Skewnorms and comparing simulations to experiment data

What I did

• Monday: Wrote code for multi-shell feff configuring
• Tuesday: Ran simulations and averaging codes
• Wednesday: Wrote code for multi-moment gaussian weightings (i.e. control skew, kurtosis)
• Thursday: Got my multi-moment weightings code working
• Friday: Weekly meeting. Compared simulation data to experimental data to test the feff parameters.
• Saturday: Fine tuning method to create different gaussian weightings.
• Sunday: I figured out how to measure the MSD for the weighted spectra

What I learned

• Monday: My code shell definitions are different from what nearest neighbor coordinations shells actually are. My definitions are better for what I’m interested in testing though. (sensitivity testing)
• Tuesday: There is not much sensitivity difference between the 3rd and 4th shells (like 43 to 55 atoms)
• Wednesday: - skew = left tailed. + skew = right tailed. High kurtosis = high peakedness. low kurtosis = fat tails.
• Thursday: Still questioning whether to adjust all the new skewed distributions so that the peak is always at zero.
• Friday: Good agreement of simulatiosn with experimental data.
• Saturday: Because I have to create all possible combinations of 3 parameters and then sample values fro those spectra, my method is \(O(n^4) ...\) I’m trying to think of a clever trick to improve efficiency, but because I need all the combinations, the best I could probably do is \(O(n^3)\). It will probably take \(10 \times 10 \times 10 \times 85\) iterations. Not great. 10 to vary the mean, 10 to vary the variance, 10 to vary the skew, and the 85 calculations to do with each spectrum.
• Sunday:

\[MSD~for~averaged~spectrum = \left( \frac{1}{standardization~factor} \right) \sum_{shifts} \left( shift^2 \times (weighting factor) \right)\]

where

\[weighting~factor = Skewnorm(shift)\]

and

\[standardization~factor = \sum weighting~factors\]

What I will do next

• Generate the training data and start on the neural network