Course: Physics-Informed Machine Learning

This course introduces the principles of physics-informed machine learning (PIML) and its applications in solving complex multi-physics problems in science and engineering. We begin with an overview of traditional ML methods, followed by a series of case studies where various PIML techniques are introduced, such as physics-informed features, domain transformation, and synthetic features. Python codes are provided and reviewed to show how to integrate these techniques with different traditional ML methods. The course aims to cover diverse physics phenomena, PIML techniques, and ML methods. These techniques result in improved robustness, accuracy, and reliability in ML models for engineering applications.

Section 1: Introduction
OFAT (One-Factor-At-A-Time) vs. DOE (Design of Experiments) vs. Iterative Machine Learning, Quick Overview of Traditional ML Methods (NN, GPR, Ensemble Methods)
Slides, Code

Section 2: Case Study on Heat Transfer
Physics-Informed Features, Loss, and Domain Transformation with Neural Networks (NN)
Slides, Code

Section 3: Case Study on Discovering Chemical Reactions
Physics-Informed Augmentation with Sparse Identification of Nonlinear Dynamics (SINDy)
Slides, Code

Section 4: Case Study on 3D Printing
Physics-Informed Synthetic Features using Finite Element with Ensemble Methods
Slides, Code

Section 5: Case Study on Adhesive Bonding Strength
Physics-Informed Domain Transformation and Dimensionality Reduction with Gaussian Process Regression (GPR)
Slides, Code