual sensing and demonstrates structural awareness of unknown nonlinear dynamics along with strong generalization across varying system topologies. Experimental results show that PiGGO significantly outperforms open-loop graph neural models and conventional filtering approaches, achieving superior robustness and estimation accuracy under model mismatch and measurement noise.

Abstract

Digital twins provide a powerful paradigm for diagnostic and prognostic tasks in the monitoring and control of engineered systems; however, their deployment for complex structures remains challenged by model-form uncertainty, arising from unknown nonlinear dynamics, and by sparse sensing. These limitations hinder reliable online state estimation using either purely physics-based or purely data-driven approaches. This work introduces the Physics-Guided Graph Neural ODE (PiGGO) framework, a physics-informed, graph-based Bayesian state estimation approach in which a learned graph neural ordinary differential equation (GNODE) serves as the continuous-time state-transition model within an extended Kalman filter. The graph representation explicitly defines the system state-space, while physics-guided inductive biases encode known structural relationships and constrain the learning of nonlinear dynamics. By integrating graph-native learned dynamics with recursive Bayesian filtering, the proposed PiGGO framework enables online virtual sensing and uncertainty-aware state estimation for nonlinear systems with unknown model form, while maintaining generalisation across topologically similar structures. Numerical case studies demonstrate improved robustness to model uncertainty and measurement noise, outperforming both open-loop graph neural models and conventional filtering approaches in online prediction tasks.

Problem

• model-form uncertainty
• sparse sensing
• nonlinear dynamics
• state estimation
• digital twins

Innovation

• Physics-informed learning
• Graph Neural ODE
• Extended Kalman Filter
• Virtual sensing
• Uncertainty-aware state estimation