# ST-PCNN: Spatio-Temporal Physics-Coupled Neural Networks for Dynamics Forecasting

arXiv: https://arxiv.org/abs/2108.05940 · HTML: https://mlsanity.com/paper/2108.05940/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 12 Aug 2021.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Memory Fusion Network for Multi-view Sequential Learning](https://mlsanity.com/paper/1802.00927/) (2018)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting](https://mlsanity.com/paper/1905.10069/) (2019)
- [Convolutional Tensor-Train LSTM for Spatio-temporal Learning](https://mlsanity.com/paper/2002.09131/) (2020)
- [Data-driven discovery of PDEs in complex datasets](https://mlsanity.com/paper/1808.10788/) (2018)
- [DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data](https://mlsanity.com/paper/1908.04463/) (2019)
- [Long-Term Mobile Traffic Forecasting Using Deep Spatio-Temporal Neural Networks](https://mlsanity.com/paper/1712.08083/) (2017)
- [Differentiable Physics-informed Graph Networks](https://mlsanity.com/paper/1902.02950/) (2019)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Revealing hidden dynamics from time-series data by ODENet](https://mlsanity.com/paper/2005.04849/) (2020)
- [Learning Partial Differential Equations from Data Using Neural Networks](https://mlsanity.com/paper/1910.10262/) (2019)
- [Physics-informed Tensor-train ConvLSTM for Volumetric Velocity Forecasting of Loop Current](https://mlsanity.com/paper/2008.01798/) (2020)
- [Visual Analysis of Spatio-Temporal Event Predictions: Investigating the Spread Dynamics of Invasive Species](https://mlsanity.com/paper/1710.07029/) (2017)
- [CSWA: Aggregation-Free Spatial-Temporal Community Sensing](https://mlsanity.com/paper/1711.05712/) (2017)

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

- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)

## Abstract (arXiv)

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial differential equations (ODEs/PDEs) -- largely dominate the whole process, irrespective of time or location. Physics-informed learning has recently emerged to learn physics for accurate prediction, but they often lack a mechanism to leverage localized spatial and temporal correlation or rely on hard-coded physics parameters. In this paper, we advocate a physics-coupled neural network model to learn parameters governing the physics of the system, and further couple the learned physics to assist the learning of recurring dynamics. A spatio-temporal physics-coupled neural network (ST-PCNN) model is proposed to achieve three goals: (1) learning the underlying physics parameters, (2) transition of local information between spatio-temporal regions, and (3) forecasting future values for the dynamical system. The physics-coupled learning ensures that the proposed model can be tremendously improved by using learned physics parameters, and can achieve good long-range forecasting (e.g., more than 30-steps). Experiments, using simulated and field-collected ocean current data, validate that ST-PCNN outperforms existing physics-informed models.