Welcome to the Homepage of Wasif Khan

EXPERIENCES

Virtual University of Islamabad, Peshawar Campus 

•    Since March 11, 2025, Mr. Khan has been serving as an Instructor of Mathematics at the Virtual University of Islamabad, Peshawar Campus. 

University of Engineering and Technology, Peshawar. (Jalozai Campus)

•         Since Feb 17, 2025, Mr. Khan has been serving as an visiting lecturer at the University of Engineering and Technology, Peshawar (Jalozai Campus)

EDUCATION

Master of Philosophy in Mathematics

• Mr. Khan his completed his Master's degree in Mathematics in 2024 at the Abdus Salam School of Mathematical Sciences, Government College University, Lahore, on a fully funded scholarship. His specialization was in Numerical Linear Algebra, with a particular focus on its applications—especially the development of preconditioners for Krylov subspace methods.

• For MS thesis please click here.

Bachelor of Science in Mathematics

• Mr. Khan completed his Bachelor's in Mathematics from the University of Peshawar, Pakistan, during the 2018-2022 session. To see my transcript, click here. 

• In his final year, he wrote a thesis on "Homothetic Vector Field of FRW Space-Time."

RESEARCH INTERESTS

Since August 2023, Mr. Khan has been engaged in his M.Phil. final year project in Numerical Algebra and its Applications, with a particular focus on developing preconditioners for Krylov subspace methods. His work delves into improving the efficiency and accuracy of numerical methods for modeling fluid flow through fractured media. This effort has resulted in the submission of several research papers introducing novel preconditioning techniques.  In parallel with his core research, Mr. Khan has explored the intersection of traditional numerical methods and machine learning. He applied classical numerical techniques and Physics-Informed Neural Networks (PINNs) to solve differential equations. His comparative study, titled "Comparative Analysis of Finite Difference Method (FDM) and Physics-Informed Neural Networks (PINNs)," evaluates the performance of both methods on linear and non-linear models.

PUBLICATIONS

• Ahmad, S., & Khan, W. (2025). Optimizing convergence: GMRES preconditioner for Darcy flow problem in a fracture network. Computational Geosciences, 29(1), 1-15. 

• Khan, W., & Ahmad, S. (2024). COMPARATIVE ANALYSIS OF FINITE DIFFERENCE METHOD (FDM) AND PHYSICS-INFORMED NEURAL NETWORKS (PINNs). I-Manager's Journal on Mathematics, 13(1). 

• Khan, W., & Ahmad, S. (2024). Novel Preconditioners for Unfitted FEM in DarcyFlow for Fractured Medium. (Preprint)

• Mr. Khan was awarded a fully funded scholarship to pursue his Master of Philosophy in Mathematics at the Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan. 

• Since October 22, 2023, Mr. Khan his been serving as a representative of "The Math Volunteers Foundation," an organization dedicated to supporting students in every aspect of mathematics education. 

• Two days international conference on Mathematical Modeling and Scientific Computing for Industrial Research, September 7/8, 2022, at Abdus Salam School of Mathematical Sciences.
  
  

• Two days international workshop on "Lie Symmetry Analysis," December 13/14, 2022, at Abdus Salam School of Mathematical Sciences.
  
  

• Seminar on "Some Mathematical Models in Real Life," January 12, 2023, at Abdus Salam School of Mathematical Sciences.
  
  

• I had attended the "Abdus Salam School of Mathematical Sciences National Mathenasium," March 2023.
  
  

• I took part in a workshop titled "Machine Learning with Mathematical Applications," held at COMSATS University Islamabad, Lahore Campus from March 5th to 6th, 2024.
  
  

• Two days international conference on Recent Trends in Mathematics, June 1/2, 2024, at Abdus Salam School of Mathematical Sciences.

• Delivered a talk entitled "Preconditions for Krylov Subspace Methods" at the Abdus Salam School of Mathematical Sciences weekly seminar on October 17, 2024.

• Delivered an online talk titled "Basic Concepts of Probability" during an online session for the Math Volunteers Foundation.
  
  

• Presentation on solving differential equations using Physics-Informed Neural Networks (PINNs) at Abdus Salam School of Mathematical Sciences, GCU Lahore.
  
  

• Presented the basic concepts of neural networks at Abdus Salam School of Mathematical Sciences, GCU Lahore.
  
  

• At the Abdus Salam School of Mathematical Sciences, attended two compulsory academic talks each week as part of the regular program.