Mini-Course Roadmap with MATLAB
This course was prepared by Dr. Khemraj Shukla, Associate Professor of Applied Mathematics at Brown University.
It includes three modules covering mixing theory, algorithms, programming, and includes examples. Lectures 2,4, 13-15 are hands-on and Dr. Shukla will cover this material as well as many segments of the lectures. Implementation of the algorithms is involved, and homework is assigned for Model-1 and 20 projects across 7 different disciplines.
Course prerequisites include ODE/PDE/linear algebra and Matlab level programming experience.
Module 1 – Basics
- Lecture 1: Deep Learning Networks – Training, optimization, neural network architectures
- Lecture 2: A primer on MATLAB for Deep Learning
Module 2 – Neural Differential Equations
- Lecture 3: Physics-Informed Neural Networks (PINNs)
Module 3 – Neural Operators
- Lecture 4: Deep Operator Network (DeepONet)
Module 4 – VIV/FSI Applications
- Lecture 5: Examples of vortex-induced vibrations and flow-structure interactions with uncertainty quantification and multi-fidelity training
This course is offered as a Github repository, which includes all slides and codes
