Pinned Grain Growth Progress Report IV

Posted by Fred Hohman, David Montes de Oca Zapiain on November 23, 2015

Outline

• Meeting with domain experts outcome
• Image segmentation revisited
• Chord length distribution expanded

• PCA input plots
• PCA output plots
• Preliminary regression results
• What’s next?

Outcome from Meeting with Domain Experts

• Meeting with a computational scientist in the area of multiscale modeling @ Sandia National Lab.

• Extremely useful meeting after which we added 2 more classes to the current simulation pool we had before.

Rolling:

Random Distribution with Random Shapes:

Obtaining Grain Boundary and Precipitates Revisited

• Image of old image segmentation algorithm

Obtaining Grain Boundary and Precipitates Revisited

• Image of new image segmentation algorithm

Chord Length Distribution Extraction Expanded

• First decided to not use the average Chord Length distribution.
• We normalized the distribution such that the area under the curve is equal to 1.
• At this point this chord length tells us the probability of finding a chord of length “X” within our MS, nevertheless it is not enough.
• We needed to add something that accounts, “weighs” more the chords of bigger size.

Chord Length Distribution Extraction Expanded

• Thus by multiplying the frequency of each chord by its size and normalizing it again, the bigger chords now have a “bigger weight” in the distribution.

PCA Input

• PACE job using 64GB of memory
• Data matrix size (n_simulations,27000000) where n_simulations=220
• 220 is the total number of simulations we were able to perform during semester

PCA Input Screen Plot

• More than 95% variance captured in first 5 PC values

PCA Output

• Chord length distributions (in general) cleaned up after new segmentation code
• Data matrix size (n_simulations, 299) where n_simulations=220

PCA Output Screen Plot

• More than 95% variance captured in first 3 PC values

Regression Test

• We now have two .m files containing our PC values for both the inputs and outputs of our model
• Used “hacked” Scikit-Learn/PyMKS module to perform linear regression on our PC values
• Objective: predict chord length distribution given a new precipitate distribution
• We can calculate the R-square value for a give combination of polynomial degree and number of PC values used
• Can create plot showing all combinations of a given set of values in degree and n_components

(Thanks David Brough!)

Regression Test

• Using all simulations (220)

Regression Test Results

• Order of Polynomial: 2
• Number of Components: 3
• R-squared Value: 0.708516065498

Next Steps

1. Further analysis on selecting input and output of our model