CSE 8803 / ME 8883 - Materials Informatics Course - Fall 2016

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20 Aug 2016

High-dimensional PES metamodel via DFT - Blog 2: High-dimensional kriging with modifications (Group:WangTran) - Report 21Sep16

CSE8803 / ME 8883 Materials Informatics

Fall 2016 Georgia Tech

Anh Tran and Zhiyu Wang

Before, we mentioned that the VASP simulation takes main input POSCAR, which describes the atoms location of Fe, Ti, H (depending on the system) and dumps output OUTCAR, which contains > 2000 lines. There is 1 line in OUTCAR containing the results, which is a decimal number. Last week we designed a shell script to quickly extract and synthesize the results, so that the inputs/outputs are purely numeric.

We have tentatively confirmed that swapping the position of Fe atom in Fe8H system will not affect the output. It seems to be a trivial observation, but the implication is profound. Namely, this observation is saying 8! input will yield the same result, so we can permutate the Fe position in every simulation.

8! = 40,320

This observation will allow us to reduce the impact of high-dimensional curse for our problem. However, for Fe2Ti2H2 system, we cannot use this observation anymore, as their permutation is only 2!2!2! = 8. We are planning to use kriging to meta-model this project, as this method also allows uncertainty quantification through mean-squared error.

One of the advantages of Kriging is the exact interpolation with adjustable correlation model. Here is an introductory description to kriging, as well as DACE (Design and Analysis of Computer Experiment) code, a widely used kriging toolbox with various correlation models and rigorous MATLAB code to some extent.

Here are the histograms of Fe atoms in x-, y-, and z-components. They are not uniformly distributed, so there is some part of missing data that we really want to capture. This is the first thing in our to-do list: redesign the sampling scheme, either by Latin hypercube sampling or stratified sampling to get a better histogram. However, it may have something to do with the initial position. We would have to check it again before proceeding to do this task.

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