NOC:Inverse Methods in Heat Transfer

Lecture 1 - Introduction to the Inverse Methods in Heat Transfer Course

Lecture 2 - Inverse Problems - Definition, History and Applications

Lecture 3 - The inverse problem solving process

Lecture 4 - Review of Basic Heat Transfer for this course

Lecture 5 - Introduction to Week - 2

Lecture 6 - Introduction to Linear Regression for Inverse Problems

Lecture 7 - Example Application of Linear regression for an inverse conduction problem

Lecture 8 - Goodness of Fit and Coefficient of Determination

Lecture 9 - Linear Regression with Quadratic Model

Lecture 10 - Summary of Week - 2

Lecture 11 - Introduction to Week - 3

Lecture 12 - Introduction to Normal Equations for linear models

Lecture 13 - Normal Equations for linear models (Continued...)

Lecture 14 - Parity Plots

Lecture 15 - Programming Inverse Methods using Normal Equations

Lecture 16 - Variants on the Linear Model for inverse problems

Lecture 17 - Summary of Week - 3

Lecture 18 - The General Inverse Methods Process

Lecture 19 - Simple nonlinear inverse problem - Transient Heat transfer

Lecture 20 - Review of required calculus results

Lecture 21 - Gradient Descent Algorithm

Lecture 22 - Gradient Descent - Simple Example

Lecture 23 - Gradient Descent for Nonlinear Inverse Problem - Theory

Lecture 24 - Gradient Descent for Nonlinear Inverse Problem - Coding Example

Lecture 25 - Newton Algorithm for a System of Equations

Lecture 26 - Gauss Newton Algorithm - Derivation and Code

Lecture 27 - Overfitting and Regularization for Linear Models

Lecture 28 - Tikhonov Regularization and Levenberg-Marquardt - Theory

Lecture 29 - Tikhonov and Levenberg-Marquardt - Example Code

Lecture 30 - Introduction to Probability for Inverse Methods

Lecture 31 - Sum and Product Rules of Probability

Lecture 32 - Bayes Theorem - Simple Examples

Lecture 33 - Independence and Expectation

Lecture 34 - Variance and Covariance

Lecture 35 - Gaussian distribution and the standard normal table

Lecture 36 - Maximum Likelihood Estimate

Lecture 37 - MLE, MAP estimates

Lecture 38 - Introduction to Bayesian Methods for Inverse Problems

Lecture 39 - Offline Bayesian Estimation

Lecture 40 - Offline Bayesian Estimation - MATLAB Demo

Lecture 41 - MHMCMC for Inverse Problems

Lecture 42 - MHMCMC for Inverse Problems - MATLAB Demo

Lecture 43 - Why Machine Learning in Inverse Heat Transfer ?

Lecture 44 - Overview of AI and ML

Lecture 45 - Supervised Machine Learning as an Inverse Problem

Lecture 46 - Introduction to Week 9 - From Linear Models to Neural Networks

Lecture 47 - Gradient Descent - Batch, Stochastic and Mini Batch

Lecture 48 - Logistic Regression - The Forward Model

Lecture 49 - Logistic Regression - Binary Entropy Cost Function and Gradient

Lecture 50 - Multiclass Classification

Lecture 51 - Linear Separability and Neural Networks

Lecture 52 - Introduction to Week 10 - XOR and Deeper networks

Lecture 53 - Forward pass through a simple neural network

Lecture 54 - Backprop in a scalar chain

Lecture 55 - Backprop in a MLP

Lecture 56 - Introduction to Week 11 - ANNs as Surrogate models

Lecture 57 - Physics Informed Neural Networks - Introduction

Lecture 58 - Physics Informed Neural Networks - an intuitive explanation

Lecture 59 - Physics Informed Neural Networks - BC incorporation

Lecture 60 - PINNs for inverse problems

Lecture 61 - Introduction to Week 12 - Sensitivity Analysis

Lecture 62 - Code Examples of Logistic Regression - OR and AND gates

Lecture 63 - Code Example of shallow neural network - XOR gate

Lecture 64 - Code walkthrough for PINNs in Burgers equation

Lecture 65 - Formulation of a PINN based inverse problem in unsteady conduction

Lecture 66 - Formulation of a surrogate model based inverse solution in unsteady conduction

Lecture 67 - Summary of course