About Course
Welcome to Machine Learning, Modeling, and Simulation Principles!
In this course, we will understand the computational tools used in engineering problem-solving and provide a mathematical basis to machine learning. We invite everyone to explore the resources that we have made available within the courseware.
Course Content
Module 1: Get Started (15 min)
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Entrance Survey
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Optional: Access to MATLAB Online
Module 2: Modeling and Simulation Fundamentals
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Key Takeaways
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Ordinary Differential Equations (ODEs) : Introduction
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ODEs: General Form
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ODEs: General Form Quiz
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ODEs: Chemistry Example
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The Forward Euler Method: Introduction
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The Forward Euler Method: True Solution vs. Approximation
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Demo: Forward Euler
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Forward Euler Quiz
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Higher-Order ODE Integrators
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Higher-Order ODE Integrators quiz
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Demo: Four-Stage Runge-Kutta
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Four-stage Runge-Kutta Demo Quiz
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Implicit Methods The Backward Euler Method
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Solving the Backward Euler Method
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Solving the Backward Euler Method Quiz
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Demo: Backward Euler
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Graded Assignment Introduction
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(Final) Implementing the Forward Euler scheme
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final quiz
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Your assignment
Module 3: Spatial Modeling
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Key Takeaways
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Partial Differential Equations (PDEs) Introduction
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Approximating Solutions to PDEs on Meshes
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Finite Difference Formulas
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Choosing a Discretization Stencil
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Choosing a Discretization Stencil Quiz
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Initial Boundary Value Problems
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Initial Boundary Value Problems Quiz
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Approximation Error in Initial Boundary Value Problems
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Approximation Error in Initial Boundary Value Problems Quiz
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Implicit Methods for Initial Boundary Value Problems
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Implicit Methods for Initial Boundary Value Problems Quiz
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Boundary Conditions
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Direct Solution Algorithms for Linear Systems
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Direct Solution Algorithms for Linear Systems Quiz
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Demo: Linear Solve
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Iterative Algorithms for Linear Systems
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Iterative Algorithms for Linear Systems Quiz
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Nonlinear Systems and Root Finding
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Root Finding: Bisection
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Demo: Bisection Method
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Root Finding: Newton-Raphson
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Root Finding Newton-Raphson Quiz
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Demo: Newton’s Method
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Assignment Introduction
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Graded Assignment Part 1 of 2
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Assignment Part 2 Introduction
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Graded Assignment Part 2 of 2
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Quizes
Module 4: Optimization and Data-Driven Modeling
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Key Takeaways
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Introduction to Optimization
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Anatomy of an Optimization Problem
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Anatomy of an Optimization Problem quiz
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Least Squares Problems
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Gradient Descent
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Gradient Descent Quiz
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Comments on Gradient Descent
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Comments on Gradient Descent Quiz
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Demo: Gradient Descent
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Newton’s Method
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Newton’s Method Quiz
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Comments on Newton’s Method
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Comments on Newton’s Method Quiz
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Demo: Gradient Descent vs. Newton’s Method
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Parameter Estimation: Introduction
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Parameter Estimation: Nonlinear Least Squares
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Optimization Methods for Nonlinear Least Squares
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Optimization Methods for Nonlinear Least Squares Quiz
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✠Graded Assignment (Assignment Introduction)
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Optimization Assignment Quiz
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(Final) Minimizing a nonlinear objective function with constraints
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(Final) Newton’s Method for Faster Convergence
Module 5: From Optimization to Machine Learning
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Key Takeaways
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Introduction to Regression
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How Regression Works
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How Regression Works Quiz
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Simplifying the Least Squares Problem
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Simplifying the Least Squares Problem Quiz
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Regression with Big and Small Data
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Regression with Big and Small Data Quiz
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Demo: Sparse Regression
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Introduction to Classification
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Logistic Regression
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Logistic Regression Quiz
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Comments on Logistic Regression
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Comments on Logistic Regression Quiz
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Demo: Multi-Valued Logistic Regression
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Empirical Risk and Very Large Datasets
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Empirical Risk and Very Large Datasets Quiz
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Comments on Stochastic Gradient Descent
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Comments on Stochastic Gradient Descent Quiz
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Holdout and Cross Validation
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Holdout and Cross Validation Quiz
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An Error vs Effort Paradox
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Regression Assignment
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Regression Assignment Quiz
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Question 5: Assessing Model Fit (External resource)
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Question 6: Choosing basis functions (External resource)
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Question 8: Stability of regression models (External resource)
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Quiz
Module 6: Probabilistic Methods
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Key Takeaways
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Introduction to Probabilistic Methods
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Solitaire and Dartboards
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Monte Carlo Simulation: Part 2
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Demo: Law of Large Numbers and Central Limit Theorem
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Dynamical Models
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Dynamical Models Quiz
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Sensitivity Analysis: Which Inputs Matter?
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Demo: Sensitivity Analysis via Monte Carlo
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Demo: Sensitivity Analysis via Monte Carlo Quiz
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Simulating Rare Events Introduction
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Importance Sampling
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Assignment Introduction
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Monte Carlo Assignment
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(Final) Warm-up: characterizing the probability density of the load
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(Final) Uncertainty propagation in beam bending
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(Final) Rare event simulation
Module 7: Case Studies
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Introduction
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Aurora Flight Sciences Case Study: Introduction
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Case Study Assignment (Part 1)
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Quiz
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Case Study Assignment (Part 2)
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Quiz
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Open Discussion
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Case Study Assignment (Part 3)
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Quiz
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Case Study Assignment (Part 4)
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Quiz
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(Final) Trade Studies: Uncertain World (Part 2) Demo
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Quiz
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BASF Introduction
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BASF Case Study Assignment
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Schlumberger Introduction
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Optional Readings
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Case Study Assignment
Module 8: Conclusion
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Where to Go Next
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