# A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Applications to COVID-19

arXiv: https://arxiv.org/abs/2208.01169 · HTML: https://mlsanity.com/paper/2208.01169/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 70 references that are in the map.
- First posted on arXiv 1 Aug 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Combining Graph Neural Networks and Spatio-temporal Disease Models to Predict COVID-19 Cases in Germany](https://mlsanity.com/paper/2101.00661/) (2021)
- [Towards the Use of Neural Networks for Influenza Prediction at Multiple Spatial Resolutions](https://mlsanity.com/paper/1911.02673/) (2019)
- [SIAN: software for structural identifiability analysis of ODE models](https://mlsanity.com/paper/1812.10180/) (2018)
- [Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update](https://mlsanity.com/paper/2004.11342/) (2020)
- [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)
- [Analysis of the Spatio-temporal Dynamics of COVID-19 in Massachusetts via Spectral Graph Wavelet Theory](https://mlsanity.com/paper/2208.01749/) (2022)

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

- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs](https://mlsanity.com/paper/2407.12598/) (2024)
- [Analysis of a mathematical model for malaria using data-driven approach](https://mlsanity.com/paper/2409.00795/) (2024)

## Abstract (arXiv)

A variety of approaches using compartmental models have been used to study the COVID-19 pandemic and the usage of machine learning methods with these models has had particularly notable success. We present here an approach toward analyzing accessible data on Covid-19's U.S. development using a variation of the "Physics Informed Neural Networks" (PINN) which is capable of using the knowledge of the model to aid learning. We illustrate the challenges of using the standard PINN approach, then how with appropriate and novel modifications to the loss function the network can perform well even in our case of incomplete information. Aspects of identifiability of the model parameters are also assessed, as well as methods of denoising available data using a wavelet transform. Finally, we discuss the capability of the neural network methodology to work with models of varying parameter values, as well as a concrete application in estimating how effectively cases are being tested for in a population, providing a ranking of U.S. states by means of their respective testing.