# Physics-informed deep learning for infectious disease forecasting

arXiv: https://arxiv.org/abs/2501.09298 · HTML: https://mlsanity.com/paper/2501.09298/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 68 references that are in the map.
- First posted on arXiv 16 Jan 2025.

## Builds on (most cited first, 16 of 16)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks](https://mlsanity.com/paper/1701.05923/) (2017)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [A physics-informed operator regression framework for extracting data-driven continuum models](https://mlsanity.com/paper/2009.11992/) (2020)
- [Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems](https://mlsanity.com/paper/2205.08304/) (2022)
- [NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators](https://mlsanity.com/paper/2208.11866/) (2022)
- [Correcting model misspecification in physics-informed neural networks (PINNs)](https://mlsanity.com/paper/2310.10776/) (2023)
- [L-HYDRA: Multi-Head Physics-Informed Neural Networks](https://mlsanity.com/paper/2301.02152/) (2023)
- [Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators](https://mlsanity.com/paper/2311.11262/) (2023)
- [Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression](https://mlsanity.com/paper/2307.08107/) (2023)
- [EINNs: Epidemiologically-informed Neural Networks](https://mlsanity.com/paper/2202.10446/) (2022)
- [AOSLO-net: A deep learning-based method for automatic segmentation of retinal microaneurysms from adaptive optics scanning laser ophthalmoscope images](https://mlsanity.com/paper/2106.02800/) (2021)
- [Physics-informed machine learning for the COVID-19 pandemic: Adherence to social distancing and short-term predictions for eight countries](https://mlsanity.com/paper/2008.08162/) (2020)

## Built on by (most cited first, 2 of 2)

- [Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble](https://mlsanity.com/paper/2503.06320/) (2025)
- [Epidemic-guided deep learning for spatiotemporal forecasting of Tuberculosis outbreak](https://mlsanity.com/paper/2502.10786/) (2025)

## Abstract (arXiv)

Accurate forecasting of contagious diseases is critical for public health policymaking and pandemic preparedness. We propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging scientific machine learning approach. By embedding a compartmental model into the loss function, our method integrates epidemiological theory with data, helping to prevent model overfitting. We further enhance the model with a sub-network that accounts for covariates such as mobility and cumulative vaccine doses, which influence the transmission rate. Using state-level COVID-19 data from California, we demonstrate that the PINN model accurately predicts cases, deaths, and hospitalizations, aligning well with existing benchmarks. Notably, the PINN model outperforms naive baseline forecasts and several sequence deep learning models, including Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRUs), and Transformers. It also achieves performance comparable to a sophisticated Gaussian infection state forecasting model that combines compartmental dynamics, a data observation model, and parameter regression. However, the PINN model features a simpler structure and is easier to implement. In summary, we systematically evaluate the PINN model's ability to forecast infectious disease dynamics, demonstrating its potential as an efficient computational tool to strengthen forecasting capabilities.