Uploaded June 2025 | Updated September 2026, 2 weeks ago
Variance and standard deviation measure the spread of a probability distribution, and are very useful quantities in probability and statistics.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
03:00 Defining Variance
04:25 Deriving an Alternate Formulation
09:35 Example: Variance of a Gaussian
10:56 Exercise: Variance is Non-Negative
11:21 Variance of Independent Sums
12:24 Outro
Variance and standard deviation measure the spread of a probability distribution, and are very useful quantities in probability and statistics.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
03:00 Defining Variance
04:25 Deriving an Alternate Formulation
09:35 Example: Variance of a Gaussian
10:56 Exercise: Variance is Non-Negative
11:21 Variance of Independent Sums
12:24 Outro
![AI/ML+Physics Part 3: Designing an Architecture [Physics Informed Machine Learning]](https://i.ytimg.com/vi/fiX8c-4K0-Q/mqdefault.jpg "AI/ML+Physics Part 3: Designing an Architecture [Physics Informed Machine Learning]
This video discusses the third stage of the machine learning process: (3) choosing an architecture with which to represent the model. This is one of the most exciting stages, including all of the new architectures, such as UNets, ResNets, SINDy, PINNs, Operator networks, and many more. There are opportunities to incorporate physics into this stage of the process, such as incorporating known symmetries through custom equivariant layers.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:03 The Architecture Zoo/Architectures Overview
06:29 What is Physics?
12:38 Case Study: Pendulum
17:10 Defining a Function Space
20:51 Case Studies: Physics Informed Architectures
23:36 ResNets
24:26 UNets
25:15 Physics Informed Neural Networks
26:50 Lagrangian Neural Networks
27:24 Deep Operator Networks
27:49 Fourier Neural Operators
28:23 Graph Neural Networks
30:02 Invariance and Equivariance
35:59 Outro")
![AI/ML+Physics Part 2: Curating Training Data [Physics Informed Machine Learning]](https://i.ytimg.com/vi/g-S0m2zcKUg/mqdefault.jpg "AI/ML+Physics Part 2: Curating Training Data [Physics Informed Machine Learning]
This video discusses the second stage of the machine learning process: (2) collecting and curating training data to inform the model. There are opportunities to incorporate physics into this stage of the process, such as data augmentation to incorporate known symmetries.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
03:02 Augmenting Data with Physics
04:16 Coordinates Matter!
06:38 Simulated vs Experimental Data
10:42 Big Data vs Diverse Data
12:48 Generalizing Models with Physics
16:31 Data is Expensive
17:42 Data is Biased
18:58 Rare Events
21:24 Small Signals
24:13 Galileo Dropped the Ball
27:10 Hidden Variables
29:22 Preview: Discovering Governing Equations
30:42 The Digital Twin
35:09 Outro")
