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Course11210631667 lectures

Inverse Methods in Heat Transfer

Prof. Balaji Srinivasan · IIT Madras

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Introduction to the Inverse Methods in Heat Transfer Course Video
  2. Inverse Problems - Definition, History and Applications Video
  3. The inverse problem solving process Video
  4. Review of Basic Heat Transfer for this course Video

week-02

  1. INTRODUCTION TO WEEK 02 Video
  2. Introduction to Linear Regression for Inverse Problems Video
  3. Example Application of Linear regression for an inverse conduction problem Video
  4. Goodness of Fit and Coefficient of Determination Video
  5. Linear Regression with Quadratic Model Video
  6. SUMMARY OF WEEK 02 Video

week-03

  1. INTRODUCTION TO WEEK 03 Video
  2. Introduction to Normal Equations for linear models Video
  3. Normal Equations for linear models (contd) Video
  4. Parity Plots Video
  5. Programming Inverse Methods using Normal Equations Video
  6. Variants on the Linear Model for inverse problems Video
  7. SUMMARY OF WEEK 03 Video

week-04

  1. The General Inverse Methods Process Video
  2. Simple nonlinear inverse problem -- Transient Heat transfer Video
  3. Review of required calculus results Video
  4. Gradient Descent Algorithm Video
  5. Gradient Descent -- Simple Example Video
  6. Gradient Descent for Nonlinear Inverse Problem -- Theory Video
  7. Gradient Descent for Nonlinear Inverse Problem -- Coding Example Video
  8. Newton Algorithm for a System of Equations Video
  9. Gauss Newton Algorithm -- Derivation and Code Video

week-05

  1. Overfitting and Regularization for Linear Models Video
  2. Tikhonov Regularization and Levenberg-Marquardt -- Theory Video
  3. Tikhonov and Levenberg-Marquardt -- Example Code Video

week-06

  1. Introduction to Probability for Inverse Methods Video
  2. Sum and Product Rules of Probability Video
  3. Bayes Theorem -- Simple Examples Video
  4. Independence and Expectation Video
  5. Variance and Covariance Video
  6. Gaussian distribution and the standard normal table Video

week-07

  1. Maximum Likelihood Estimate Video
  2. MLE, MAP estimates Video
  3. Introduction to Bayesian Methods for Inverse Problems Video
  4. Offline Bayesian Estimation Video
  5. Offline Bayesian Estimation -- MATLAB Demo Video
  6. MHMCMC for Inverse Problems Video
  7. MHMCMC for Inverse Problems -- MATLAB Demo Video

week-08

  1. Why Machine Learning in Inverse Heat Transfer? Video
  2. Overview of AI and ML Video
  3. Supervised Machine Learning as an Inverse Problem Video

week-09

  1. Introduction to Week 9 - From Linear Models to Neural Networks Video
  2. Gradient Descent - Batch, Stochastic and Mini Batch Video
  3. Logistic Regression - The Forward Model Video
  4. Logistic Regression - Binary Entropy Cost Function and Gradient Video
  5. Multiclass Classification Video
  6. Linear Separability and Neural Networks Video

week-10

  1. Introduction to Week 10 - XOR and Deeper networks Video
  2. Forward pass through a simple neural network Video
  3. Backprop in a scalar chain Video
  4. Backprop in a MLP Video

week-11

  1. Introduction to Week 11-- ANNs as Surrogate models Video
  2. Physics Informed Neural Networks -- Introduction Video
  3. Physics Informed Neural Networks -- an intuitive explanation Video
  4. Physics Informed Neural Networks -- BC incorporation Video
  5. PINNs for inverse problems Video

week-12

  1. Introduction to Week 12-- Sensitivity Analysis Video
  2. Code Examples of Logistic Regression -- OR and AND gates Video
  3. Code Example of shallow neural network -- XOR gate Video
  4. Code walkthrough for PINNs in Burgers equation Video
  5. Formulation of a PINN based inverse problem in unsteady conduction Video
  6. Formulation of a surrogate model based inverse solution in unsteady conduction Video
  7. Summary of course Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Mechanical Engineering
Teacher
Prof. Balaji Srinivasan
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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