5 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…
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…
Fractional differential equations of a reaction-diffusion SIR model involving the Caputo-fractional time-derivative and a nonlinear diffusion operator
Achraf Zinihi, Moulay Rchid Sidi Ammi, Delfim F. M. Torres
The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and e…