Moussa ZIGGAF

Research interests

• Mathematical Modeling

I work on the design and analysis of finite volume and hybrid schemes (e.g., finite volume/finite element), from first-order accurate schemes with improved precision to higher-order methods. I also focus on structure-preserving schemes (e.g., well-balanced and positivity-preserving), discretization of diffusion operators, adaptive mesh refinement, and error estimation.

• Numerical analysis

Analysis of finite volume schemes, development of first-order schemes with improved precision as well as higher-order schemes. Design of numerical schemes that preserve the structure of partial differential equations, the "well-balanced" schemes. Approximation of hyperbolic PDEs and discretization of diffusion operators. Hybrid methods combining finite volume and finite element methods. Mesh refinement and error estimation.

• Scientific Computing and High-Performance Computing (HPC)

I work on the simulation of realistic flow scenarios using large-scale computational resources and parallel codes. This includes the shallow water equations (with equilibrium preservation and comparison to experimental results), multilayer Saint-Venant systems, solid material transport, three-dimensional Euler equations, and compressible Navier–Stokes equations. My work involves the implementation of efficient algorithms for high-performance computing and their optimization for parallel architectures.

• Machine Learning and Neural Networks Applied to PDEs

I develop hybrid approaches combining supervised learning with numerical schemes for conservation laws. This includes adaptive flux selection using classifiers (Random Forest, XGBoost, LightGBM, CatBoost), Physics-Informed Neural Networks (PINNs) for direct and inverse PDE problems, Deep Operator Networks (DeepONets), Fourier Neural Operators (FNOs), and scientific machine learning for model reduction, fast prediction, and reconstruction of physical fields from partial or noisy data.

Topics 

• Numerical methods: finite differences, finite volumes, finite elements, SUPG, OSS, Global Flux, FVC schemes

• Numerical analysis of PDEs and structure-preserving schemes

• Computational fluid dynamics (CFD) and hyperbolic conservation laws

• Coastal wave modeling and pollutant/sediment transport

• Time integration: Euler, TVD RK3, SSPRK, Defect Correction scheme

• Calibration and validation using experimental data

• Hybrid physics-informed/data-driven methods for PDEs

• Adaptive flux selection using classifiers (Random Forest, XGBoost, LightGBM, CatBoost)

• Physics-Informed Neural Networks (PINNs) for direct and inverse PDE problems

• Deep operator learning (DeepONets, Fourier Neural Operators - FNOs)

• Machine learning for model reduction, fast prediction, and field reconstruction from partial/noisy data

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