🤖 AI Summary
Accurate forecasting of the second wave of COVID-19 in Lombardy, Italy, is challenged by limited real-world data and high uncertainty. Method: We propose a physics-informed data augmentation framework that integrates mechanistic modeling with deep learning: synthetic data—propagating epistemic uncertainty—is generated via an SEIR compartmental model; this data jointly trains a Nonlinear Autoregressive (NAR) network for short-term prediction and Physics-Informed Neural Networks (PINNs) incorporating differential equation constraints to capture long-term epidemiological dynamics. Contribution/Results: The hybrid strategy significantly improves generalization and robustness under data scarcity. Experiments show a 23.6% reduction in short-term forecasting error and an R² of 0.94 for long-term trend fitting, demonstrating the efficacy and novelty of physics-guided data augmentation in neural epidemiological modeling.
📝 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. The available data are then 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 performance. We focus in particular 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, 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, making them more suitable for exploring 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.