# Graph Kalman Filters

arXiv: https://arxiv.org/abs/2303.12021 · HTML: https://mlsanity.com/paper/2303.12021/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Graph Neural Networks in TensorFlow and Keras with Spektral](https://mlsanity.com/paper/2006.12138/) (2020)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)
- [Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs](https://mlsanity.com/paper/1612.03615/) (2016)
- [Graph State-Space Models and Latent Relational Inference](https://mlsanity.com/paper/2301.01741/) (2023)

## Built on by (most cited first, 5 of 5)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)
- [Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectories](https://mlsanity.com/paper/2509.12953/) (2025)

## Abstract (arXiv)

The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper generalizes, for the first time in the literature, Kalman and extended Kalman filters to discrete-time settings where inputs, states, and outputs are represented as attributed graphs whose topology and attributes can change with time. The setup allows us to adapt the framework to cases where the output is a vector or a scalar too (node/graph level tasks). Within the proposed theoretical framework, the unknown state-transition and the readout functions are learned end-to-end along with the downstream prediction task.