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

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20 Aug 2016

High-dimensional PES metamodel via DFT - Blog 7: Simulating and searching for the MEP on PES (Group:WangTran)

CSE8803 / ME 8883 Materials Informatics

Fall 2016 Georgia Tech

Anh Tran and Zhiyu Wang



As a fresh reminder, MEP refers to the minimum energy path, PES refers to the potential energy surface. These surfaces are high dimensional, and a suitable technique is needed to use against. Otherwise, it is hopeless to exhaustively search and reconstruct the PES. We use a special technique which combines permutation, sorting algorithm to help the meta model accurately locate the minima, not to mention the conjugate gradient (CG) method is running on the top of it. But since the CG methods can also be viewed as a direct method, we regard it as a sub-solver to achieve the goal of searching for local minima.

Back to where we are, we are at the stage of running simulation on PACE, which has been for almost 10 days. The code is slow, due to MATLAB construction. MATLAB is good for prototyping, but is never good for running actual exercise on high-performance cluster (HPC). There are many more techniques to accelerate, but since the algorithm is pre-constructed by our former members, we just use it as is.

The algorithm benchmark was performed on two numerical testing functions, Rastrigin and Schwefel functions – two widely used testing functions in optimization, genetic, and searching algorithm. The results are promising, in the way that the algorithm can locate local minima and climb the curve up to the saddle point. We are looking forward to move on to the titanium alloy system, where there are more locally stable configurations, compared to the bcc iron system.

Here are some preliminary results for testing potential function, including LEPS, Rastrigin, and Schwefel. Among all of them, only the LEPS has physical meaning, where the other 2 aims to test the fundamental construction of the algorithm

LEPS

LEPSa.png

LEPSb.png

Rastrigin

Rastrigina.png

Rastriginb.png

Schwefel

Schwefela.png

Schwefelb.png

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