Augmented data and neural networks for robust epidemic forecasting: Application to COVID-19 in Italy

Giacomo Dimarco; Federica Ferrarese; Lorenzo Pareschi; Giacomo Dimarco; Federica Ferrarese; Lorenzo Pareschi

doi:10.3934/mbe.2026019

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 2: 474-498. doi: 10.3934/mbe.2026019

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Augmented data and neural networks for robust epidemic forecasting: Application to COVID-19 in Italy

1.
Department of Mathematics and Computer Science & Center for Modeling, Computing and Statistics (CMCS), University of Ferrara, via Machiavelli 30, 44121 Ferrara, Italy
2.
Maxwell Institute and Department of Mathematics School of Mathematical and Computer Sciences Heriot-Watt University, Edinburgh, UK

Received: 10 October 2025 Revised: 11 November 2025 Accepted: 14 November 2025 Published: 09 January 2026

In this work, we propose a data augmentation strategy aimed at improving the training phase of neural networks and, consequently, the accuracy of their predictions. Our approach relies on generating synthetic data through a suitable compartmental model combined with the incorporation of uncertainty. Available data are used to calibrate the model, which is further integrated with deep learning techniques to produce additional synthetic data for training. The results show that neural networks trained on these augmented datasets exhibit significantly improved predictive performances. In particular, we focus on two different neural network architectures: Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models. The NAR approach proves especially effective for short-term forecasting, thereby providing accurate quantitative estimates by directly learning the dynamics from data and avoiding the additional computational cost of embedding physical constraints into the training. In contrast, PINNs yield less accurate quantitative predictions but capture the qualitative long-term behavior of the system, thus making them more suitable to explore broader dynamical trends. Numerical simulations of the second phase of the COVID-19 pandemic in the Lombardy region (Italy) validate the effectiveness of the proposed approach.
- mathematical epidemiology,
- physics-informed neural networks,
- non-linear autoregressive deep learning,
- COVID-19 data
Citation: Giacomo Dimarco, Federica Ferrarese, Lorenzo Pareschi. Augmented data and neural networks for robust epidemic forecasting: Application to COVID-19 in Italy[J]. Mathematical Biosciences and Engineering, 2026, 23(2): 474-498. doi: 10.3934/mbe.2026019

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Abstract

In this work, we propose a data augmentation strategy aimed at improving the training phase of neural networks and, consequently, the accuracy of their predictions. Our approach relies on generating synthetic data through a suitable compartmental model combined with the incorporation of uncertainty. Available data are used to calibrate the model, which is further integrated with deep learning techniques to produce additional synthetic data for training. The results show that neural networks trained on these augmented datasets exhibit significantly improved predictive performances. In particular, we focus on two different neural network architectures: Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models. The NAR approach proves especially effective for short-term forecasting, thereby providing accurate quantitative estimates by directly learning the dynamics from data and avoiding the additional computational cost of embedding physical constraints into the training. In contrast, PINNs yield less accurate quantitative predictions but capture the qualitative long-term behavior of the system, thus making them more suitable to explore broader dynamical trends. Numerical simulations of the second phase of the COVID-19 pandemic in the Lombardy region (Italy) validate the effectiveness of the proposed approach.

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