Inverse Methods in Heat Transfer

Lecture 1 - Introduction to inverse problems

Lecture 2 - Fermi estimation

Lecture 3 - Forward/Direct and Inverse problems

Lecture 4 - Key drivers for studying inverse methods in engineering

Lecture 5 - Formulation for inverse problems

Lecture 6 - Statistical tools for estimation

Lecture 7 - Statistical description of errors

Lecture 8 - Well-posed and ill-posed problems

Lecture 9 - Probability and Statistics Brief overview - I

Lecture 10 - Probability and Statistics Brief overview - II

Lecture 11 - Gaussian distribution

Lecture 12 - Gaussian distribution (Continued...), and Maximum Likelihood Estimation (MLE)

Lecture 13 - Linear least square regression

Lecture 14 - Linear least square regression (Continued...)

Lecture 15 - Alternatives to Linear least square

Lecture 16 - Polynomial regression

Lecture 17 - Inverse problems in transient conduction - I

Lecture 18 - Inverse problems in transient conduction - II

Lecture 19 - Non-linear regression

Lecture 20 - Gauss-Newton algorithm (GNA)

Lecture 21 - Gauss-Newton algorithm (GNA) Example

Lecture 22 - Levenberg-Marquardt algorithm (LMA)

Lecture 23 - Tikhonov regularization

Lecture 24 - Jacobian and its calculation

Lecture 25 - Bayesian methods

Lecture 26 - Bayesian methods (Continued...)

Lecture 27 - Metropolis-Hastings algorithm (MH) and Markov Chain Monte Carlo Methods (MCMC)

Lecture 28 - Introduction to machine learning in heat transfer

Lecture 29 - Overview of machine learning

Lecture 30 - Calculation in a neural network model

Lecture 31 - Gradient Descent method

Lecture 32 - Gradient Descent method (Continued...)

Lecture 33 - Back propagation

Lecture 34 - Neural network as a surrogate forward model

Lecture 35 - PINN for an inverse problem

Lecture 36 - PINN for an inverse problem (Continued...)

Lecture 37 - Inverse methods in heat transfer - Summary