# Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectories

arXiv: https://arxiv.org/abs/2509.12953 · HTML: https://mlsanity.com/paper/2509.12953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 72 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [Message passing all the way up](https://mlsanity.com/paper/2202.11097/) (2022)
- [Autobahn: Automorphism-based Graph Neural Nets](https://mlsanity.com/paper/2103.01710/) (2021)
- [Fully Convolutional Multi-scale Residual DenseNets for Cardiac Segmentation and Automated Cardiac Diagnosis using Ensemble of Classifiers](https://mlsanity.com/paper/1801.05173/) (2018)
- [State Space Models on Temporal Graphs: A First-Principles Study](https://mlsanity.com/paper/2406.00943/) (2024)
- [Graph convolutional regression of cardiac depolarization from sparse endocardial maps](https://mlsanity.com/paper/2009.14068/) (2020)
- [Graph Kalman Filters](https://mlsanity.com/paper/2303.12021/) (2023)
- [Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systems](https://mlsanity.com/paper/2305.01773/) (2023)
- [Learning Modular Simulations for Homogeneous Systems](https://mlsanity.com/paper/2210.16294/) (2022)
- [Graph State-Space Models and Latent Relational Inference](https://mlsanity.com/paper/2301.01741/) (2023)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)

## Abstract (arXiv)

We present a probabilistic framework for modeling structured spatiotemporal dynamics from sparse observations, focusing on cardiac motion. Our approach integrates neural ordinary differential equations (NODEs), graph neural networks (GNNs), and neural processes into a unified model that captures uncertainty, temporal continuity, and anatomical structure. We represent dynamic systems as spatiotemporal multiplex graphs and model their latent trajectories using a GNN-parameterized vector field. Given the sparse context observations at node and edge levels, the model infers a distribution over latent initial states and control variables, enabling both interpolation and extrapolation of trajectories. We validate the method on three synthetic dynamical systems (coupled pendulum, Lorenz attractor, and Kuramoto oscillators) and two real-world cardiac imaging datasets - ACDC (N=150) and UK Biobank (N=526) - demonstrating accurate reconstruction, extrapolation, and disease classification capabilities. The model accurately reconstructs trajectories and extrapolates future cardiac cycles from a single observed cycle. It achieves state-of-the-art results on the ACDC classification task (up to 99% accuracy), and detects atrial fibrillation in UK Biobank subjects with competitive performance (up to 67% accuracy). This work introduces a flexible approach for analyzing cardiac motion and offers a foundation for graph-based learning in structured biomedical spatiotemporal time-series data.