12 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 Fractional-Memory Physics-Informed Neural Network with Fast History Compression for Tempered Fractional Coupled Phase-Field Systems
Shubham Kumar, Himanshu Kumar Dwivedi, Matthias Ehrhardt +1
Tempered time-fractional coupled phase-field (tTFCP) systems are used to model interfacial phenomena involving memory-dependent transport and relaxation mechanisms. Numerical solut…
Structure-Preserving Schemes for a Fractional SVIR Epidemic Model with a Hybrid Mittag-Leffler-Caputo-Fabrizio Operator
Seham M. Al-Mekhlafi, Ahmed Boudaoui, Matthias Ehrhardt
This paper proposes and analyzes a fractional-order SVIR epidemic model based on a hybrid Mittag-Leffler-Caputo-Fabrizio (MLCF) fractional operator with a nonsingular kernel. This…
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 Generalized Hacker Dynamics Model with Nonlinear Incidence: Analysis and Positivity-Preserving Numerical Simulation
Manh Tuan Hoang, Hoai Thu Pham, Matthias Ehrhardt
We propose and analyze a generalized compartment model for hacker dynamics in cybersecurity systems. This model is an extension of a recently introduced framework, replacing the bi…