10 papers
Structure-Preserving Neural ODEs via Nonstandard Finite Difference Discretization
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
Although neural ordinary differential equations (NODEs) are a powerful framework for learning continuous-time dynamics, they generally do not preserve essential qualitative propert…
A Nonstandard Finite Difference Scheme for a Nonlinear Parabolic Equation with p-Laplacian-Type Diffusion
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We propose and analyze a nonstandard finite difference (NSFD) scheme for nonlinear parabolic equations involving a p-Laplacian-type diffusion operator in one- and two-dimensional s…
A Koopman-PINN Framework for Epidemic Models: Parameter Inference and Forecasting
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We propose a Koopman-enhanced physics-informed neural network (K--PINN) framework for parameter inference and forecasting in nonlinear epidemic models. This method combines Koopman…
Constraint-Aware Physics-Informed Neural Networks for SEIR Reaction-Diffusion Epidemic Models with Vital Dynamics
Achraf Zinihi, Matthias Ehrhardt
Reaction-diffusion epidemic models with vital dynamics are an important framework for describing the spatial and temporal spread of infectious diseases. In this work, we present a…
Identifying Memory Effects in Epidemics via a Fractional SEIRD Model and Physics-Informed Neural Networks
Achraf Zinihi
We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into…
A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious…