Data-Driven Design & Analysis of Structures & Materials (3dasm)

Miguel A. Bessa | miguel_bessa@brown.edu | Associate Professor

Introduction

What: This course aims to be an introduction to machine learning from a probabilistic perspective.

Where: This notebook comes from this repository

Reference: Murphy, Kevin P. Probabilistic machine learning: an introduction. MIT press, 2022. Available online here

How: We try to follow Murphy's book closely, but the sequence of Chapters and Sections is different. The intention is to use notebooks as an introduction to the topic and Murphy's book as a resource.

• If working offline: Go through this notebook and read the book.
• If attending class in person: listen to me (!) but also go through the notebook in your laptop at the same time. Read the book.
• If attending lectures remotely: listen to me (!) via Zoom and (ideally) use two screens where you have the notebook open in 1 screen and you see the lectures on the other. Read the book.

Folder structure

• The "Lectures" folder contains each lecture in a separate folder "LectureX" where X is the lecture number.
• Each "LectureX" folder contains:
  1. A jupyter notebook "3dasm_LectureX.ipynb" that you can run locally or in servers like Google Colab.
  2. A pdf "3dasm_LectureX slides.pdf" with the slides of that lecture.
  3. A "your_data" folder that you can use to create data or other things in your own computer.
• The preferred method to follow the course is to look directly into the jupyter notebook, as it contains additional notes and working code.

Grading

Homeworks 30%, Midterm 30%, and Final Project 40%.

Homeworks will be graded only with 5 levels: A+ (100%; fully correct), A (90%; has minor error), B (75%; has significant error), C (60%; mostly incorrect but homework was delivered), D (0%, not delivered). If you deliver something with an honest attempt at solving the homework you get 60% for that homework.

Note

Late Homework can only get up to A (90%).

The worst Homework is removed from the final grade.

Course outline

DATE	SUBJECT	Notebook	PDF	Homework	Colab
Wed 9/4	Introduction: Basics of univariate statistics	Lecture 1	Slides	HW1 assigned
Fri 9/6	Practical tutorial: Handling data with Pandas	Lecture 2	Slides
Mon 9/9	Bayes' rule: joint & conditional distributions	Lecture 3	Slides
Wed 9/11	Multivariate statistics: visualization of joint & conditional distributions	Lecture 4	Slides	HW1 due & HW2 assigned
Fri 9/13	Bayesian inference for one hidden rv: Example with Gaussian likelihood and Uniform prior (Part I)	Lecture 5	Slides
Mon 9/16	Bayesian inference for one hidden rv: Example with Gaussian likelihood and Uniform prior (Part II)	Lecture 6	Slides
Wed 9/18	Bayesian inference for one hidden rv: Redo example but now with Gaussian prior	Lecture 7	Slides	HW2 due & HW3 assigned
Fri 9/20	Machine Learning without going Bayesian: Point Estimates	Lecture 8	Slides
Mon 9/23	Linear Regression: Practical tutorial (Part I: noiseless 1D example; underfitting vs. overfitting; interpolation vs. extrapolation)	Lecture 9	Slides
Wed 9/25	Linear Regression: Practical tutorial (Part II: noiseless vs. noisy datasets; train/test dataset split; multi-dimensional example)	Lecture 10	Slides	HW3 due & HW4 assigned
Fri 9/27	Linear Regression: Linear Least Squares model (Gaussian likelihood, Uniform prior, and Point Estimate)	Lecture 11	Slides
Mon 9/30	Linear Regression: Ridge, Lasso and Bayesian linear regression models (different likelihoods, priors and posteriors)	Lecture 12	Slides
Wed 10/2	Gaussian process regression: theory	Lecture 13	Slides	HW4 due & HW5 assigned
Fri 10/4	Gaussian process regression: One dimensional tutorial (Part I: noiseless)	Lecture 14	Slides
Mon 10/7	Gaussian process regression: One dimensional tutorial (Part II: noisy)	Lecture 14 (continued)	Slides
Wed 10/9	Gaussian process regression: Multidimensional tutorial & importance of dataset scaling	Lecture 15	Slides	HW5 due & HW6 assigned
Fri 10/11	Bayesian model selection & Hyperparameter optimization	Lecture 16	Slides
Mon 10/14	HOLIDAY 🥹
Wed 10/16	Q&A session			HW6 due
Fri 10/18	MIDTERM Exam 🦾
Mon 10/21	Framework for Data-Driven Design & Analysis of Structures & Materials: f3dasm	Lecture 17	Slides
Wed 10/23	f3dasm tutorial: Data-driven process; Sampling methods; Simple model selection example	Lecture 18	Slides	HW7 assigned
Fri 10/25	f3dasm tutorial: General use case (object oriented)	Lecture 19	Slides
Mon 10/28	Final Project Overview & Assignment 🦾	Lecture 20	Slides	Final Project assigned
Wed 10/30	Introduction to classification: Tutorial with 3 simple classifiers on Iris dataset	Lecture 21	Slides	HW7 due & HW8 assigned
Fri 11/1	Logistic regression classifier: Classification as a regression task; Bernoulli observation distribution; the sigmoid trick	Lecture 22	Slides
Mon 11/4	Logistic regression classifier: Point estimate (e.g. MLE) as nonlinear optimization; classification as the mode of PPD	Lecture 22 (continued)	Slides
Wed 11/6	Gaussian discriminant analysis (GDA) classifier: Classification by a generative model	Lecture 23	Slides	HW8 due & HW9 assigned
Fri 11/8	Optimization: Part I	Lecture 24	Slides
Mon 11/11	Optimization: Part II	Lecture 25	Slides
Wed 11/13	Optimization: Part III	Lecture 26	Slides
Fri 11/15	Artificial Neural Networks: Part I	Lecture 27	Slides
Mon 11/18	Artificial Neural Networks: Part II	Lecture 28	Slides
Wed 11/20	Artificial Neural Networks: Part III	Lecture 29	Slides	HW9 due
Fri 11/22	Artificial Neural Networks: Part IV	Lecture 30	Slides
Mon 11/25	Thanksgiving week 🦃
Wed 11/27	Thanksgiving week 🦃
Fri 11/29	Thanksgiving week 🦃
Mon 12/02	TBD	Lecture 31	Slides
Wed 12/04	TBD	Lecture 32	Slides
Fri 12/06	Final Project presentations 🦾			Final Project report due

Installation instructions

OPTION 1. Run this notebook locally in your computer:

Homework 1 contains detailed instructions to install the virtual environment with all the packages required for this course. Below are more concise instructions for people familiar with installing mamba and tensorflow:

1. Install Mamba as described here. (See Homework 1 for additional instructions)
2. Install Jupyter notebook and extensions in base environment

mamba install -c anaconda notebook nb_conda rise

3. Create a virtual enviroment for this course called '3dasm':

mamba create -n 3dasm python==3.10 numpy scipy matplotlib pandas scikit-learn ipykernel ipywidgets f3dasm

4. Install git, open command window & clone the repository to your computer:

git clone https://github.com/bessagroup/3dasm_course

5. Install tensorflow in the '3dasm' virtual environment. (See Homework 1 for additional instructions)

6. Install scikeras in '3dasm' virtual environment:

mamba activate 3dasm
pip install scikeras

After you installed every package, you are ready to go!

• Open a (mamba) command window and load jupyter notebook (it will open in your internet browser):

jupyter notebook

• Open notebook (for example: 3dasm_course/Lectures/Lecture1/3dasm_Lecture1.ipynb) and choose the '3dasm' kernel.

You're all set!

OPTION 2. Use Google's Colab (no installation required, but times out if idle):

1. go to Google Colab
2. Login with your credentials
3. File > Open notebook
4. Click on Github (no need to login or authorize anything)
5. paste the git link: https://github.com/bessagroup/3dasm_course
6. click search and then click on the notebook (for example: 3dasm_course/Lectures/Lecture1/3dasm_Lecture1.ipynb)