# Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics

arXiv: https://arxiv.org/abs/2203.08655 · HTML: https://mlsanity.com/paper/2203.08655/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 16 Mar 2022.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [Learning Dynamical Systems from Partial Observations](https://mlsanity.com/paper/1902.11136/) (2019)
- [Differentiable Physics-informed Graph Networks](https://mlsanity.com/paper/1902.02950/) (2019)
- [HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systems](https://mlsanity.com/paper/1806.07439/) (2018)
- [Physics-Incorporated Convolutional Recurrent Neural Networks for Source Identification and Forecasting of Dynamical Systems](https://mlsanity.com/paper/2004.06243/) (2020)
- [A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data](https://mlsanity.com/paper/2011.14965/) (2020)
- [Learning Localized Spatio-Temporal Models From Streaming Data](https://mlsanity.com/paper/1802.03334/) (2018)

## Abstract (arXiv)

In this paper, we address the problem of predicting complex, nonlinear spatiotemporal dynamics when available data is recorded at irregularly-spaced sparse spatial locations. Most of the existing deep learning models for modeling spatiotemporal dynamics are either designed for data in a regular grid or struggle to uncover the spatial relations from sparse and irregularly-spaced data sites. We propose a deep learning model that learns to predict unknown spatiotemporal dynamics using data from sparsely-distributed data sites. We base our approach on Radial Basis Function (RBF) collocation method which is often used for meshfree solution of partial differential equations (PDEs). The RBF framework allows us to unravel the observed spatiotemporal function and learn the spatial interactions among data sites on the RBF-space. The learned spatial features are then used to compose multilevel transformations of the raw observations and predict its evolution in future time steps. We demonstrate the advantage of our approach using both synthetic and real-world climate data.