## Theme: Modeling and Simulation

The theme emphasizes modeling, numerical methods and their implementation on physical problems motivated by phenomena involving biomechanics, heat-transfer, structural analysis, control theory, fluid-flow, electrical conduction, diffusion, etc. This theme focuses on the development of intuition about the strengths and weaknesses of a variety of modeling and numerical methods.

#### Modeling and Simulation Microcourses

#### E267A: Modeling and simulation of infectious diseases-the cutting edge: microscale transmission, decontamination and macroscale propagation

#### E264: An Introduction to Continuum Mechanics and Modern Applications

This course is designed to introduce students to the basics of continuum mechanics and its modern applications. Continuum mechanics is a powerful method of modeling physical systems of a very large variety. In this course students will learn the basic elements for describing system state and how balance laws are formulated to ensure correct system response. The developed methodology will first be applied to basic problems in elasticity, followed by application to poroelastic systems, batteries, and piezoelectric material systems.

The foundations gained from this course will allow students to understand how continua, both simple and complex, are properly modeled. It will set them up to be able to formulate continuum mechanical problems and it will allow them to more fully understand numerical solutions that are arrived at via modern computational methods, such as the finite element method. This course sets students up for the ability to contribute a sophisticated perspective on modeling questions that arise in a wide variety of engineering problem classes.

#### E261B: Computational Fluid Dynamics

Our lives heavily depend on the two most important fluids on earth: Air and Water. They are everywhere: they make the atmosphere, most of the earth’s surface is covered with water, and most of our body is composed of water. Fluid Mechanics is the science of understanding how fluids, including air and water, behave. The challenge is that equations that govern dynamics of Fluids are very complex, impeding analytical solutions. Running experiments are also very expensive and difficult to conduct and measure. The advent of high performance computers, however, has given us a new tool to understand and analyze fluid mechanics problems. The objective of this mini-course is to introduce basics of Fluid Mechanics and Numerical Simulations to those who are interested to learn about this state-of-the-art technique. This is a project-based course and we will learn about conducting computational analysis via a commercial CFD software while working on a real-life problem. Computational Fluid Dynamics is becoming one of the most needed expertise in many industries including aerospace, ocean industries, chemical engineering, automobile industries, computers (particularly for cooling), and nearly all hardware industries.

#### E260A: Models in Engineering

The first session begins with foundational concepts and an overview of the use of models in engineering. What is a model? What is the role of data and measurements? What are mechanistic, data-based, and mixed models? What are static and dynamical models? Where do optimization theory and control theory fit in? The second session will be devoted to mechanistic models: those that are built on prior physical principles. We will classify these into static and dynamical models. For static models we will introduce finite differences as a fundamental numerical technique, as well as give a glimpse of more advanced approaches such as FEM. For dynamical models we will review the role of ordinary differential equations, and run numerical experiments with PID feedback control. The third session will focus on data-based models, culminating with the modern techniques of deep learning. In the process we will learn the basic techniques of linear regression and logistic regression, as well as practical considerations such as training versus testing data sets and over-fitting.

#### E263: Uncertainty and state estimation for complex systems

Almost all modern technology relies on automatic control for safe and efficient functioning. Complex systems rely on a variety of sensors to infer the system’s state, which is then used to take decisions on desirable actions. In this course, we will cover some methods and tools used for state estimation of such systems, with a particular focus of the Kalman Filter. The course will recapitulate modeling uncertainty using random variables, and then use this language to develop state estimation strategies. In addition to the Kalman filter for linear systems, we will give an overview of the extensions for nonlinear systems (the Extended Kalman Filter, and the Unscented Kalman Filter). We will also introduce the Particle Filter as another approach for state estimation, and discuss the conditions under which the different methods may be appropriate. At the end of the course the student will have an understanding for why the strategies work (and when they may not work), and be able to implement them.

#### E261C: Modeling and Simulation of Advanced Manufacturing Processes

Many modern manufacturing methods involve a series of steps to process a material in order to obtain characteristics that the raw material does not possess. This course provides the student with modern modeling and simulation methods to analyze and optimize classical and cutting edge manufacturing processes in a systematic, scientific and self-consistent manner, with special emphasis on 3D printing, simulation and machine-learning.

#### E260B: Understanding the Finite Element Method

Finite Element Analysis has become an indispensable tool for modern engineering. In the 21st century, every engineer should have had a course in Finite Element Methods. This is an introductory course on the finite element method and is intended for seniors in engineering and applied science disciplines. The course covers the basic topics of finite element technology, including domain discretization, polynomial interpolation, application of boundary conditions, assembly of global arrays, and solution of the resulting algebraic systems. Finite element formulations for several important applied field equations. Assignments will involve both analytical and computer exercises. Computer-based assignments will emphasize the practical aspects of finite element model construction, analysis and application to research and industrial problems.

#### E261A: Basic Modeling and Simulation Tools for Industrial Research Applications

To enable students to model and simulate industrial systems- Coverage of the modeling and simulation of modern engineering systems and their synthesis. The goal of this course is to provide students with the general multipurpose tools needed for successful industrial research. The course will help students develop intuition about modeling physical systems and strengths and weaknesses of a variety of numerical methods. Instructor’s class notes will be used. Some commonly recurring mathematical tools needed are • Modeling of complex physical systems,

• Discretization of differential equations,

• Formulation of optimal systems,

• Gradient methods for convex optimization and

• Machine learning algorithms for nonconvex optimization

#### E262: Complex Non-linear Systems: An Overview

Exploration of basic concepts of nonlinear phenomena and their dynamics leading to chaos and complexity. We will try to look at a variety of natural objects and processes, and their mathematical counterparts to see if we can characterize such features as ruggedness, structure, contingency, “butterfly effect”. The focus will be on the development of intuition and on applications coupled with some mathematical derivations. Expected outcome: development of a new Weltanschauung and thinking about scaling laws, sensitivity to initial conditions, small changes and large effects.