A. Zinihi

Applied Mathematics · Ph.D.

Achraf Zinihi

Doctor of Philosophy in Applied Mathematics

Mathematical Modeling, Numerical Analysis and Scientific Machine Learning for Linear/Nonlinear Dynamical Systems.

MAIS Laboratory · AMNEA Team
Faculty of Sciences and Techniques of Errachidia (FSTE),
Moulay Ismail University of Meknes (UMI), Morocco

AZ
17journal articles
9journals refereed
8talks & seminars
4countries of research mobility

About

Dr. Achraf ZINIHI is an applied mathematician whose research lies at the intersection of mathematical modeling, numerical analysis, scientific computing, and scientific machine learning for nonlinear dynamical systems.

He received his Ph.D. in Applied Mathematics from the Faculty of Sciences and Techniques of Errachidia (FSTE), Moulay Ismail University of Meknes (UMI), Morocco, where he was a member of the Mathematics, Computer Science and Applications Doctoral Program (Mathématiques, Informatique et Applications) and the MAIS Laboratory (Mathématiques Appliquées et Informatiques des Systèmes), within the AMNEA research team (Analyse Mathématique et Numérique des EDPs et Applications).

He obtained his Master of Science in Applied Mathematics from FSTE-UMI in 2022. His master's research focused on optimal control and reaction-diffusion epidemic models involving fractional differential equations, laying the foundation for his doctoral research in mathematical modeling and computational methods for complex dynamical systems.

His research combines rigorous mathematical analysis with the development of advanced computational methods for ordinary, partial, stochastic, and fractional differential equations. His work spans structure-preserving numerical methods, optimal control, inverse problems, reaction-diffusion systems, and modern data-driven techniques including Physics-Informed Neural Networks (PINNs), Neural Ordinary Differential Equations (Neural ODEs), and Koopman operator-based learning. He is particularly interested in designing computational algorithms that preserve the underlying mathematical properties of dynamical systems while enabling efficient simulation, parameter estimation, forecasting, and predictive modeling.

Dr. ZINIHI has authored numerous publications in international peer-reviewed journals and has participated in several international research collaborations and mobility programs in France, Germany, Portugal, and Turkey. He has also served as a reviewer for leading journals in applied mathematics, numerical analysis, and scientific computing, and has taught undergraduate and graduate courses in applied mathematics, numerical analysis, image processing, and fractional differential equations.

In recognition of his academic achievements, he has received several competitive awards and fellowships, including the National Centre for Scientific and Technical Research (CNRST) PhD Associate Scholarship (PASS), French Government Scholarships for research mobility, and the European Mathematical Society Committee for Developing Countries (EMS CDC) Grant.

Research Interests

Nonstandard finite difference (NSFD) schemes, PINNs, Neural ODEs and Koopman operator-based learning for simulation, parameter estimation and prediction, with applications to epidemiological, biological and physical systems.

Differential equations

Ordinary (ODEs), partial (PDEs), stochastic (SDEs) and fractional (FDEs) differential equations; reaction–diffusion systems; $p$-Laplacian models.

Numerical methods

Structure-preserving NSFD schemes, simulation, parameter estimation, forecasting.

Control & inverse problems

Optimal control theory, necessary optimality conditions, epidemic control strategies.

Scientific machine learning

Physics-Informed Neural Networks (PINNs), Neural ODEs, Koopman operator-based learning.

Dynamics in Motion

Linear ODEs

Phase portrait: trajectories spiralling into an equilibrium.

Nonlinear ODEs

SIR epidemic: susceptible (S), infected (I) and recovered (R).

Linear PDEs

Heat diffusion smoothing an initial profile.

Nonlinear PDEs

Reaction–diffusion front with $p$-Laplacian diffusion.

SDEs

Sample paths scattering around the deterministic mean.

FDEs

Caputo relaxation with memory, for α = 1, 0.8, 0.6, 0.4.

Mixed Reaction–Diffusion Systems

Pattern formation in a coupled PDE system.

Optimal Control

Infection peak with and without a control strategy.

PINNs

Schematic: a network converging to the solution of an ODE.

Koopman Operator

Nonlinear dynamics become linear in Koopman coordinates: straight lines on a log scale.

