# Adaptive Runge-Kutta Dynamics for Spatiotemporal Prediction

arXiv: https://arxiv.org/abs/2405.14504 · HTML: https://mlsanity.com/paper/2405.14504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 18 of 18)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Video Swin Transformer](https://mlsanity.com/paper/2106.13230/) (2021)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Unsupervised Learning of Video Representations using LSTMs](https://mlsanity.com/paper/1502.04681/) (2015)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction](https://mlsanity.com/paper/2003.01460/) (2020)
- [SimVP: Simpler yet Better Video Prediction](https://mlsanity.com/paper/2206.05099/) (2022)
- [Earthformer: Exploring Space-Time Transformers for Earth System Forecasting](https://mlsanity.com/paper/2207.05833/) (2022)
- [OpenSTL: A Comprehensive Benchmark of Spatio-Temporal Predictive Learning](https://mlsanity.com/paper/2306.11249/) (2023)
- [A Dynamic Multi-Scale Voxel Flow Network for Video Prediction](https://mlsanity.com/paper/2303.09875/) (2023)
- [SwinLSTM:Improving Spatiotemporal Prediction Accuracy using Swin Transformer and LSTM](https://mlsanity.com/paper/2308.09891/) (2023)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Earthfarseer: Versatile Spatio-Temporal Dynamical Systems Modeling in One Model](https://mlsanity.com/paper/2312.08403/) (2023)

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

- [Multiscale fusion enhanced spiking neural network for invasive BCI neural signal decoding](https://mlsanity.com/paper/2410.03533/) (2024)

## Abstract (arXiv)

Spatiotemporal prediction is important in solving natural problems and processing video frames, especially in weather forecasting and human action recognition. Recent advances attempt to incorporate prior physical knowledge into the deep learning framework to estimate the unknown governing partial differential equations (PDEs) in complex dynamics, which have shown promising results in spatiotemporal prediction tasks. However, previous approaches only restrict neural network architectures or loss functions to acquire physical or PDE features, which decreases the representative capacity of a neural network. Meanwhile, the updating process of the physical state cannot be effectively estimated. To solve the problems mentioned above, we introduce a physical-guided neural network, which utilizes an adaptive second-order Runge-Kutta method with physical constraints to model the physical states more precisely. Furthermore, we propose a frequency-enhanced Fourier module to strengthen the model's ability to estimate the spatiotemporal dynamics. We evaluate our model on both spatiotemporal and video prediction tasks. The experimental results show that our model outperforms several state-of-the-art methods and performs the best in several spatiotemporal scenarios with a much smaller parameter count.