Learn · Inverse Methods in Heat Transfer
Lecture 34 of 67week-06
Variance and Covariance
Prof. Balaji Srinivasan · IIT Madras
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- Inverse Methods in Heat Transfer, IIT Madras (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Introduction to the Inverse Methods in Heat Transfer Course
- Inverse Problems - Definition, History and Applications
- The inverse problem solving process
- Review of Basic Heat Transfer for this course
- INTRODUCTION TO WEEK 02
- Introduction to Linear Regression for Inverse Problems
- Example Application of Linear regression for an inverse conduction problem
- Goodness of Fit and Coefficient of Determination
- Linear Regression with Quadratic Model
- SUMMARY OF WEEK 02
- INTRODUCTION TO WEEK 03
- Introduction to Normal Equations for linear models
- Normal Equations for linear models (contd)
- Parity Plots
- Programming Inverse Methods using Normal Equations
- Variants on the Linear Model for inverse problems
- SUMMARY OF WEEK 03
- The General Inverse Methods Process
- Simple nonlinear inverse problem -- Transient Heat transfer
- Review of required calculus results
- Gradient Descent Algorithm
- Gradient Descent -- Simple Example
- Gradient Descent for Nonlinear Inverse Problem -- Theory
- Gradient Descent for Nonlinear Inverse Problem -- Coding Example
- Newton Algorithm for a System of Equations
- Gauss Newton Algorithm -- Derivation and Code
- Overfitting and Regularization for Linear Models
- Tikhonov Regularization and Levenberg-Marquardt -- Theory
- Tikhonov and Levenberg-Marquardt -- Example Code
- Introduction to Probability for Inverse Methods
- Sum and Product Rules of Probability
- Bayes Theorem -- Simple Examples
- Independence and Expectation
- Variance and Covariance
- Gaussian distribution and the standard normal table
- Maximum Likelihood Estimate
- MLE, MAP estimates
- Introduction to Bayesian Methods for Inverse Problems
- Offline Bayesian Estimation
- Offline Bayesian Estimation -- MATLAB Demo
- MHMCMC for Inverse Problems
- MHMCMC for Inverse Problems -- MATLAB Demo
- Why Machine Learning in Inverse Heat Transfer?
- Overview of AI and ML
- Supervised Machine Learning as an Inverse Problem
- Introduction to Week 9 - From Linear Models to Neural Networks
- Gradient Descent - Batch, Stochastic and Mini Batch
- Logistic Regression - The Forward Model
- Logistic Regression - Binary Entropy Cost Function and Gradient
- Multiclass Classification
- Linear Separability and Neural Networks
- Introduction to Week 10 - XOR and Deeper networks
- Forward pass through a simple neural network
- Backprop in a scalar chain
- Backprop in a MLP
- Introduction to Week 11-- ANNs as Surrogate models
- Physics Informed Neural Networks -- Introduction
- Physics Informed Neural Networks -- an intuitive explanation
- Physics Informed Neural Networks -- BC incorporation
- PINNs for inverse problems
- Introduction to Week 12-- Sensitivity Analysis
- Code Examples of Logistic Regression -- OR and AND gates
- Code Example of shallow neural network -- XOR gate
- Code walkthrough for PINNs in Burgers equation
- Formulation of a PINN based inverse problem in unsteady conduction
- Formulation of a surrogate model based inverse solution in unsteady conduction
- Summary of course