Modeling & Simulation is a rapidly developing field that brings together mathematicians, physicians, computer scientists, and engineers. It combines various topics from basic science, computer science, and engineering that lead to a better understanding and handling of complex phenomena.

 The Master in Modeling and Simulation is an interdisciplinary program designed to provide knowledge and essential skills to deal with real-world applications in a wide range of industries. This program focuses on the following areas: numerical computing, discrete and fast algorithms, modeling and simulation, data science, inverse problems, statistical models, multi-physics, large data analysis, and related applications. With such knowledge and skills, graduates will be capable of working and thinking more dynamically when it comes to solving challenging problems.

The Master Degree in Modeling and Simulation at the Mathematics department within KFUPM opens the door to more attractive employment opportunities in a broad spectrum of industries. 

Admission Requirements

University Requirements:

• A Grade-Point Average (GPA) of 2.5 or higher on a scale of 4.00.
• No GRE or GMAT is required.
• IELTS score of 6+ or TOEFL of 70+ (waived for KFUPM graduates and Graduates from English Speaking Countries)
• At least two letters of recommendation.

 Program Requirements:

• Four-year bachelor's or masters' degree (or equivalent) in Mathematics, Statistics, Computer Science or any related area in Science and Engineering.
• Grades of at least B (or equivalent) in most Mathematics and Statistics courses.
• The admission process goes beyond meeting the minimum requirements. In particular, the list of courses, offered at KFUPM, which are equivalent to the required preparatory undergraduate instruction in calculus, linear algebra, and programming are required to be eligible for admission.

Satisfying the minimum admission requirements does not guarantee admission into the program, as final admission is subject to an evaluation of the entire application, and the personal interview. Based on the assessment of the applicant file and the personal interview, the admission committee might offer conditional acceptance for students who need to take deficiency courses. 

Degree Plan

Two-Year Degree Plan of MX-Modeling and Simulation

Course Description

MATH 557:  Applied Linear Algebra                                                                                                                                         (3-0-3)

Description: Basics concepts from linear algebra and numerical analysis. Direct methods for large, sparse linear systems, Cholesky and LU factorizations. Regularization of ill-conditioned least squares problems. SVD and QR factorizations. Sensitivity and conditioning of linear systems and least square problems. Stationary and non-stationary iterative methods, multigrid methods. Matrix theory including spectral decompositions, and eigenvalue perturbation theory. Eigenvalue and QR algorithm, and computations of SVD. Applications.

Prerequisite: Graduate Standing

MATH 576:  Applied Numerical Methods I                                                                                                                             (3-0-3)

Description: This course introduces implementable numerical methods for solving initial value problems, stability and convergence. One-step, multistep, and Runge-Kutta methods. Shooting and bisection methods. Finite difference methods and applications to equilibrium and non-equilibrium models including steady-state, heat, and wave problems. 

Prerequisite: Graduate Standing

MATH 578: Applied Numerical Methods II                                                                                                                            (3-0-3)

Description: This course introduces finite element, finite difference, and finite volume methods. Applications of these methods to steady-state, diffusion and wave models. Stability and convergence. Homogenization, upscale and multiscale methods. Implementations and computer labs.

Prerequisites: MATH 576

Note: Not to be taken for credit with 572

MATH 585: Computational Inverse Problem                                                                                                                        (3-0-3)

Description: This course introduces students to fundamental concepts in linear and nonlinear inverse problems. Emphasis is placed on describing how to integrate various information sources from measured data and prior knowledge about the inverted model. Subjects studied will include topics and tools such as: Regression, Least squares, Maximum likelihood estimation, Rank deficiency, Ill-conditioning, Generalized and Truncated SVD solutions, regularizations (Tikohonov, spectral filtering), proximal and primal-dual iterative schemes, Nonlinear inverse (gradient-based and global optimization methods), OCCAM method. Computer lab sessions will be organized to combine classroom learning with hands-on applications.

Prerequisites: MATH 557

Note: Not to be taken for credit with Math 485

MATH 619: Project                                                                                                                                                                        (0-0-6)

Description: A graduate student will arrange with a faculty member to conduct an industrial research project related to program field. Subsequently the students shall acquire skills and gain experiences in developing and running actual industry-based project. This project culminates in the writing of a technical report, and an oral technical presentation in front of a board of professors and industry experts.

Prerequisites: Graduate standing

COE 588: Modeling and Simulation                                                                                                                                           (3-0-3)

Description: Approaches to the simulation problem (event scheduling, process-based, etc.). Modeling and simulation of queuing systems. Probability, stochastic processes, and statistics in simulation. Random number generation. Monte Carlo methods. Building valid and credible simulation models. Output data analysis. Simulation formalisms. Software techniques for building simulators. Using contemporary tools like Matlab and SimEvents. Case studies in science and engineering.