Neural ODEs

Illustration: points transported by a continuous learned flow.

Parameter Inference

SciML: the model fit converges to noisy epidemic data.

Publications

Publications in Motion

Output per Year

Papers, chapters, preprints and talks per year, colored by type.

Collaboration Network

Co-authors around the author; node size grows with joint papers.

Research Keywords

Core methods and application areas of the research.

Education

  1. Ph.D. in Applied Mathematics

    FSTE, UMI, Morocco. MAIS Laboratory, AMNEA group.

    Thesis: “Optimal Control and Neural Networks Applied to Epidemics: Theoretical Analysis and Numerical Simulations.”

    MATLABLaTeXPython

    Thesis jury
    • Prof. Dr. Moha HAJARFSTE, UMI, Errachidia, MoroccoChairman
    • Prof. Dr. Martin BOHNERMissouri S&T, Missouri, USARapporteur
    • Prof. Dr. Mouhcine TILIOUAFSTE, UMI, Errachidia, MoroccoRapporteur
    • Prof. Dr. Ahmed YOUSSFIENSAF, USMBA, Fez, MoroccoRapporteur
    • Prof. Dr. M. A. AZIZ-ALAOUIFST, ULHN, Le Havre, FranceExaminer
    • Prof. Dr. Khalil BEN HADDOUCHENSAF, USMBA, Fez, MoroccoExaminer
    • Prof. Dr. Matthias EHRHARDTSMNS, BUW, Wuppertal, GermanyInvited Guest
    • Prof. Dr. Moulay Rchid SIDI AMMIFSTE, UMI, Errachidia, MoroccoSupervisor

  2. M.Sc.T. in Mathematical Analysis and Applications

    FSTE, UMI.

    MATLABLaTeXPython

  3. B.Sc.T. in Applied Mathematics, Numerical Analysis

    FSTE, UMI.

    MATLABLaTeXC/C++

  4. Diploma of Scientific and Technical University Studies (DEUST) · Mathematics, Informatics, Physics (MIP)

    FSTE, UMI.

  5. Baccalaureate in Mathematical Sciences A

    High School Mohamed V, Tan-Tan, Morocco.

Teaching & Supervision

Mobilities & Visits

  1. Le Havre Normandie University, France

    Doctoral mobility, Laboratory of Applied Mathematics (LMAH, FR-CNRS-3335).

  2. University of Wuppertal, Germany

    Two-month research stay, School of Mathematics and Natural Sciences.

  3. University of Aveiro, Portugal

    International Workshop on Optimization, Dynamics and Convex Analysis (WODCA'2025). Talk on necessary optimality conditions for a Caputo-fractional reaction–diffusion SIR model with the $p$-Laplacian operator.

  4. Le Havre Normandie University, France

    Doctoral mobility, LMAH.

  5. Çanakkale, Turkey

    International Communication in the New World Congress (ICNWC'24). Talk on multi-city epidemic modeling with population migration using neural network–based approaches.

Professional Activities

Peer Review

Organizing Committees

Honors, Awards, Grants & Scholarships

  1. PhD-ASsociate Scholarship (PASS)

    Excellence scholarship of the National Centre for Scientific and Technical Research (CNRST), Morocco.

  2. French Government Scholarship (BGF)

    Research stay at Le Havre Normandie, funded by the Embassy of France and the French Institute of Morocco with CNRST.

  3. Mobility grant, University of Wuppertal

    Covering accommodation, travel and local transport.

  4. European Mathematical Society Committee for Developing Countries (EMS CDC) Grant

    To attend the International Workshop on Optimization, Dynamics and Convex Analysis (WODCA'2025), Aveiro, Portugal.

  5. Delfim F. M. Torres Award

    Best PhD student presentation at the International Meeting on Applied Mathematics in Errachidia (IMAME'2025).

  6. French Government Scholarship (BGF)

    Research stay at Le Havre Normandie.

  7. Higher Education Scholarship

    National Office of Academic, Social and Cultural Works (ONOUSC), Morocco.

  8. Valedictorian Grant

    Students Reward Programme, MSc major, FSTE.

Contact & Links

a.zinihi@edu.umi.ac.ma achrafzinihi99@gmail.com

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