Examples

Overview

Start with the following notebooks if you are new to PyMKS.

• PyMKS Introduction
  • Reading the Experimental Data
  • Calculating the 2-point Stats
  • Multiple Synthetic Microstructures
  • Principle Component Analysis
  • References
• PyMKS (Dask) Introduction
  • Quantify Microstructures using 2-Point Statistics
  • Predict Homogenized Properties
  • Predict Local Properties
• Checkerboard Microstructure
  • Introduction - What are 2-Point Spatial Correlations (also called 2-Point Statistics)?
  • 2-Point Statistics for Checkerboard Microstructure
  • Compute Periodic 2-Point Statistics
  • Compute Non-Periodic 2-Point Statistics
  • References

Homogenization

• Effective Stiffness of a Composite Material
  • Introduction
  • Linear Elasticity and Effective Elastic Modulus
  • Data Generation
  • View Microstructures
  • Homogenization Workflow
  • Modeling
  • Visualize the task graph
  • Observing variance changes with components
  • Optimize hyper-parameters
  • Check the low-dimensional representation
  • Prediction using Homogenization Pipeline
  • References
• Effective Stiffness of Fiber Composite
  • Introduction
  • Data Generation
  • View Microstructures
  • The Model
  • Training and testing data sets
  • Visualize the task graph
  • Cross Validation
  • Structures in PCA space
  • Parity Plot
• Using GraSPI
  • Reproduce Previous Work
  • Generate Microstructures to Test Speed
  • Using Pipelines

Localization

• Linear Elasticity in 2D
  • Introduction
  • Modeling with MKS
  • Resizing the Coefficients to use on Larger Microstructures
  • References
• Linear Elasticity in 2D for 3 Phases
  • Introduction
  • Modeling with MKS
  • Resizing the Coefficeints to use on Larger Microstructures
  • References
• Linear Elasticity in 3D
  • Introduction
  • Modeling with MKS
  • Resizing the Coefficeints to use on Larger Microstructures
  • References
• Filter Example
• Cahn-Hilliard Example
  • Cahn-Hilliard Equation
  • Calibration Datasets
  • Predict Microstructure Evolution
• Cahn-Hilliard with Primitive and Legendre Bases
  • Cahn-Hilliard Equation
  • Basis Functions for the Microstructure Function and Influence Function