The Atomic Simulation Environment and genetic algorithms

Transcription

1 The Atomic Simulation Environment and genetic algorithms Steen Lysgaard Department of energy conversion and storage Technical University of Denmark

2 Outline Genetic algorithms (GA) in materials science The GA in the Atomic Simulation Environment (ASE) Alloy nanoparticles (Cu-Ni, Cu-Au) Combining machine learning with GA More examples at ASE website (bulk systems for ammonia storage, small particles on support) Quick intro to ASE Introduction to the following tutorial 2

3 GA intro Very simple principle based on natural selection Random initial population Define fitness function (stability, storage capacity, band gap, mechanical property) Selection of fittest candidates Procreation operators Population evolves 3

4 GA advanced Jennings, Lysgaard, Hummelshøj, Vegge, Bligaard (in preparation) 4

5 GA in materials science Two major areas where GAs have been employed in materials science Nanoparticles / nanoalloys Crystal structure prediction Deaven and Ho, Phys Rev Lett. 75, 288 (1995) Johnston, Ferrando, Fortunelli... Prediction of crystal structure from composition [1, 2, 3] [1] Glass, Oganov and Hansen, Comput. Phys. Commun., 2006, 175, [2] Abraham and Probert, Phys. Rev. B, 2006, 73, [3] Trimarchi and Zunger, Phys. Rev. B, 2007, 75,

6 When to use genetic algorithms? When a complete sampling is not possible Massive materials combinations (multiple mixing elements) Structural prediction Corrugated energy landscapes Geometrical relaxation possible Any parameter can be optimized 6

7 Genetic algorithms for nanoparticle alloys Population Operators Initial Population Generation Crossover 3. Mutate/Permutate com2surf poor2rich... Ranked according to fitness Evaluation Lysgaard, Landis, Bligaard, Vegge, Topics in Catalysis 57, 33 (2014) 7

8 Optimizing a 309 atom Cu-Ni nanoparticle fixed composition Tailored operators needed when search space is large The GA shows the development of an icosahedral structure with a Cu skin for a 50:50 composition Dynamic operators are more efficient Lysgaard, Landis, Bligaard, Vegge, Topics in Catalysis 57, 33 (2014) 8

9 Optimizing a 309 atom Cu-Ni nanoparticle fixed composition Tailored operators needed when search space is large The GA shows the development of an icosahedral structure with a Cu skin for a 50:50 composition Dynamic operators are more efficient Lysgaard, Landis, Bligaard, Vegge, Topics in Catalysis 57, 33 (2014) 9

10 Cu-Au nanoparticles variable composition E mix =E (Cu x Au y ) E (Cu 309) x E ( Au 309) y N N Cu Au Lysgaard, Hansen, Myrdal, Vegge, Phys. Chem. Chem. Phys. 17, (2015) 10

11 Cu-Au nanoparticles variable composition Lysgaard, Hansen, Myrdal, Vegge, Phys. Chem. Chem. Phys. 17, (2015) 11

12 Cu-Au nanoparticles variable composition Lysgaard, Hansen, Myrdal, Vegge, Phys. Chem. Chem. Phys. 17, (2015) 12

13 Cu-Au nanoparticles variable composition Unfortunately the Au-Cu clusters tend to retain the scaling relation for steps Lysgaard, Hansen, Myrdal, Vegge, Phys. Chem. Chem. Phys. 17, (2015) 13

14 Combining Machine Learning and GA Five repetitions to check the robustness 104 Serial GA # Energy evaluations 10 3 Niching GA 102 Veto GA MLGA 101 MLaGA 100 Pt Jennings, Lysgaard, Hummelshøj, Vegge, Bligaard (in preparation) Au 20

15 Combining Machine Learning and GA Identification of the convex hull with the different approaches MLaGA: ~250 x speed-up Emix Pt Jennings, Lysgaard, Hummelshøj, Vegge, Bligaard (in preparation) Au 21

16 Atomic simulation environment A Python library for working with atoms 22

17 Atomic simulation environment An object-oriented scripting interface to a legacy electronic structure code, Sune R. Bahn and Karsten W. Jacobsen, Comput. Sci. Eng., Vol. 4, 56-66, 2002 The Atomic Simulation Environment A Python library for working with atoms, Ask Hjorth Larsen, Jens Jørgen Mortensen, Jakob Blomqvist, Ivano E. Castelli, Rune Christensen, Marcin Dulak, Jesper Friis, Michael N. Groves, Bjørk Hammer, Cory Hargus, Eric D. Hermes, Paul C. Jennings, Peter Bjerre Jensen, Kristen Kaasbjerg, James Kermode, John R. Kitchin, Esben Leonhard Kolsbjerg, Joseph Kubal, Steen Lysgaard, Jón Bergmann Maronsson, Tristan Maxson, Thomas Olsen, Lars Pastewka, Andrew Peterson, Carsten Rostgaard, Jakob Schiøtz, Ole Schütt, Mikkel Strange, Kristian Thygesen, Tejs Vegge, Lasse Vilhelmsen, Michael Walter, Zhenhua Zeng, and Karsten Wedel Jacobsen, Journal of Physics: Condensed Matter, 29 (2017)

18 A small example 24

19 Calculators in ASE 25

20 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Real use: looking for catalysts to break the scaling relations 26

21 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Number of combinations N = 24 16,777,216 candidates (symmetry not accounted for) Brute force search not relevant, intelligent search is necessary N N! i! ( N i)! i=0 27

22 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Number of combinations Population type Rank based across composition All compositions equally likely to evolve Constructive interplay due to similar chemical ordering 28

23 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Number of combinations Population type Rank based across composition All compositions equally likely to evolve Constructive interplay due to similar chemical ordering 29

24 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Number of combinations Population type Operators Cut-splice crossover Permutation Substitution 30

25 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Number of combinations Population type Operators Duplicate detection Avoid superfluous calculations Keep population diverse 31

26 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Number of combinations Population type Operators Duplicate detection Convex hull 32

27 Tutorial on ASE GA Goal: Determine the convex hull of a binary alloy slab Toofget started with the tutorial go to: Number combinations nomad-handson.github.io Population type Operators Thanks for the attention Good luck! Duplicate detection Convex hull 33

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