# SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemics

arXiv: https://arxiv.org/abs/2211.08277 · HTML: https://mlsanity.com/paper/2211.08277/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 11 Nov 2022.

## Builds on (most cited first, 20 of 20)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [The Random Feature Model for Input-Output Maps between Banach Spaces](https://mlsanity.com/paper/2005.10224/) (2020)
- [Implicit Regularization of Random Feature Models](https://mlsanity.com/paper/2002.08404/) (2020)
- [Extracting Sparse High-Dimensional Dynamics from Limited Data](https://mlsanity.com/paper/1707.08528/) (2017)
- [A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics](https://mlsanity.com/paper/1904.04326/) (2019)
- [Learning Dynamical Systems from Partial Observations](https://mlsanity.com/paper/1902.11136/) (2019)
- [Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach](https://mlsanity.com/paper/2105.04869/) (2021)
- [Generalization Bounds for Sparse Random Feature Expansions](https://mlsanity.com/paper/2103.03191/) (2021)
- [Exact Gap between Generalization Error and Uniform Convergence in Random Feature Models](https://mlsanity.com/paper/2103.04554/) (2021)
- [HARFE: Hard-Ridge Random Feature Expansion](https://mlsanity.com/paper/2202.02877/) (2022)
- [SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruning](https://mlsanity.com/paper/2112.04002/) (2021)
- [SRMD: Sparse Random Mode Decomposition](https://mlsanity.com/paper/2204.06108/) (2022)
- [Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators](https://mlsanity.com/paper/2203.06269/) (2022)

## Built on by (most cited first, 4 of 4)

- [Dispersion based Recurrent Neural Network Model for Methane Monitoring in Albertan Tailings Ponds](https://mlsanity.com/paper/2411.06741/) (2024)
- [Generalization Bound for Diffusion Models using Random Features](https://mlsanity.com/paper/2310.04417/) (2023)
- [Learning Coupled System Dynamics under Incomplete Physical Constraints and Missing Data](https://mlsanity.com/paper/2512.23761/) (2025)
- [Simulation-based Methods for Optimal Sampling Design in Systems Biology](https://mlsanity.com/paper/2511.07197/) (2025)

## Abstract (arXiv)

Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify the population into compartments according to health status and model the dynamics of these compartments using dynamical systems. However, these predefined systems may not capture the true dynamics of the epidemic due to the complexity of the disease transmission and human interactions. In order to overcome this drawback, we propose Sparsity and Delay Embedding based Forecasting (SPADE4) for predicting epidemics. SPADE4 predicts the future trajectory of an observable variable without the knowledge of the other variables or the underlying system. We use random features model with sparse regression to handle the data scarcity issue and employ Takens' delay embedding theorem to capture the nature of the underlying system from the observed variable. We show that our approach outperforms compartmental models when applied to both simulated and real data.