Uploaded February 2025 | Updated September 2026, 2 weeks ago
It is often helpful to work with a "standard unit normal" distribution, which is a Gaussian with zero mean and unit standard deviation. It is possible to transform other normal distributions into this standard form, through a simple mean-centering and scaling procedure, after which it is easy to compute probabilities. For example, if I want to know what percentile my height is in the USA, I could first transform the normal distribution of heights to standard unit normal, and then see where my transformed height lies. This will allow me to easily compute various quantities.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
02:53 The Standard Unit Normal
05:57 Defining the CDF
10:24 The Standard Deviation
12:17 Example: 400 Coins
16:09 Outro
It is often helpful to work with a "standard unit normal" distribution, which is a Gaussian with zero mean and unit standard deviation. It is possible to transform other normal distributions into this standard form, through a simple mean-centering and scaling procedure, after which it is easy to compute probabilities. For example, if I want to know what percentile my height is in the USA, I could first transform the normal distribution of heights to standard unit normal, and then see where my transformed height lies. This will allow me to easily compute various quantities.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
02:53 The Standard Unit Normal
05:57 Defining the CDF
10:24 The Standard Deviation
12:17 Example: 400 Coins
16:09 Outro
![AI/ML+Physics: Preview of Upcoming Modules and Bootcamps [Physics Informed Machine Learning]](https://i.ytimg.com/vi/_ObvDgPMWkU/mqdefault.jpg "AI/ML+Physics: Preview of Upcoming Modules and Bootcamps [Physics Informed Machine Learning]
This video provides a brief preview of the upcoming modules and bootcamps in this series on Physics Informed Machine Learning. Topics include: (1) Parsimonious modeling and SINDy; (2) Physics informed neural networks (PINNs); (3) Operator methods, like DeepONets and Fourier Neural Operators; (4) Symmetries in physics and machine learning; (5) Digital Twin technology; and (6) Case studies in engineering.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro & Recap
01:06 Reviewing the 5 Stages
04:08 Reviewing Physics in the Stages
05:11 Why Physical Models: Cost & Data Scale
07:53 Why Physical Models: Generalized Models
10:01 Why Physcial Models: Discovering Physics
11:40 Holistic Impact of Embedding Physics // Struggling to find a good wording here
12:55 Case Study: Pendulum Data and SINDy
15:20 Case Study: Symbolic Regression and Evolutionary Optimization
16:45 Case Study: Lagrangian Neural Networks
18:34 Architectures and Symmetries
19:36 Applications in Engineering
21:21 The Digital Twin
22:15 Benchmark Problems
23:35 Outro")
