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

arXiv: https://arxiv.org/abs/2604.26593 · HTML: https://mlsanity.com/paper/2604.26593/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 68 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 30 of 33)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Deep Graph Library: A Graph-Centric, Highly-Performant Package for Graph Neural Networks](https://mlsanity.com/paper/1909.01315/) (2019)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems](https://mlsanity.com/paper/2211.05520/) (2022)
- [Graph Neural Networks Designed for Different Graph Types: A Survey](https://mlsanity.com/paper/2204.03080/) (2022)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
- [Foundations of Population-Based SHM, Part IV: The Geometry of Spaces of Structures and their Feature Spaces](https://mlsanity.com/paper/2103.03655/) (2021)
- [Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations](https://mlsanity.com/paper/2405.05987/) (2024)
- [Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2110.08607/) (2021)
- [A digital twin framework for civil engineering structures](https://mlsanity.com/paper/2308.01445/) (2023)
- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Physics-informed machine learning for Structural Health Monitoring](https://mlsanity.com/paper/2206.15303/) (2022)
- [Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems](https://mlsanity.com/paper/2210.04165/) (2022)
- [Physics-informed Graphical Neural Network for Power System State Estimation](https://mlsanity.com/paper/2312.17738/) (2023)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Graph Kalman Filters](https://mlsanity.com/paper/2303.12021/) (2023)
- [Graph Transformers for inverse physics: reconstructing flows around arbitrary 2D airfoils](https://mlsanity.com/paper/2501.17081/) (2025)
- [Sequential Bayesian Inference for Uncertain Nonlinear Dynamic Systems: A Tutorial](https://mlsanity.com/paper/2201.08180/) (2022)
- [Response Estimation and System Identification of Dynamical Systems via Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.01340/) (2024)
- [Using Graph Neural Networks and Frequency Domain Data for Automated Operational Modal Analysis of Populations of Structures](https://mlsanity.com/paper/2407.06492/) (2024)

## Built on by (most cited first, 1 of 1)

- [Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver](https://mlsanity.com/paper/2609.24021/) (2026)

## Abstract (arXiv)

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.