Computational Mathematics: ML, PINNs, Stochastic Modeling

Faraz Mukhtiar

Applied Mathematics Statistical Learning Stochastic Modelling

***************@*****.*** Karachi, Pakistan ORCID Google Scholar LinkedIn EDUCATION

MS in Engineering Sciences (Applied Mathematics) 2023–2025 Ghulam Ishaq Khan Institute (GIKI), Topi, Pakistan

• GPA: 3.46/4.00

• Thesis: Statistical Process Control Based on Machine Learning Techniques (see Master’s Thesis below) BS in Mathematics 2018–2022

Quaid-e-Awam University, Nawabshah, Pakistan

• GPA: 3.82/4.00, Distinction (Ranked 3rd in Faculty of Science)

• Thesis: Development of Finite Difference Method for the Estimation of Unsteady Plane Poiseuille Flow for a Newtonian Fluid

RESEARCH INTERESTS

Statistical Learning and Scientific Machine Learning; Statistical Process Monitoring and Anomaly Detection; Se- quential and Time-Series Modelling; Uncertainty Quantification; Physics-Informed Neural Networks and Digital Twins; Applied Probability and Monte Carlo Methods. PEER-REVIEWED JOURNAL PUBLICATIONS

1. Mukhtiar, F., Zaman, B., Butt, N. R., Ajab, M., & Faraz, M. I. (2026). Data-driven control charts for monitoring Gamma-distributed manufacturing processes using machine learning. The International Journal of Advanced Manufacturing Technology. DOI

2. Mukhtiar, F., Zaman, B., & Butt, N. R. (2025). Enhanced process monitoring using machine learning-based control charts for Poisson-distributed data. Engineering Applications of Artificial Intelligence, 157, 111227. DOI

3. Ajab, M., Zaman, B., Mukhtiar, F., Butt, N. R., & Faraz, M. I. (2026). Enhancing statistical process control with machine learning: The Iso-CUSUM control chart for multivariate process. Computers & Industrial Engineering, 212, 111750. DOI

4. Shaheen, A., Zaman, B., Nadir, S., Mukhtiar, F., & Butt, N. R. (2026). Semi-parametric Bayesian physics- informed neural network-based digital twin for dynamical systems. Expert Systems with Applications. Ad- vance online publication. DOI

RESEARCH EXPERIENCE

Member, Interdisciplinary ML Initiative Lab

GIK Institute, Topi, Pakistan Jun 2023–Present

• Contribute to research on physics-informed neural networks and digital twins for dynamical systems, with an emphasis on integrating statistical modelling, physical information, and uncertainty estimation.

• Develop machine-learning-based statistical monitoringmethods for non-Gaussian and multivariate processes, with applications to anomaly and change-point detection.

• Design Monte Carlo simulation studies to evaluate false-alarm rates, detection delay, average run length, and robustness under distribution shifts.

MASTER’S THESIS

Statistical Process Control Based on Machine Learning Techniques 2023–2024 GIK Institute, Topi, Pakistan

• Developed ML-based monitoring methods for stochastic and non-Gaussian processes, integrating classical control-chart theory with predictive models.

• Designed Monte Carlo simulation studies to evaluate monitoring performance under varying distributional as- sumptions and decision thresholds.

MANUSCRIPTS AND PREPRINTS

In Revision

1. Ajab, M., Zaman, B., Mukhtiar, F., et al. A Novel S 2–EWMAM Control Chart for Enhanced Process Dispersion Monitoring Using Möbius Transformation: Application to the Human Development Index. Quality and Reliability Engineering International.

Under Review

1. Mukhtiar, F., Zaman, B., Butt, N. R., & Faraz, M. I. Machine Learning-Based Control Charts for Modelling and Monitoring Binomial Manufacturing Processes. The International Journal of Advanced Manufacturing Tech- nology.

2. Mukhtiar, F., Butt, N. R., & Zaman, B. Machine Learning-Based Control Charts for Industrial Process Monitoring: An Integrated Approach to Anomaly Detection. Engineering Applications of Artificial Intelligence. In Preparation

1. Mukhtiar, F., et al. Process-Informed Neural Networks for Sequential Anomaly Detection. In preparation.

• Embeds Shewhart, EWMA, and CUSUM statistics into a neural-network training objective through process- informed gradient regularization.

Preprint

1. Mukhtiar, F., Zaman, B., & Butt, N. R. (2024). Enhancing process anomaly detection using machine learning- based control charts: A comparative study with classical control charts. SSRN Electronic Journal. https:

//doi.org/10.2139/ssrn.5045114

TECHNICAL SKILLS

• Statistical Methods: Statistical Process Control; Anomaly and Change-Point Detection; Sequential Monitoring; Monte Carlo Simulation; Uncertainty Quantification.

• Machine Learning: scikit-learn, TensorFlow, XGBoost; Predictive Modelling; Statistical Learning.

• Programming and Tools: Python, MATLAB, R (working knowledge), LATEX.

• Mathematical Background: Probability and Statistics; Stochastic Processes; Linear Algebra; Optimization; Nu- merical Analysis; Functional Analysis.

TEACHING EXPERIENCE

Lecturer, Department of Computer Science Oct 2025–Present Al-Kawthar University, Karachi, Pakistan

• Teach undergraduate mathematics courses, including Calculus and Linear Algebra, for computing students. Lecturer, Department of Computer Science Jan 2025–Oct 2025 Salim Habib University, Karachi, Pakistan

• Taught Probability and Statistics, Linear Algebra, and Calculus with Analytical Geometry. Graduate Assistant, Faculty of Engineering Sciences Jan 2023–Dec 2024 GIK Institute, Topi, Pakistan

• Supported instruction in Probability and Statistics, Calculus I–II, and Advanced Linear Algebra. HONORS AND AWARDS

• Fully Funded Scholarship with Graduate Assistantship for MS studies, GIK Institute 2023–2024

• Third Position in the Faculty of Science, BS Mathematics, QUEST

• Vice Chancellor’s Award for securing 2nd Position in Department of Mathematics (up to 4th Semester), QUEST, Nawabshah

PROFESSIONAL ACTIVITIES: INVITED TALKS AND PRESENTATIONS

• Research Experience: Practices, and Insights for Postgraduate Students. 06 Dec 2025 Guest lecture: Faculty of Computing and Engineering Sciences, SZABIST (Gharo Campus)

• Mathematical Foundations of Artificial Intelligence 25 Jul 2025 Invited talk at the Faculty Development Program, Salim Habib Centre of Learning and Teaching, SHU, Karachi, Pakistan.

• Mathematics Behind Deep Learning 09 Aug 2024

Speaker at the 4th Summer School “New Trends in Mathematical Sciences,” University of Swat, Shangla, Pak- istan.

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