# Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling

arXiv: https://arxiv.org/abs/2210.09081 · HTML: https://mlsanity.com/paper/2210.09081/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 58 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread](https://mlsanity.com/paper/2206.12625/) (2022)
- [Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics](https://mlsanity.com/paper/2110.00293/) (2021)
- [Vaccination and SARS-CoV-2 variants: how much containment is still needed? A quantitative assessment](https://mlsanity.com/paper/2102.08704/) (2021)
- [Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty](https://mlsanity.com/paper/2106.05122/) (2021)

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

- [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 Viscoelastic Parameter Identification in Multiscale Blood Flow Modeling](https://mlsanity.com/paper/2604.06287/) (2026)

## Abstract (arXiv)

With the rapid advance of Machine Learning techniques and the deep increase of availability of scientific data, data-driven approaches have started to become progressively popular across science, causing a fundamental shift in the scientific method after proving to be powerful tools with a direct impact in many areas of society. Nevertheless, when attempting to analyze dynamics of complex multiscale systems, the usage of standard Deep Neural Networks (DNNs) and even standard Physics-Informed Neural Networks (PINNs) may lead to incorrect inferences and predictions, due to the presence of small scales leading to reduced or simplified models in the system that have to be applied consistently during the learning process. In this Chapter, we will address these issues in light of recent results obtained in the development of Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic models with diffusive scaling. Several numerical tests show how APNNs provide considerably better results with respect to the different scales of the problem when compared with standard DNNs and PINNs, especially when analyzing scenarios in which only little and scattered information is available.