Inverse Methods in Heat Transfer

ABOUT THE COURSE: The principal objective of the course is to give the students an overview of inverse problems in heat transfer and ways of formulating and solving them through examples. A wide range of inverse techniques including classical techniques, probabilistic techniques as well as modern techniques involving Machine Learning will be covered.INTENDED AUDIENCE: UG/PGPREREQUISITES: Undergraduate course in Heat Transfer would be useful. Knowledge of probability, calculus and matrix algebra.INDUSTRY SUPPORT: Thermal Engineers in the industry. Professionals interested in inverse methods (including in medical imaging)

Syllabus

Week 1:Introduction to inverse problemsWeek 2:Statistical description of errors, Inverse problems as optimization problemsWeek 3:Classical Techniques, Calculation of sensitivity coefficientsWeek 4:Parameter and Function estimation. Introduction to Nonlinear TechniquesWeek 5:The Levenberg-Marquardt method, Tikhonov regularizationWeek 6:Probability Theory, Bayesian Framework, Week 7:Markov Chain Monte Carlo Methods (MCMC)Week 8:Metropolis-Hastings algorithm (MH), Computational ImplementationWeek 9:Introduction to Machine LearningWeek 10:Deep Learning – ANNs, CNNs, RNNsWeek 11:Surrogate Models for Inverse problems, Genetic AlgorithmsWeek 12:Physics Informed Neural Networks for forward and inverse problems