# Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics

arXiv: https://arxiv.org/abs/2510.13601 · HTML: https://mlsanity.com/paper/2510.13601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 67 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations](https://mlsanity.com/paper/1703.10230/) (2017)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers](https://mlsanity.com/paper/2212.12474/) (2022)
- [Delta-PINNs: physics-informed neural networks on complex geometries](https://mlsanity.com/paper/2209.03984/) (2022)
- [Hierarchical Deep Learning with Generative Adversarial Network for Automatic Cardiac Diagnosis from ECG Signals](https://mlsanity.com/paper/2210.11408/) (2022)
- [Physics-constrained Deep Learning for Robust Inverse ECG Modeling](https://mlsanity.com/paper/2107.12780/) (2021)
- [Multi-resolution Multi-task Gaussian Processes](https://mlsanity.com/paper/1906.08344/) (2019)
- [Automated Identication of Atrial Fibrillation from Single-lead ECGs Using Multi-branching ResNet](https://mlsanity.com/paper/2306.15096/) (2023)
- [MUSE-Net: Missingness-aware mUlti-branching Self-attention Encoder for Irregular Longitudinal Electronic Health Records](https://mlsanity.com/paper/2407.00840/) (2024)
- [Geometry-aware Active Learning of Spatiotemporal Dynamic Systems](https://mlsanity.com/paper/2504.19012/) (2025)
- [Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting](https://mlsanity.com/paper/2507.03855/) (2025)
- [The Effect of Different Optimization Strategies to Physics-Constrained Deep Learning for Soil Moisture Estimation](https://mlsanity.com/paper/2403.08154/) (2024)

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

- [P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution](https://mlsanity.com/paper/2606.19303/) (2026)

## Abstract (arXiv)

Recent advances in sensing and imaging technologies have enabled the collection of high-dimensional spatiotemporal data across complex geometric domains. However, effective modeling of such data remains challenging due to irregular spatial structures, rapid temporal dynamics, and the need to jointly predict multiple interrelated physical variables. This paper presents a physics-augmented multi-task Gaussian Process (P-M-GP) framework tailored for spatiotemporal dynamic systems. Specifically, we develop a geometry-aware, multi-task Gaussian Process (M-GP) model to effectively capture intrinsic spatiotemporal structure and inter-task dependencies. To further enhance the model fidelity and robustness, we incorporate governing physical laws through a physics-based regularization scheme, thereby constraining predictions to be consistent with governing dynamical principles. We validate the proposed P-M-GP framework on a 3D cardiac electrodynamics modeling task. Numerical experiments demonstrate that our method significantly improves prediction accuracy over existing methods by effectively incorporating domain-specific physical constraints and geometric prior.