Izaz Ur Rahman

1. Energy consumption patterns are important for sustainable economic growth and environmental objectives, particularly in a country that consumes a lot of energy, such as the United States (Kaur e...

Industrial applications involving coupled mass and heat transfer have motivated the present study of steady, two‐dimensional magnetohydrodynamic (MHD) nanofluid flow on a linearly stretching sheet, with viscous dissipation, temperature‐dependent viscosity, chemical reactions, and Soret effects. Traditional numerical solvers remain computationally intensive for extensive parametric analyses of these highly nonlinear multiphysics systems, particularly when fully coupled impacts are considered over stretching surfaces. This study addresses the gap by developing a novel hybrid machine learning framework, a feed‐forward artificial neural network (FFANN) with 10 hidden neurons and log‐sigmoid activation, optimized through the Levenberg–Marquardt backpropagation algorithm (FFANN‐BLMA), trained on high‐fidelity reference data. The governing partial differential equations are reduced to nonlinear ordinary differential equations via similarity transformation and solved accurately using the fourth‐order Runge–Kutta method in Mathematica. The trained model demonstrates exceptional predictive performance, with absolute errors ranging from 10 ⁻⁶ to 10 ⁻⁹ across the dimensionless velocity f ^′ , temperature g , and concentration h profiles for nanoparticle volume fractions ϑ = 0.1, 0.2, and 0.3. Mean squared errors reach the order of 10 ⁻¹² to 10 ⁻¹⁴ , and regression indices approach unity ( R ≈ 1), confirming the robustness and accuracy of the FFANN‐BLMA framework. Parametric experiments indicate that the amplification of ϑ suppresses the velocity profile while thickening the thermal and solutal boundary layers due to augmented effective thermal conductivity in addition to species diffusivity. The suggested FFANN‐BLMA paradigm offers a computationally efficient, precise, and scalable alternative to the traditional numerical solvers that allows rapid design optimization and exploration of parameters in industrial thermal systems, such as electronics cooling, stretch‐coating operations, and energy‐efficient heat exchangers. This article highlights the transformative nature of machine learning in the development of modeling capabilities in applications of complex fluid dynamics and heat transfer.

Systems with memory, hereditary effects, and nonlocal temporal dynamics are naturally described by the fractional partial differential equations (FPDEs). However, the history‐dependent operators in FPDEs pose significant challenges for traditional numerical and physics‐informed methods. This study introduces a Caputo fractional physics‐informed neural network (PINN‐CFA) framework to solve nonlinear time‐fractional Gardner and wound‐healing models. The main mathematical novelty of this work is the explicit use of a full‐memory, Caputo‐consistent Grünwald–Letnikov history operator in the physics‐informed residual. The fractional residual is dependent on all the earlier neural network states; hence, there is no short‐memory truncation in the Caputo operator. This nonlocal temporal convolution is coupled with automatic differentiation of the local spatial derivatives, and the governing equation, initial conditions, and boundary conditions are embedded into a single optimization problem. The applicability is explored for two classes of FPDEs: one‐ and two‐dimensional wound‐healing equations with diffusion and convection terms and the nonlinear dispersive Gardner equation, which features quadratic and cubic nonlinearities and a third‐order spatial derivative. For the integer‐order case, a comparison to the available exact solutions shows good agreement, and a residual evaluation for the fractional orders shows stability of the approximations. Under the same network architectures and training conditions, the proposed GL‐based loss yields lower relative L ₂ errors for the problems studied, smaller, more spatially uniform PDE residuals, and smoother loss convergence than the implemented L1 loss. The GL residuals are less than 10 ⁻² for the fractional Gardner equation over the range of reported final times. Refinement of the temporal history grid from N = 50 to N = 100 decreases the mean squared error by about 40%. The results illustrate that the discretization of the fractional operator is a fundamental part of the PINN residual and can significantly affect the accuracy, optimization performance, and compliance with the governing physical laws. PINN‐CFA then offers a common computational framework for problems in biological transport and nonlinear waves with Caputo fractional dynamics.

