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Dr. Khaliq’s area of expertise is Numerical Analysis and Scientific Computing, with specialization in the “Development of Stable and Efficient Numerical Methods for Large Scale Systems of Partial Differential Equations (PDEs)”. His primary research interest lies at the interface of applied mathematics and computational science. His research includes the development of new and robust algorithms using partial differential equations with applications to complex financial and physical systems. In addition, Dr. Khaliq’s current research interest is the Numerical solutions of Fractional Partial Differential Equations (FPDEs), solving and learning PDEs with deep neural networks, Data driven modeling and simulation of complex PDE systems. Scalable algorithms in the numerical solutions of stiff stochastic differential equations (SDEs). Development and Analysis of algorithms using Quantum Neural Networks.