Explore a comprehensive video series that demonstrates how to enhance machine learning by integrating known physics principles and discover new physical laws through advanced computational methods. Master the fundamental approaches to physics-informed machine learning, starting with high-level overviews of AI and ML applications in science and engineering, then progressing through essential components including model selection, training data curation, architecture design, loss function crafting, and optimization algorithms. Dive deep into sparse identification of nonlinear dynamics (SINDy) methodology across multiple modules covering training data preparation, model disambiguation, effective coordinate systems, candidate nonlinearity libraries, and optimization techniques. Learn to implement cutting-edge neural network architectures specifically designed for physical systems, including Hamiltonian Neural Networks (HNN), Lagrangian Neural Networks (LNN), Neural Implicit Flow (NIF), Neural ODEs (NODEs), Residual Networks (ResNet), Fourier Neural Operators (FNO), Deep Operator Networks (DeepONet), and Physics Informed Neural Networks (PINNs). Discover how to use deep learning for coordinate discovery in dynamical systems through autoencoders, apply Python Symbolic Regression (PySR) for equation discovery, and develop discrepancy modeling techniques that bridge theoretical physics with machine learning applications while promoting interpretable and generalizable models through low-dimensional and sparse representations.

Syllabus

Physics Informed Machine Learning: High Level Overview of AI and ML in Science and Engineering
AI/ML+Physics Part 1: Choosing what to model [Physics Informed Machine Learning]
AI/ML+Physics Part 2: Curating Training Data [Physics Informed Machine Learning]
AI/ML+Physics Part 3: Designing an Architecture [Physics Informed Machine Learning]
AI/ML+Physics Part 4: Crafting a Loss Function [Physics Informed Machine Learning]
AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]
AI/ML+Physics: Recap and Summary [Physics Informed Machine Learning]
AI/ML+Physics: Preview of Upcoming Modules and Bootcamps [Physics Informed Machine Learning]
Deep Learning to Discover Coordinates for Dynamics: Autoencoders & Physics Informed Machine Learning
Sparse Identification of Nonlinear Dynamics (SINDy): Sparse Machine Learning Models 5 Years Later!
Sparse Nonlinear Dynamics Models with SINDy, Part 2: Training Data & Disambiguating Models
Sparse Nonlinear Dynamics Models with SINDy, Part 3: Effective Coordinates for Parsimonious Models
Sparse Nonlinear Dynamics Models with SINDy, Part 4: The Library of Candidate Nonlinearities
Sparse Nonlinear Dynamics Models with SINDy, Part 5: The Optimization Algorithms
Discrepancy Modeling with Physics Informed Machine Learning
Hamiltonian Neural Networks (HNN) [Physics Informed Machine Learning]
Lagrangian Neural Network (LNN) [Physics Informed Machine Learning]
Neural Implicit Flow (NIF) [Physics Informed Machine Learning]
Neural ODEs (NODEs) [Physics Informed Machine Learning]
Python Symbolic Regression (PySR) [Physics Informed Machine Learning]
Residual Networks (ResNet) [Physics Informed Machine Learning]
Fourier Neural Operator (FNO) [Physics Informed Machine Learning]
Deep Operator Networks (DeepONet) [Physics Informed Machine Learning]
Physics Informed Neural Networks (PINNs) [Physics Informed Machine Learning]