Teaching

AY2025-26 Semester I

ME 691-XVII Scientific Machine Learning for Thermofluids

Course Contents:

This course introduces the fundamental principles of Scientific Machine Learning (SciML) by combining traditional computational methods - such as finite volume/element techniques - with modern data-driven approaches. Designed for students familiar with numerical methods, the course emphasizes integrating physics-guided machine learning models to solve engineering problems in areas like heat transfer and fluid dynamics. Through a combination of theoretical lectures and hands-on projects described in the modules below, the course covers SciML topics including neural network fundamentals, differential equation solvers (such as PINNs and Neural ODEs), advanced operator learning (DeepONet) and probabilistic machine learning methods.

Module 1: Fundamentals of Scientific Machine Learning 

• Overview of SciML and its engineering applications 

• Introduction to neural networks, including perceptrons 

• Basic classification, regression, and reduced order models 

Module 2: Differential Equation Solvers with Neural Networks 

• Finite volume/element methods for PDEs 

• Applications for heat transfer, fluid dynamics (e.g., forward/inverse modeling of Burger’s equation) 

• Physics-Informed Neural Networks (PINNs) for ordinary and partial differential equations 

• Deep Operator Networks (DeepONet) for learning complex mappings 

Module 3: Neural Ordinary Differential Equations (Neural ODEs) and other SciML Learning Techniques 

• ResNets and Neural ODEs 

• Automatic differentiation and its role in training neural networks 

• Other operator learning and SciML techniques 

Module 4: Probabilistic Machine Learning Methods 

• Bayesian regression, Bayesian neural networks, and uncertainty quantification 

• Gaussian processes for function approximation 

Module 5: SciML Integration and Project (Builds through Semester) * 

• Defining an application-driven engineering problem of student’s interest 

• Design and implement a SciML model solution based on earlier modules. 

• Critical evaluation of model performance, and communicating results through presentation and a conference style paper 

Teaching