# Spatio-Temporal Functional Neural Networks

arXiv: https://arxiv.org/abs/2009.05665 · HTML: https://mlsanity.com/paper/2009.05665/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Non-linear Functional Modeling using Neural Networks](https://mlsanity.com/paper/2104.09371/) (2021)
- [Neural Networks for Scalar Input and Functional Output](https://mlsanity.com/paper/2208.05776/) (2022)
- [A Functional approach for Two Way Dimension Reduction in Time Series](https://mlsanity.com/paper/2301.00357/) (2023)

## Abstract (arXiv)

Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance from both the methodology development and real-world application perspectives. Given the observed spatially encoded time series covariates and real-valued response data samples, the goal of spatio-temporal regression is to leverage the temporal and spatial dependencies to build a mapping from covariates to response with minimized prediction error. Prior arts, including the convolutional Long Short-Term Memory (CovLSTM) and variations of the functional linear models, cannot learn the spatio-temporal information in a simple and efficient format for proper model building. In this work, we propose two novel extensions of the Functional Neural Network (FNN), a temporal regression model whose effectiveness and superior performance over alternative sequential models have been proven by many researchers. The effectiveness of the proposed spatio-temporal FNNs in handling varying spatial correlations is demonstrated in comprehensive simulation studies. The proposed models are then deployed to solve a practical and challenging precipitation prediction problem in the meteorology field.