arXiv subjects

Mohamed Abdelhamid

Publications and source records attributed to Mohamed Abdelhamid.

9 recordsLinked to original sources

arXiv2026

On the Calculation of the Brinkman Penalization Term in Density-Based Topology Optimization of Fluid-Dependent Problems

In topology optimization of fluid-dependent problems, there is a need to interpolate within the design domain between fluid and solid in a continuous fashion. In density-based methods, the concept of inverse permeability as of a volumetric force is utilized to enforce zero fluid velocity in non-fluid regions. This volumetric force consists of a scalar term multiplied by fluid velocity. This scalar term takes a value between two limits as determined by a convex interpolation function. The maximum inverse permeability limit is typically chosen through a trial and error analysis of the initial form of the optimization problem; such that the fields resolved resemble those obtained through an analysis of a pure fluid domain with a body-fitted mesh. In this work, we investigate the dependency of the maximum inverse permeability limit on mesh size and flow conditions through analyzing the Navier-Stokes equation in its strong and discretized finite element forms.

math.NA↗

arXiv2025

What is Reproducibility in Artificial Intelligence and Machine Learning Research?

In the rapidly evolving fields of Artificial Intelligence (AI) and Machine Learning (ML), the reproducibility crisis underscores the urgent need for clear validation methodologies to maintain scientific integrity and encourage advancement. The crisis is compounded by the prevalent confusion over validation terminology. In response to this challenge, we introduce a framework that clarifies the roles and definitions of key validation efforts: repeatability, dependent and independent reproducibility, and direct and conceptual replicability. This structured framework aims to provide AI/ML researchers with the necessary clarity on these essential concepts, facilitating the appropriate design, conduct, and interpretation of validation studies. By articulating the nuances and specific roles of each type of validation study, we aim to enhance the reliability and trustworthiness of research findings and support the community's efforts to address reproducibility challenges effectively.

cs.CY↗

arXiv2024

Balancing the Scales: A Comprehensive Study on Tackling Class Imbalance in Binary Classification

Class imbalance in binary classification tasks remains a significant challenge in machine learning, often resulting in poor performance on minority classes. This study comprehensively evaluates three widely-used strategies for handling class imbalance: Synthetic Minority Over-sampling Technique (SMOTE), Class Weights tuning, and Decision Threshold Calibration. We compare these methods against a baseline scenario of no-intervention across 15 diverse machine learning models and 30 datasets from various domains, conducting a total of 9,000 experiments. Performance was primarily assessed using the F1-score, although our study also tracked results on additional 9 metrics including F2-score, precision, recall, Brier-score, PR-AUC, and AUC. Our results indicate that all three strategies generally outperform the baseline, with Decision Threshold Calibration emerging as the most consistently effective technique. However, we observed substantial variability in the best-performing method across datasets, highlighting the importance of testing multiple approaches for specific problems. This study provides valuable insights for practitioners dealing with imbalanced datasets and emphasizes the need for dataset-specific analysis in evaluating class imbalance handling techniques.

cs.LG↗

arXiv2023

Density-Based Topology Optimization of High-Fidelity Fluid-Structure Interaction Problems with Large Deformations

The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure interactions is still lagging behind, mainly due to the multidisciplinary and complex nature of such systems. In this work, we implement topology optimization of high-fidelity, fully-coupled fluid-structure interaction problems with large deformations. We use the arbitrary Lagrangian-Eulerian approach to deform the fluid mesh as a pseudo-structural system such that structural deformations are completely reflected in the fluid flow mesh. The fluid-structure interaction problem is formulated using the three-field formulation and the sensitivity analysis is derived using the discrete adjoint approach. We show through numerical examples the effect of the projection and interpolation parameters on the convergence and topology of the optimized designs and demonstrate the effect of considering the structural deformations in the fluid mesh.

math.NA↗

arXiv2023

Topology Optimization of Fluid-Structure Interaction Problems with Total Stress Equilibrium

This work extends force coupling in the topology optimization of fluid-structure interaction problems from hydrostatic to total stresses through the inclusion of viscous stress components. The superconvergent patch recovery technique is implemented to remove the discontinuities in velocity derivatives over the finite elements boundaries. The sensitivity analysis is derived analytically for the superconvergent patch recovery approach and further verified through the use of the complex-step derivative approximation method. Numerical examples demonstrate a differentiation in the optimized designs using pressure vs. total stress coupling depending on the flow characteristics of the design problem.

math.NA↗

arXiv2022

Direction-Oriented Stress-Constrained Topology Optimization of Orthotropic Materials

Efficient optimization of topology and raster angle has shown unprecedented enhancements in the mechanical properties of 3D printed materials. Topology optimization helps reduce the waste of raw material in the fabrication of 3D printed parts, thus decreasing production costs associated with manufacturing lighter structures. Fiber orientation plays an important role in increasing the stiffness of a structure. This paper develops and tests a new method for handling stress constraints in topology and fiber orientation optimization of 3D printed orthotropic structures. The stress constraints are coupled with an objective function that maximizes stiffness. This is accomplished by using the modified solid isotropic material with penalization method with the method of moving asymptotes as the mathematical optimizer. Each element has a fictitious density and an angle as the main design variables. To reduce the number of stress constraints and thus the computational cost, a new clustering strategy is employed in which the highest stresses in the principal material coordinates are grouped separately into two clusters using an adjusted $P$-norm. A detailed description of the formulation and sensitivity analysis is discussed. While we present an analysis of 2D structures in the numerical examples section, the method can also be used for 3D structures, as the formulation is generic. Our results show that this method can produce efficient structures suitable for 3D printing while thresholding the stresses.

cs.GR↗

arXiv2022

Revisiting Non-Convexity in Topology Optimization of Compliance Minimization Problems

Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods. Design/Methodology/Approach: Starting from the global optimum of the compliance minimization problem, we employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum, and how the initial guess has some weight in determining the final optimum. Findings: The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application. Originality/Value: In this article, we present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. We put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

math.OC↗

arXiv2021

On Mesh Deformation Techniques for Topology Optimization of Fluid-Structure Interaction Problems

Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based optimization is the most popular approach in topology optimization currently. Hence, it's a necessity to utilize mesh deformation techniques that have continuous, smooth derivatives. In this work, we address mesh deformation techniques for structured, quadrilateral meshes. We discuss and comment on two legacy mesh deformation techniques; namely the spring analogy model and the linear elasticity model. In addition, we propose a new technique based on the Yeoh hyperelasticity model. We focus on mesh quality as a gateway to mesh admissibility. We propose layered selective stiffening such that the elements adjacent to the fluid-structure interface - where the bulk of the mesh distortion occurs - are stiffened in consecutive layers. The legacy and the new models are able to sustain large deformations without deprecating the mesh quality, and the results are enhanced with using layered selective stiffening.

math.NA↗

arXiv2017

Applying the Residue Number System to Network Inference

This work explores the lesser studied objective of optimizing the multiply-and-accumulates executed during evaluation of the network. In particular, we propose using the Residue Number System (RNS) as the internal number representation across all layer evaluations, allowing us to explore usage of the more power-efficient RNS multipliers and adders. Using results from simulation of our RNS arithmetic block implementations, we show theoretical power advantages of using RNS for an end-to-end evaluator.

cs.AR↗