# Physics-Coupled Spatio-Temporal Active Learning for Dynamical Systems

arXiv: https://arxiv.org/abs/2108.05385 · HTML: https://mlsanity.com/paper/2108.05385/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 56 references that are in the map.
- First posted on arXiv 11 Aug 2021.

## Builds on (most cited first, 15 of 15)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems](https://mlsanity.com/paper/1809.08327/) (2018)
- [ViewAL: Active Learning with Viewpoint Entropy for Semantic Segmentation](https://mlsanity.com/paper/1911.11789/) (2019)
- [Data-driven discovery of PDEs in complex datasets](https://mlsanity.com/paper/1808.10788/) (2018)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data](https://mlsanity.com/paper/1908.04463/) (2019)
- [Differentiable Physics-informed Graph Networks](https://mlsanity.com/paper/1902.02950/) (2019)
- [Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations](https://mlsanity.com/paper/2005.05092/) (2020)
- [Hybrid Spatio-Temporal Graph Convolutional Network: Improving Traffic Prediction with Navigation Data](https://mlsanity.com/paper/2006.12715/) (2020)
- [A Comprehensive Benchmark Framework for Active Learning Methods in Entity Matching](https://mlsanity.com/paper/2003.13114/) (2020)
- [Revealing hidden dynamics from time-series data by ODENet](https://mlsanity.com/paper/2005.04849/) (2020)
- [Calendar Graph Neural Networks for Modeling Time Structures in Spatiotemporal User Behaviors](https://mlsanity.com/paper/2006.06820/) (2020)
- [Physics-Information-Aided Kriging: Constructing Covariance Functions using Stochastic Simulation Models](https://mlsanity.com/paper/1809.03461/) (2018)

## Built on by (most cited first, 2 of 2)

- [BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields](https://mlsanity.com/paper/2509.26005/) (2025)
- [Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems](https://mlsanity.com/paper/2304.07485/) (2023)

## Abstract (arXiv)

Spatio-temporal forecasting is of great importance in a wide range of dynamical systems applications from atmospheric science, to recent COVID-19 spread modeling. These applications rely on accurate predictions of spatio-temporal structured data reflecting real-world phenomena. A stunning characteristic is that the dynamical system is not only driven by some physics laws but also impacted by the localized factor in spatial and temporal regions. One of the major challenges is to infer the underlying causes, which generate the perceived data stream and propagate the involved causal dynamics through the distributed observing units. Another challenge is that the success of machine learning based predictive models requires massive annotated data for model training. However, the acquisition of high-quality annotated data is objectively manual and tedious as it needs a considerable amount of human intervention, making it infeasible in fields that require high levels of expertise. To tackle these challenges, we advocate a spatio-temporal physics-coupled neural networks (ST-PCNN) model to learn the underlying physics of the dynamical system and further couple the learned physics to assist the learning of the recurring dynamics. To deal with data-acquisition constraints, an active learning mechanism with Kriging for actively acquiring the most informative data is proposed for ST-PCNN training in a partially observable environment. Our experiments on both synthetic and real-world datasets exhibit that the proposed ST-PCNN with active learning converges to near optimal accuracy with substantially fewer instances.