Introduction to Digital Twins

1. Introductory lectures - From simulation to digital twin [video lecture][lecture notes (marked)]

2. Prediction module in digital twins - ODE (Part 1) [video lecture][lecture notes][lecture notes (marked)]

3. Prediction module in digital twins - ODE (Part 2) [video lecture][lecture notes][lecture notes (marked)]

4. Prediction module in digital twins - ODE (part 3) [video lecture][lecture notes][lecture notes (marked)]

5. Prediction module in digital twins - ODE (part 4) [video lecture][lecture notes][lecture notes (marked)]

6. Prediction module in digital twins - ODE (part 5) [video lecture][lecture notes][lecture notes (marked)]

7. Prediction module in digital twins - SDE (part 1) [video lecture][lecture notes][lecture notes (marked)]

8. Prediction module in digital twins - SDE (part 2) [video lecture][lecture notes][lecture notes (marked)]

9. Prediction module in digital twins - conclusion [video lecture][lecture notes][lecture notes (marked)]

10. Update module in digital twins -physics-based digital twin (part 1 [video lecture][lecture notes][lecture notes (marked)]

11. Update module in digital twins -physics-based digital twin (part 2) [video lecture][lecture notes][lecture notes (marked)]

12. Update module in digital twins - Gaussian process (part 1) [video lecture][lecture notes][lecture notes (marked)]

13. Update module in digital twins - Gaussian process (part 2) [video lecture][lecture notes][lecture notes (marked)]

14. Data driven models - GP based DT and VAE [video lecture][lecture notes][lecture notes (marked)]

15. Data driven models - GAN [video lecture][lecture notes][lecture notes (marked)]

16. Data driven digital twins - deep digital twin [video lecture][lecture notes][lecture notes (marked)]

17. Gray-box models - HMM (part 1) [video lecture][lecture notes][lecture notes (marked)]

18. Gray-box models - HMM (part 2) [video lecture][lecture notes][lecture notes (marked)]

19. Gray-box models - SSM (part 1) [video lecture][lecture notes][lecture notes (marked)]

20. Gray-box models - SSM (part 2) [video lecture][lecture notes][lecture notes (marked)]

21. Gray-box modelling based DT and way ahead [video lecture][lecture notes][lecture notes (marked)]

• Computational tools in science and technology, From computational techniques to digital twins, Different tools in digital twin

• Physics-based digital twin in dynamical systems - solution of ODEs and PDEs, Time-domain simulation of dynamical systems.

• Digital twin for dynamical systems - frequency domain analysis

• Digital twin for dynamical systems - time domain analysis

• Data-driven digital twins.

• Bayesian methods in digital twin technology – Kalman filter based approaches.

• Digital twin for multi-timescale dynamical systems - Mixture of Gaussian Process and Expectation maximization.

• Digital twin from multi-fidelity data.

• Digital twin for systems with partially known physics.

• Deep learning in digital twin technology - GANS and VAEs.

• Way forward - challenges and possible wayouts.

Lecture notes and references will be provided on the course web site. The following books are recommended for the ML part.

• Iserles, A. (2009). A first course in the numerical analysis of differential equations (No. 44). Cambridge university press.

• Bishop, C.M. Pattern recognition and Machine learning, Springer, 2007.

• Murphy, K.P. Machine learning: A Probabilistic Perspective, MIT press, 2012.

• C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, 2006 (a free ebook is also available from the Gaussian Processes web site).

• Additional references will be provided with lecture notes

1. Homework 1: Numerical integration [HW1][Solution][Codes]

2. Homework 2: Stochastic differential equations [HW2][Solution][Codes]

1. Practical 1: Numerical integration [Pr1][Solution][Codes]

2. Practical 2: Stochastic differential equation [Pr2][Solution][Codes]

• Instruction on project [video link]

Credit: 3 Units (2-0-2)

Lectures and practicals/tutorial: TF 6:30 - 7:30 PM

Instructor: Dr. Souvik Chakraborty, Block IV, Room 342-C, souvik@am.iitd.ac.in

Teaching Assistants: Shailesh Garg, Tapas Tripura (amz218313@iitd.ac.in), Tushar, Aarya Sheetal Desai (Aarya.Sheetal.Desai.ama20@am.iitd.ac.in), Shashank Jain (Shashank.Jain.ama20@am.iitd.ac.in), Aashish Kumar (ama202248@am.iitd.ac.in)

Course Objective: This course is designed to introduce students to the idea of digital twin with a particular focus on its application in engineering mechanics. At the end of this course, a student is expected to have a clear understanding of the digital twin technology and its application.

Intended audience: UG students. PG and Ph.D. students may also seat through this course.