Data Science in Mechanics of Materials

Learning Objective:

Focus of this course is on exploring applications of data science to mechanics of materials related models and experiments. Emphasis on (a) hands on use of finite element related models for formulating data science problems (e.g. N-point correlation functions to describe material microstructures, data science procedures to formulate material constitutive behavior etc.) And (b) on correlating design of experiments with automated data extraction in high throughput experiments such as indentation experiments and sensor data fusion type of experiments. A third part of course is focused on analyzing available options in high volume data processing and analytics with emphasis on mechanics of materials applications.

Description:

By the end of course students are expected to understand fundamental insights into the following questions:

1. How different data science procedures are related to mechanics of materials simulations and how students can benefit from them in their own research?
2. How they can design high throughput experimental data collection to feed into data science based improvements?
3. How a combination of simulations and high throughput experiments can be useful for engineering problem solving?

The course is expected to fill gap between data science method development and realistic applications of data science by adopting a practical approach.

Spring 2025 Syllabus

Topics Covered:

• Introduction to data science, survey of data science methods in mechanics of Materials
• Feature engineering
  • Homework 1 Deliverable: FE data runs
• Regression including GPR and Bayesian Regression for limited data
  • Homework 2 Deliverable: GPR prediction of material properties based on limited FE runs
• Microstructure engineering based on PCA and SVM
  • Homework 3 Deliverable: PCA runs on deformed FE microstructures in PyMKS
• Neural networks
  • Homework 4 Deliverable: neural network applied to deformed FE microstructure images to predict deformation patterns
• Model validation approaches and corresponding statistics
  • Homework 5 Deliverable: predict accuracy of various homework predictions using discussed model accuracy metrices
• Deep learning approaches in mechanics
  • Homework 6 Deliverable: 5 slide presentation on a research paper using deep learning
• Approaches for time series forecasting
  • Homework 7 Deliverable: time series prediction of a given dataset and comparison of various methods
• Statistical issues including non-Gaussian processes and Markov chain

Prerequisites:

Necessary Background:

1. Mechanics of Materials and Structural Analysis
   1. Review websites:
      1. Undergraduate Mechanics:  http://web.mst.edu/~mecmovie/
      2. Graduate Mechanics: http://solidmechanics.org/
2. Linear Algebra
   1. Review Website: http://www.sosmath.com/matrix/matrix.html
3. MATLAB Tutorial
   1. http://www.mathworks.com/academia/student_center/tutorials/launchpad.html
4. ABAQUS basic software runs and basic python (basic training material will be provided in class)

Applied / Theory:

70/30

Web Address:

https://purdue.brightspace.com

Homework:

Homeworks will be strictly based on lectures

Projects:

Students choose their work related project. Instructor also provides a project.

Exams:

Take home exams

Textbooks:

Instructor provides notes and access to different state of the art resources.

Computer Requirements:

A normal laptop purchased within the last 3-4 years is okay.

We will use online Google collab. We will go through basic Python. Codes will be provided. Emphasis is on using ML in Python so no ground up coding experience necessary.