# Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread

arXiv: https://arxiv.org/abs/2206.12625 · HTML: https://mlsanity.com/paper/2206.12625/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 25 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks](https://mlsanity.com/paper/1905.01205/) (2019)
- [Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity](https://mlsanity.com/paper/2203.08802/) (2022)
- [A SIDARTHE Model of COVID-19 Epidemic in Italy](https://mlsanity.com/paper/2003.09861/) (2020)
- [Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics](https://mlsanity.com/paper/2110.00293/) (2021)

## Built on by (most cited first, 10 of 10)

- [Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets](https://mlsanity.com/paper/2306.15891/) (2023)
- [Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling](https://mlsanity.com/paper/2210.09081/) (2022)
- [A data augmentation strategy for deep neural networks with application to epidemic modelling](https://mlsanity.com/paper/2502.21033/) (2025)
- [Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations](https://mlsanity.com/paper/2506.10636/) (2025)
- [Augmented data and neural networks for robust epidemic forecasting: application to COVID-19 in Italy](https://mlsanity.com/paper/2510.09192/) (2025)
- [Two-scale Neural Networks for Partial Differential Equations with Small Parameters](https://mlsanity.com/paper/2402.17232/) (2024)
- [A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts](https://mlsanity.com/paper/2410.11545/) (2024)
- [GlueNN: gluing patchwise analytic solutions with neural networks](https://mlsanity.com/paper/2601.05889/) (2026)
- [Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.08742/) (2026)
- [Asymptotic-Preserving Neural Networks for Viscoelastic Parameter Identification in Multiscale Blood Flow Modeling](https://mlsanity.com/paper/2604.06287/) (2026)

## Abstract (arXiv)

When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibration phase, often made even more challenging by the scarcity and uncertainty of the observed data reported by official sources. In this context, Physics-Informed Neural Networks (PINNs), by embedding the knowledge of the differential model that governs the physical phenomenon in the learning process, can effectively address the inverse and forward problem of data-driven learning and solving the corresponding epidemic problem. In many circumstances, however, the spatial propagation of an infectious disease is characterized by movements of individuals at different scales governed by multiscale PDEs. This reflects the heterogeneity of a region or territory in relation to the dynamics within cities and in neighboring zones. In presence of multiple scales, a direct application of PINNs generally leads to poor results due to the multiscale nature of the differential model in the loss function of the neural network. To allow the neural network to operate uniformly with respect to the small scales, it is desirable that the neural network satisfies an Asymptotic-Preservation (AP) property in the learning process. To this end, we consider a new class of AP Neural Networks (APNNs) for multiscale hyperbolic transport models of epidemic spread that, thanks to an appropriate AP formulation of the loss function, is capable to work uniformly at the different scales of the system. A series of numerical tests for different epidemic scenarios confirms the validity of the proposed approach, highlighting the importance of the AP property in the neural network when dealing with multiscale problems especially in presence of sparse and partially observed systems.