# EINNs: Epidemiologically-informed Neural Networks

arXiv: https://arxiv.org/abs/2202.10446 · HTML: https://mlsanity.com/paper/2202.10446/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 60 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Self-supervised Learning: Generative or Contrastive](https://mlsanity.com/paper/2006.08218/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Incorporating Domain Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2103.00180/) (2021)
- [Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs](https://mlsanity.com/paper/2109.07143/) (2021)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Interpretable Sequence Learning for COVID-19 Forecasting](https://mlsanity.com/paper/2008.00646/) (2020)
- [Inter-Series Attention Model for COVID-19 Forecasting](https://mlsanity.com/paper/2010.13006/) (2020)
- [CAMul: Calibrated and Accurate Multi-view Time-Series Forecasting](https://mlsanity.com/paper/2109.07438/) (2021)
- [When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting](https://mlsanity.com/paper/2106.03904/) (2021)
- [Steering a Historical Disease Forecasting Model Under a Pandemic: Case of Flu and COVID-19](https://mlsanity.com/paper/2009.11407/) (2020)
- [Back2Future: Leveraging Backfill Dynamics for Improving Real-time Predictions in Future](https://mlsanity.com/paper/2106.04420/) (2021)
- [GrADE: A graph based data-driven solver for time-dependent nonlinear partial differential equations](https://mlsanity.com/paper/2108.10639/) (2021)
- [Deep diffusion-based forecasting of COVID-19 by incorporating network-level mobility information](https://mlsanity.com/paper/2111.05199/) (2021)
- [Overcoming Digital Gravity when using AI in Public Health Decisions](https://mlsanity.com/paper/2111.07779/) (2021)

## Built on by (most cited first, 21 of 21)

- [PINNACLE: PINN Adaptive ColLocation and Experimental points selection](https://mlsanity.com/paper/2404.07662/) (2024)
- [Differentiable Agent-based Epidemiology](https://mlsanity.com/paper/2207.09714/) (2022)
- [Performative Time-Series Forecasting](https://mlsanity.com/paper/2310.06077/) (2023)
- [Epidemic-guided deep learning for spatiotemporal forecasting of Tuberculosis outbreak](https://mlsanity.com/paper/2502.10786/) (2025)
- [PEMS: Pre-trained Epidemic Time-series Models](https://mlsanity.com/paper/2311.07841/) (2023)
- [Physics-guided Active Sample Reweighting for Urban Flow Prediction](https://mlsanity.com/paper/2407.13605/) (2024)
- [Pre-training Epidemic Time Series Forecasters with Compartmental Prototypes](https://mlsanity.com/paper/2502.03393/) (2025)
- [Simulation as Supervision: Mechanistic Pretraining for Scientific Discovery](https://mlsanity.com/paper/2507.08977/) (2025)
- [Physics-informed deep learning for infectious disease forecasting](https://mlsanity.com/paper/2501.09298/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [How (Not) to Hybridize Neural and Mechanistic Models for Epidemiological Forecasting](https://mlsanity.com/paper/2602.06323/) (2026)
- [Utilising physics-guided deep learning to overcome data scarcity](https://mlsanity.com/paper/2211.15664/) (2022)
- [SpatialEpiBench: Benchmarking Spatial Information and Epidemic Priors in Forecasting](https://mlsanity.com/paper/2605.06530/) (2026)
- [Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs](https://mlsanity.com/paper/2304.06234/) (2023)
- [Machine Learning for Infectious Disease Risk Prediction: A Survey](https://mlsanity.com/paper/2308.03037/) (2023)
- [Global Prediction of COVID-19 Variant Emergence Using Dynamics-Informed Graph Neural Networks](https://mlsanity.com/paper/2401.03390/) (2024)
- [MP-PINN: A Multi-Phase Physics-Informed Neural Network for Epidemic Forecasting](https://mlsanity.com/paper/2411.06781/) (2024)
- [Epidemiology-informed Graph Neural Network for Heterogeneity-aware Epidemic Forecasting](https://mlsanity.com/paper/2411.17372/) (2024)
- [Developing cholera outbreak forecasting through qualitative dynamics: Insights into Malawi case study](https://mlsanity.com/paper/2503.14009/) (2025)
- [A Physics-Informed Neural Networks-Based Model Predictive Control Framework for SIR Epidemics](https://mlsanity.com/paper/2509.12226/) (2025)
- [TERN: A Delta-rule Memory with a Seasonal Reference and Online Adaptation for Epidemic Forecasting](https://mlsanity.com/paper/2609.18407/) (2026)

## Abstract (arXiv)

We introduce EINNs, a framework crafted for epidemic forecasting that builds upon the theoretical grounds provided by mechanistic models as well as the data-driven expressibility afforded by AI models, and their capabilities to ingest heterogeneous information. Although neural forecasting models have been successful in multiple tasks, predictions well-correlated with epidemic trends and long-term predictions remain open challenges. Epidemiological ODE models contain mechanisms that can guide us in these two tasks; however, they have limited capability of ingesting data sources and modeling composite signals. Thus, we propose to leverage work in physics-informed neural networks to learn latent epidemic dynamics and transfer relevant knowledge to another neural network which ingests multiple data sources and has more appropriate inductive bias. In contrast with previous work, we do not assume the observability of complete dynamics and do not need to numerically solve the ODE equations during training. Our thorough experiments on all US states and HHS regions for COVID-19 and influenza forecasting showcase the clear benefits of our approach in both short-term and long-term forecasting as well as in learning the mechanistic dynamics over other non-trivial alternatives.