arXiv subjects

Youssef Mesri

Publications and source records attributed to Youssef Mesri.

6 recordsLinked to original sources

arXiv2026

Compositional Neural Operators for Multi-Dimensional Fluid Dynamics

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim to provide universal surrogates, typical encoding-decoding approaches suffer from high pretraining costs and limited interpretability. In this paper, we propose Compositional Neural Operators (CompNO) for 2D systems, a framework that decomposes complex PDEs into a library of Foundation Blocks. Each block is a specialized Neural Operator pretrained on elementary physics. This modular library contains convection, diffusion, and nonlinear convection blocks as well as a Poisson Solver, enabling the framework to address the pressure-velocity coupling. These experts are assembled via an Adaptation Block featuring an Aggregator. This aggregator learns nonlinear interactions by minimizing data loss and physics-based residuals driven from governing equations. The proposed approach has been evaluated on the Convection-Diffusion equation, the Burgers' equation, and the Incompressible Navier-Stokes equation. Our results demonstrate that learning from elementary operators significantly improves adaptability, enhances model interpretability and facilitates the reuse of pretrained blocks when adapting to new physical systems.

cs.LG↗

arXiv2026

CompNO: A Novel Foundation Model approach for solving Partial Differential Equations

Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent Scientific Foundation Models (SFMs) aim to alleviate this cost by learning universal surrogates from large collections of simulated systems, yet they typically rely on monolithic architectures with limited interpretability and high pretraining expense. In this work we introduce Compositional Neural Operators (CompNO), a compositional neural operator framework for parametric PDEs. Instead of pretraining a single large model on heterogeneous data, CompNO first learns a library of Foundation Blocks, where each block is a parametric Fourier neural operator specialized to a fundamental differential operator (e.g. convection, diffusion, nonlinear convection). These blocks are then assembled, via lightweight Adaptation Blocks, into task-specific solvers that approximate the temporal evolution operator for target PDEs. A dedicated boundary-condition operator further enforces Dirichlet constraints exactly at inference time. We validate CompNO on one-dimensional convection, diffusion, convection--diffusion and Burgers' equations from the PDEBench suite. The proposed framework achieves lower relative L2 error than strong baselines (PFNO, PDEFormer and in-context learning based models) on linear parametric systems, while remaining competitive on nonlinear Burgers' flows. The model maintains exact boundary satisfaction with zero loss at domain boundaries, and exhibits robust generalization across a broad range of Peclet and Reynolds numbers. These results demonstrate that compositional neural operators provide a scalable and physically interpretable pathway towards foundation models for PDEs.

cs.LG↗

arXiv2025

InfinityEBSD : Metrics-Guided Infinite-Size EBSD Map Generation With Diffusion Models

Materials performance is deeply linked to their microstructures, which govern key properties such as strength, durability, and fatigue resistance. EBSD is a major technique for characterizing these microstructures, but acquiring large and statistically representative EBSD maps remains slow, costly, and often limited to small regions. In this work, we introduce InfinityEBSD, a diffusion-based method for generating monophase realistic EBSD maps of arbitrary size, conditioned on physically meaningful microstructural metrics. This approach supports two primary use cases: extending small experimental EBSD maps to arbitrary sizes, and generating entirely new maps directly from statistical descriptors, without any input map. Conditioning is achieved through eight microstructural descriptors, including grain size, grain perimeter, grain inertia ratio, coordination number and disorientation angle distribution, allowing the model to generate maps that are both visually realistic and physically interpretable. A patch-wise geometric extension strategy ensures spatial continuity across grains, enabling the model to produce large-scale EBSD maps while maintaining coherent grain boundaries and orientation transitions. The generated maps can also be exported as valid Channel Text Files (CTF) for immediate post-processing and analysis in software such as MTEX or simulation environments like DIGIMU. We quantitatively validate our results by comparing distributions of the guiding metrics before and after generation, showing that the model respects the statistical targets while introducing morphological diversity. InfinityEBSD demonstrates that diffusion models, guided by physical metrics, can bridge the gap between synthetic and realistic materials representation, paving the way for future developments such as 3D realistic microstructure generation from 2D data.

cond-mat.mtrl-sci↗

arXiv2025

Benchmark-based Study of CPU/GPU Power-Related Features through JAX and TensorFlow

Power management has become a crucial focus in the modern computing landscape, considering that {\em energy} is increasingly recognized as a critical resource. This increased the importance of all topics related to {\em energy-aware computing}. This paper presents an experimental study of three prevalent power management techniques that are {\em power limitation, frequency limitation}, and {\em ACPI/P-State governor modes} (OS states related to power consumption). Through a benchmark approach with a set of six computing kernels, we investigate {\em power/performance} trade-off with various hardware units and software frameworks (mainly TensorFlow and JAX). Our experimental results show that {\em frequency limitation} is the most effective technique to improve {\em Energy-Delay Product (EDP)}, which is a convolution of energy and running time. We also observe that running at the highest frequency compared to a reduced one could lead to a reduction of factor $\frac{1}{10}$ in EDP. Another noticeable fact is that frequency management shows a consistent behavior with different CPUs, whereas opposite effects sometimes occur between TensorFlow (TF) and JAX with the same power management settings.

cs.PF↗

arXiv2023

Identification of vortex in unstructured mesh with graph neural networks

Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD configuration for corresponding flow characteristics. Convolutional Neural Network (CNN) is one of the most popular algorithms used to extract and identify flow features. However its use, without any additional flow field interpolation, is limited to the simple domain geometry and regular meshes which limits its application to real industrial cases where complex geometry and irregular meshes are usually used. Aiming at the aforementioned problems, we present a Graph Neural Network (GNN) based model with U-Net architecture to identify the vortex in CFD results on unstructured meshes. The graph generation and graph hierarchy construction using algebraic multigrid method from CFD meshes are introduced. A vortex auto-labeling method is proposed to label vortex regions in 2D CFD meshes. We precise our approach by firstly optimizing the input set on CNNs, then benchmarking current GNN kernels against CNN model and evaluating the performances of GNN kernels in terms of classification accuracy, training efficiency and identified vortex morphology. Finally, we demonstrate the adaptability of our approach to unstructured meshes and generality to unseen cases with different turbulence models at different Reynolds numbers.

physics.flu-dyn↗

arXiv2023

Energy Concerns with HPC Systems and Applications

For various reasons including those related to climate changes, {\em energy} has become a critical concern in all relevant activities and technical designs. For the specific case of computer activities, the problem is exacerbated with the emergence and pervasiveness of the so called {\em intelligent devices}. From the application side, we point out the special topic of {\em Artificial Intelligence}, who clearly needs an efficient computing support in order to succeed in its purpose of being a {\em ubiquitous assistant}. There are mainly two contexts where {\em energy} is one of the top priority concerns: {\em embedded computing} and {\em supercomputing}. For the former, power consumption is critical because the amount of energy that is available for the devices is limited. For the latter, the heat dissipated is a serious source of failure and the financial cost related to energy is likely to be a significant part of the maintenance budget. On a single computer, the problem is commonly considered through the electrical power consumption. This paper, written in the form of a survey, we depict the landscape of energy concerns in computer activities, both from the hardware and the software standpoints.

cs.CY↗