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

A new framework for solving nonlinear partial differential equations (PDEs) has been proposed, integrating perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). This method decomposes nonlinear PDEs into linear subproblems, which are solved using a Multi-Head PINN. The approach allows for quick adaptation to new PDE instances with varying conditions, achieving errors around 1e-3 and adaptation times under 0.2 seconds, demonstrating comparable accuracy to classical solvers.

Neuro-Spectral Architectures (NeuSA) have been introduced as a new class of Physics-Informed Neural Networks (PINNs) aimed at solving complex partial differential equations (PDEs). Traditional MLP-based PINNs often struggle with convergence in intricate initial value problems, leading to solutions that can violate causality. NeuSA addresses these challenges by learning a projection of the underlying PDE onto a spectral basis, thus improving convergence and enforcing causality through its integration with Neural ODEs.