This manuscript examines a reformulation‐based benchmarking system to assess the performance of Physics‐Informed Neural Networks (PINNs) to address the coupled system of nonlinear fractional partial differential equations (fPDEs). The proposed method bypasses the incompatibility between automatic differentiation and nonlocal fractional operators by calculating analytically Caputo fractional derivative terms by using known exact solutions and embedding them as modified source terms. The resulting transformation creates the original fPDE system into an equivalent integer‐order formulation (valid specifically for benchmarking problems with known analytical solutions) and permits the standard PINN architectures to be used, without depending on unstable or computationally costly numerical approximations of fractional derivatives. This reformulation purposely takes off the fractional operator of the training loop, serving as a high‐precision benchmarking tool that isolates neural‐network approximation error from fractional‐operator discretization error. The paradigm is tested across three benchmark problems using power‐law, polynomial, and hyperbolic exact solutions with fractional orders ranging from 1.3 to 1.5. Numerical performance is characterized by high predictive accuracy, with mean absolute errors ranging between 10 ⁻³ and 10 ⁻⁴ , and convergent behavior is stable at a training less than 10 ⁻⁴ after 15,000 epochs. The main contribution of this work is not a general‐purpose fPDE solver but a high‐precision validation tool that disconnects the approximation properties of the neural network from the effects of the complexities of the fractional calculus, which determines a predictable performance standard in PINNs on the coupled fractional equations. The paper clearly indicates the limitations of the method, such as its reliance on known analytical solutions, and provides future directions on how to perform generalization through numerical fractional operators or neural approximations. This research provides a fundamental base for the development and verification of the mesh‐free solvers of memory‐dependent problems in areas like viscoelasticity, biophysics, and finance.

Fibromyalgia is a chronic widespread pain disorder affecting individuals of different age groups, sex and socio cultural background. It is estimated to affect 2-5% of western population. Fibromyalgia is a chronic non inflammatory, non-autoimmune central afferent processing disorder leading to a diffuse pain syndrome. The symptoms include widespread pain, fatigue, stiffness and sleep disturbance, cognitive problems and mood disorders (anxiety, depression or both)

Corona Virus Disease 2019 (COVID-19) pandemic has increased the importance of Virtual Learning Environments (VLEs) instigating students to study from their homes. Every day a tremendous amount of data is generated when students interact with VLEs to perform different activities and access learning material. To make the generated data useful, it must be processed and managed by the proper machine learning (ML) algorithm. ML algorithms’ applications are many folds with Education Data Mining (EDM) and Learning Analytics (LA) as their major fields. ML algorithms are commonly used to process raw data to discover hidden patterns and construct a model to make future predictions, such as predicting students’ performance, dropouts, engagement, etc. However, in VLE, it is important to select the right and most applicable ML algorithm to give the best performance results. In this study, we aim to improve those ML and DL algorithms’ performance that give an inferior performance in terms of performance, accuracy, precision, recall, and F1 score. Several ML algorithms were applied on Open University Learning Analytics (OULA) dataset to reveal which one offers the best results in terms of performance, accuracy, precision, recall, and F1 score. Two popular ML algorithms called Decision Tree (DT) and Feed-Forward Neural Network (FFNN) provided unsatisfactory results. They were selected and experimented with various techniques such as grid search cross-validation, adaptive boosting, extreme gradient boosting, early stopping, feature engineering, and dropping inactive neurons to improve their performance scores. Moreover, we also determined the feature weights/importance in predicting the students’ study performance, leading to the design and development of the adaptive learning system. The ML techniques and the methods used in this research study can be used by instructors/administrators to optimize learning content and provide informed guidance to students, thus improving their learning experience and making it exciting and adaptive.

Selective image segmentation is one of the most significant subjects in medical imaging and real-world applications. We present a robust selective segmentation model based on local spatial distance utilizing a dual-level set variational formulation in this study. Our concept tries to partition all objects using a global level set function and the selected item using a different level set function (local). Our model combines the marker distance function, edge detection, local spatial distance, and active contour without edges into one. The new model is robust to noise and gives better performance for images having intensity in-homogeneity (background and foreground). Moreover, we observed that the proposed model captures objects which do not have uniform features. The experimental results show that our model is robust to noise and works better than the other existing models.

Distributed network attacks are referred to, usually, as Distributed Denial of Service (DDoS) attacks. These attacks take advantage of specific limitations that apply to any arrangement asset, such as the framework of the authorized organization’s site. In the existing research study, the author worked on an old KDD dataset. It is necessary to work with the latest dataset to identify the current state of DDoS attacks. This paper, used a machine learning approach for DDoS attack types classification and prediction. For this purpose, used Random Forest and XGBoost classification algorithms. To access the research proposed a complete framework for DDoS attacks prediction. For the proposed work, the UNWS-np-15 dataset was extracted from the GitHub repository and Python was used as a simulator. After applying the machine learning models, we generated a confusion matrix for identification of the model performance. In the first classification, the results showed that both Precision (PR) and Recall (RE) are $\sim 89$ % for the Random Forest algorithm. The average Accuracy (AC) of our proposed model is ~89% which is superb and enough good. In the second classification, the results showed that both Precision (PR) and Recall (RE) are approximately 90% for the XGBoost algorithm. The average Accuracy (AC) of our suggested model is ~90%. By comparing our work to the existing research works, the accuracy of the defect determination was significantly improved which is approximately 85% and 79%, respectively.