Muhammad Omer Bin Saeed

Ali Haider Shah, Naveed R. Butt, Asif Ahmad et al.

This paper presents intersection of Physics informed neural networks (PINNs) and Lie symmetry group to enhance the accuracy and efficiency of solving partial differential equation (PDEs). Various methods have been developed to solve these equations. A Lie group is an efficient method that can lead to exact solutions for the PDEs that possessing Lie Symmetry. Leveraging the concept of infinitesimal generators from Lie symmetry group in a novel manner within PINN leads to significant improvements in solution of PDEs. In this study three distinct cases are discussed, each showing progressive improvements achieved through Lie symmetry modifications and adaptive techniques. State-of-the-art numerical methods are adopted for comparing the progressive PINN models. Numerical experiments demonstrate the key role of Lie symmetry in enhancing PINNs performance, emphasizing the importance of integrating abstract mathematical concepts into deep learning for addressing complex scientific problems adequately.

Muhammad Saqib Sohail, Muhammad Omer Bin Saeed, Syed Zeeshan Rizvi et al.

Particle swam optimization (PSO) is a popular stochastic optimization method that has found wide applications in diverse fields. However, PSO suffers from high computational complexity and slow convergence speed. High computational complexity hinders its use in applications that have limited power resources while slow convergence speed makes it unsuitable for time critical applications. In this paper, we propose two techniques to overcome these limitations. The first technique reduces the computational complexity of PSO while the second technique speeds up its convergence. These techniques can be applied, either separately or in conjunction, to any existing PSO variant. The proposed techniques are robust to the number of dimensions of the optimization problem. Simulation results are presented for the proposed techniques applied to the standard PSO as well as to several PSO variants. The results show that the use of both these techniques in conjunction results in a reduction in the number of computations required as well as faster convergence speed while maintaining an acceptable error performance for time-critical applications.

Muhammad Omer Bin Saeed, Muhammad Saqib Sohail, Syed Zeeshan Rizvi et al.

The particle swarm approach provides a low complexity solution to the optimization problem among various existing heuristic algorithms. Recent advances in the algorithm resulted in improved performance at the cost of increased computational complexity, which is undesirable. Literature shows that the particle swarm optimization algorithm based on comprehensive learning provides the best complexity-performance trade-off. We show how to reduce the complexity of this algorithm further, with a slight but acceptable performance loss. This enhancement allows the application of the algorithm in time critical applications, such as, real-time tracking, equalization etc.