Ahmed Ratnani

Mariarosa Mazza, Carla Manni, Ahmed Ratnani et al.

Alfvén-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex application, we focus on a parameter-dependent curl-div problem that can be seen as a prototype of an Alfvén-like operator, and we discretize it using isogeometric analysis based on tensor-product B-splines. The involved coefficient matrices can be very ill-conditioned, so that standard numerical solution methods perform quite poorly here. In order to overcome the difficulties caused by such ill-conditioning, a two-step strategy is proposed. First, we conduct a detailed spectral study of the coefficient matrices, highlighting the critical dependence on the different physical and approximation parameters. Second, we exploit such spectral information to design fast iterative solvers for the corresponding linear systems. For the first goal we apply the theory of (multilevel block) Toeplitz and generalized locally Toeplitz sequences, while for the second we use a combination of multigrid techniques and preconditioned Krylov solvers. Several numerical tests are provided both for the study of the spectral problem and for the solution of the corresponding linear systems.

Alaeddine Zahir, Khalide Jbilou, Ahmed Ratnani

Multi-view clustering has been widely used in recent years in comparison to single-view clustering, for clear reasons, as it offers more insights into the data, which has brought with it some challenges, such as how to combine these views or features. Most of recent work in this field focuses mainly on tensor representation instead of treating the data as simple matrices. This permits to deal with the high-order correlation between the data which the based matrix approach struggles to capture. Accordingly, we will examine and compare these approaches, particularly in two categories, namely graph-based clustering and subspace-based clustering. We will conduct and report experiments of the main clustering methods over a benchmark datasets.

Zakaria El Hasnaoui, Ahmed Ratnani

This paper presents a novel multilevel projection-based stabilization method for advection-dominated advection--diffusion--reaction problems within the framework of Isogeometric Analysis (IGA). The proposed approach extracts and penalizes fine-scale fluctuations using continuous B-spline quasi-interpolants, avoiding both the highly sensitive parameter tuning typical of SUPG methods and the discontinuous auxiliary spaces required by classical Local Projection Stabilization. Stabilization is applied hierarchically across nested levels of the discrete space via explicit mesh-dependent weights. We establish the mathematical soundness of the method by proving a priori error estimates, supplemented by a discrete inf-sup condition established for the one-dimensional setting with constant advection under a numerically validated stability hypothesis that ensures robust streamline derivative control. Numerical experiments on stringent benchmarks demonstrate the method's ability to effectively suppress spurious oscillations across a variety of regimes, including the limiting cases of pure advection and advection--reaction. Notably, despite being a fully linear formulation, the method achieves significant reduction of undershoots near sharp layers, delivering performance comparable to complex nonlinear shock-capturing schemes. Furthermore, by utilizing a robust global parameter scaling, the proposed approach significantly alleviates the parameter sensitivity that typically affects residual-based alternatives, reducing the strong dependence on problem-dependent tuning.

Alaeddine Zahir, Khalide Jbilou, Ahmed Ratnani

This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning as it requires the integration of information from multiple data sources or views to cluster data points accurately. The suggested approach makes use of the structural characteristics of multi-view data tensors, introducing a non-convex tensor norm to identify correlations between these views. In contrast to conventional methods, this approach demonstrates superior clustering accuracy across several benchmark datasets. Despite the non-convex nature of the tensor norm used, the proposed method remains amenable to efficient optimization using existing algorithms. The approach provides a valuable tool for multi-view data analysis and has the potential to enhance our understanding of complex systems in various fields. Further research can explore the application of this method to other types of data and extend it to other machine-learning tasks.

Bernardin Ligan, Khalide Jbilou, Fahd Kalloubi et al.

Foundation models have achieved great success across diverse domains, including remote sensing (RS), thanks to their versatility and strong generalization abilities. However, most RS foundation models are designed for multispectral data, while hyperspectral imagery (HSI) - with its hundreds of spectral bands - remains less explored. Fine-tuning such models for downstream tasks is also challenging, often demanding considerable memory and storage. In this paper, we propose an efficient framework to fine-tune SpectralGPT, a multispectral foundation model, for hyperspectral image classification (HSIC). We explore several Parameter-Efficient Fine-Tuning (PEFT) methods, including Low-Rank Adaptation (LoRA), Kronecker-based adaptation (KronA), Low-Rank Kronecker (LoKr), and the recent LoRA+, which uses distinct learning rates for low-rank adapters scaled by a factor lambda. Inspired by LoRA+, we introduce KronA+, which applies a similar mechanism to the Kronecker matrices. We evaluate our approach on five datasets from different sensors, showing competitive performance with state-of-the-art HSI models. Our full fine-tuning (FFT) setup for SpectralGPT even outperforms a dedicated hyperspectral foundation model on some datasets while requiring only a quarter of the training epochs. Under the same number of epochs, KronA+ reaches similar performance with far fewer trainable parameters - just 0.056 percent - and adds only approximately 0.2 megabytes of storage, making it the most effective PEFT method tested.