Muhammad Ilyas

Jérôme Droniou, Muhammad Ilyas, Bishnu Lamichhane et al.

We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to formulate our saddle point problem and the finite element method. The new formulation allows us to use the $H^1$-conforming Lagrange finite element spaces to approximate the solution. We prove a priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.

Muhammad Ilyas, Bishnu P. Lamichhane

We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal convergence. We use the biorthogonal system for efficient numerical computation and introduce a stabilisation term so that the problem is coercive on the whole space. Numerical examples are presented to verify the algebraic formulation of the problem.

Muhammad Ilyas

Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality. However, they face challenges in scalability and adaptability to real-time problems. In this article, we develop a hybrid approach that combines finite element discretisations with neural network integration to enable efficient and adaptive data-informed predictions. We use a finite element solver for the steady-state diffusion-reaction equation to generate a dataset across varying diffusivity, reaction and inflow conditions. We then build a proper orthogonal decomposition (POD), which reduces dimensionality, and a neural network (NN) that maps parameters to reduced coefficients. A numerical study presented on a simplified model demonstrates the proof-of-concept for predicting nutrient transport and salinity distribution. Numerical experiments show that the NN surrogate achieve a speed-up of approximately 956x compared to a regular FEM solver while maintaining an accuracy of mean relative L2-errors of 15% across the test set, with occasional higher deviations, which is sufficient for rapid scenario screening and parametric studies. These results highlight the method's potential as a fast and accurate surrogate for nutrient and salinity prediction, offering a balance between FEM reliability and NN adaptability for sustainable agromaritime management.

Nazish Ashfaq, Zubair Nawaz, Muhammad Ilyas

For the development of successful share trading strategies, forecasting the course of action of the stock market index is important. Effective prediction of closing stock prices could guarantee investors attractive benefits. Machine learning algorithms have the ability to process and forecast almost reliable closing prices for historical stock patterns. In this article, we intensively studied NASDAQ stock market and targeted to choose the portfolio of ten different companies belongs to different sectors. The objective is to compute opening price of next day stock using historical data. To fulfill this task nine different Machine Learning regressor applied on this data and evaluated using MSE and R2 as performance metric.

Muhammad Ilyas, Hina Rehman, Amine Nait-ali

In 2019, the entire world is facing a situation of health emergency due to a newly emerged coronavirus (COVID-19). Almost 196 countries are affected by covid-19, while USA, Italy, China, Spain, Iran, and France have the maximum active cases of COVID-19. The issues, medical and healthcare departments are facing in delay of detecting the COVID-19. Several artificial intelligence based system are designed for the automatic detection of COVID-19 using chest x-rays. In this article we will discuss the different approaches used for the detection of COVID-19 and the challenges we are facing. It is mandatory to develop an automatic detection system to prevent the transfer of the virus through contact. Several deep learning architecture are deployed for the detection of COVID-19 such as ResNet, Inception, Googlenet etc. All these approaches are detecting the subjects suffering with pneumonia while its hard to decide whether the pneumonia is caused by COVID-19 or due to any other bacterial or fungal attack.