Inverse Methods in Heat Transfer

By Prof. Balaji Srinivasan   |   IIT Madras
Learners enrolled: 69
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.


PREREQUISITES: 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)
Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 23 Jan 2023
End Date : 14 Apr 2023
Exam Date : 30 Apr 2023 IST
Enrollment Ends : 30 Jan 2023
Category :
  • Mechanical Engineering
Credit Points : 3
Level : Undergraduate/Postgraduate

Page Visits

Course layout

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

Books and references

1. Beck, J. V., Blackwell, B., & St Clair Jr, C. R. Inverse Heat Conduction: Ill-Posed Problems. 1985. A WileyInterscience, New York.
2. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B., Bayesian data analysis. Chapman and Hall/CRC, 2004
3. Balaji, C. Essentials of thermal system design and optimization. Ane Books Pvt., New Delhi, 2011.

Instructor bio

Prof. Balaji Srinivasan

IIT Madras
Prof. Balaji Srinivasan is currently a Professor in Mechanical Engineering at IIT-Madras. He finished his PhD from Stanford University in 2006. His current research interests are in Computational Heat Transfer, Numerical Analysis, Inverse Methods and Scientific Machine Learning.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 30 April 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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