Prerequisite: Graduate Standing

ICS 502: Machine Learning                                                                                                                                                         (3-0-3)

Description: Introduction to machine learning; supervised learning (linear regression, logistic regression, classification, support vector machines, kernel methods, decision tree, Bayesian methods, ensemble learning, neural networks); unsupervised learning (clustering, EM, mixture models, kernel methods, dimensionality reduction); learning theory (bias/variance tradeoffs); and reinforcement learning and adaptive control.

Prerequisite: Graduate Standing.

Note: Not to be taken for credit with ICS 485

ICS 574: Big Data Analytics                                                                                                                                                         (3-0-3)

Description: Introduction and foundation of big data and big-data analytics. Sources of big data. Smart clouds. Hadoop file system and Apache Spark. Storage management for big data. Machine learning and visualization with big data. Applications of big data. Big data and security, privacy, societal impacts.

Prerequisite: Graduate Standing

Note: Not to be taken for credit with ICS 474

PETE 547: Computational Multiphysics Modeling                                                                                                                (3-0-3)

Description: Multiphysics is essential for many applications, it involves the analysis of multiple, simultaneous physical phenomena. This course exposes students to advanced concepts involving Multiphysics modeling. While concentrating more on Multiphysics modeling in fluid flow and heat transfer, Multiphysics modeling in other areas such as solid mechanics and electromagnetics will be covered as well. The course introduces the students to the derivations of the fundamental equations used in the various areas of modeling, detailing how and why the physical processes are coupled and briefly mentioning the approaches to solving such coupled problems. Main topics: Single-Phase Flow, Reaction Advection Dispersion Equation, Conservation of Momentum in Fluid Flow, Non-isothermal Flow of Fluids, MP Phenomena in Solid Mechanics, Multiphysics Phenomena in Electromagnetic Waves.

List of courses from other professional master programs for students who took similar courses in BS

 MATH 503: Mathematics for Data Science                                                                                                                            (3-0-3)

Description: Selected topics from linear algebra, multivariate calculus, and optimization for Data Science with an emphasis on the implementation using numerical and symbolic software, toolboxes, and libraries for data science like NumPy, SciPy, Pandas, SymPy. Topics include data transformation using linear algebra, vector spaces, linear transformations, matrix representations, matrix decompositions (eigenvectors, LU, QR, SVD, Cholesky); multivariate calculus for continuous, convex, and non-convex optimization methods; Basic neural network design.

Prerequisite: Graduate Standing

MATH 506: Fundamentals of Data Science                                                                                                                            (2-1-3)

Description: All aspects of the data science pipeline using the software, toolboxes, and libraries like NumPy, SciPy, Pandas, Matplotlib, and Seaborn: data acquisition, cleaning, handling missing data, EDA, visualization, feature engineering, modeling, model evaluation, bias-variance tradeoff, sampling, training, testing, experimenting with a classical model.

Prerequisite: Graduate Standing

STAT 503: Probability and Statistics for Data Science                                                                                                        (3-0-3)

Description: Selected topics from Probability theory, Statistical Inference, and Information Theory for Data Science with an emphasis on the implementation using statistical software, toolboxes, and libraries like R, NumPy, SciPy, Pandas, and Stats models. Topics include Probability; Conditional Probability; Bayes’ Theorem; Random variables; Discrete and Continuous Distributions; Central Limit Theorem; Point Estimation MLE and MAP; Confidence Interval Estimation; Hypothesis Testing; Non-parametric Statistics; Synthetic Data; Entropy, Mutual Information; Information Gain.

Prerequisite: Graduate Standing

STAT 523: Forecasting Methods                                                                                                                                                (3-0-3)

Description: Time Series Basics; Autocorrelation; Modeling and forecasting with MA, AR, ARMA, ARIMA models; Seasonal and non-seasonal models; Model validation; Parameter selection; Smoothing and decomposition methods; Advanced forecasting methods, Multivariate models, State Space Models, Arch and Garch Models; projects using various software, toolboxes, and libraries like R, Scikit-Learn, and Stats models.

Prerequisite: STAT 503

Note: Not to be taken for credits with ISE 487

ICS 504: Deep Learning                                                                                                                                                               (3-0-3)

Description: Deep Learning models and their applications in real world.  Foundations of deep learning networks training and optimization. Deep learning models for spatial and temporal data processing. Analysis of prominent deep learning models such as Convolutional Neural Networks (CNNs), Recurrent and Recursive Networks, Long-Short Term Memory (LSTM), Residuals Networks, and Generative Adversarial Networks (GANs). One-Shot Learning and Deep Reinforcement Learning

Prerequisite:  ICS 502

Note: Not to be taken for credit with ICS 471