Efficient Crystal Structure Prediction using Universal Neural Network Potential and Genetic Algorithm ○Takuya Shibayama, Hideaki Imamura, Katsuhiko Nishimra, Chikashi Shinagawa, So Takamoto Preferred Networks, Inc.

2 ● CSP is a method to discover new materials using quantum chemistry calculations. ● Genetic algorithms (GA) are widely used as the search algorithm. ● Neural network potentials (NNP) have started to be used for CSP. Problems: ● The computational cost of the density function theory (DFT) calculations is expensive. It takes weeks with a supercomputer to reproduce phase diagram of binary or ternary systems. ● The accuracy of some NNPs are not enough for capturing small differences of formation energy of crystals. ● Some NNPs support only limited range of elements, which will become problem when applying CSP to different multi-element systems. Crystal Structure Prediction (CSP) We need to cover wide parameter space to reconstruct phase diagrams.

3 Universal NNP for 72 elements and various systems. No fine-tuning is required. Much faster than DFT : 0.3 seconds for 3000 Pt system with single V100 GPU. Universal NNP: PreFerred Potential (PFP) From https://matlantis.com S. Takamoto et al., Nat. Commun., 2022, 13, 299 Energy above hull comparison with DFT (using Materials Project structures) Related presentation: “Neural Network Potential for Arbitrary Combination of 72 Elements Trained Against Large Scale Dataset” DS06.05.03 (Nov 28, 3:00 PM) Visit Booth #523 of Preferred Computational Chemistry VASP [eV/atom] PFP [eV/atom] MAE = 28 meV/atom

4 Method Overview Structure Sampling Structure Relaxation Evaluation Energy eval. Evaluation First‐principle calculation DFT Software Select hull-breaking structures 💎 New Crystal 💎 Energy Genetic Algorithms Universal NNP “PFP” We developed a CSP system using PFP to search for new crystals and reconstruct phase diagrams. The resultant crystal structures on the convex hull are evaluated with DFT calculations. Target: Reconstruction of phase diagram, discovery of new crystals

5 Proposed Method: The main idea (1) Enable a massive number of trial evaluations ● Fast structure relaxation by PFP ● Large-scale parallel computation using the genetic algorithm ● But, the existing method sticks to the most stable composition in the given elemental system. ● Rather than focusing the search on stable compositions, we want to deeply explore a wide range of compositions. Update the entire convex hull in the composition-energy space

6 Proposed Method: The main idea (2) ● Updating the entire convex hull in the composition-energy space is similar to the approximation of the Pareto front in multi-objective optimization field. Utilize the insights of multi-objective optimization in CSP Objective 1 Objective 2 Multi-objective optimization The point on the Pareto-front Composition Energy Crystal Structure Prediction The structures on the convex hull

7 Proposed Method: How Select the Elite Population? ● The proposed method allows for the exploration of structures of various compositions as the generations change. Ti-O search by proposed method Gen #0 Gen #50 Gen #100 Gen #137 (last) Ti-O search by existing method Gen #0 Gen #50 Gen #100 Gen #137 (last)

8 Proposed Method: How Perform Crossover/Mutation? We have devised the crossover/mutation in the following way. Variable heredity crossover ● Modified to allow crossover between parent structures with different atomic numbers and the generation of child structures with different atomic numbers. Remove random atom mutation ● Generates a child structure by randomly removing one of the atoms in the parent structure. Generate random structure mutation ● Generates a child structure by random.

9 ● We conducted CSP searches for binary and ternary systems. ● The condition of local optimization is 0K and 0Pa. ● No structures of Materials Project (MP) is used for the search. ● 10,000 trials finish in about 100 min. The total search time is 10-20 hours with 10 GPUs. ● Resultant structures on the hull are evaluated with DFT calculations. Experiment Settings Main search Pre search for each binary Trials 50,000 10,000 Population size 128 32 Max # of atoms 64 64 Parallelism (# of workers) 100 30 # of GPUs 10 3 We used NVIDIA V100 GPUs in our in-house supercomputer MN-2.

10 ● The phase diagrams produced by CSP show good consistency with the known ones of Materials Project. Red areas of the figure below show updated part. ● We discovered new crystals with lower energy than known convex hull of MP in different element systems. Some of them updates the hull by more than 10 meV/atom. Results: Phase Diagrams ー MP ー Our CSP ■ New In-Li Ga-Au-Ca Ti-Sr-O Below MP hull Above MP hull Materials Project Our CSP Materials Project Our CSP

11 ● Our CSP can handle nitrides, transition metal oxides, phosphides and phosphates without changing or fine-tuning the NNP. ● Hubbard U correction and GGA/GGA+U mixing correction are applied for transition metal oxides. Results: Different Chemical Species Mn-Mo-N W-Ti-N Fe-P-O Below MP hull Above MP hull

12 Results: Crystal Structures Updating Known Ones New Ti2O Known Ti2O New Ca3P2 Known Ca3P2 New Al2MnCu Known Al2MnCu ● New Ti2O and Al2MnCu have different repeating patterns from the known ones. New structures look reasonable and have lower energy with DFT. ● We have only checked the Materials Project. These structures may be known in other datasets.

13 13 new crystals are found below the MP hull. AuCaGa3 updates the known hull of Materials Project by 39 meV/atom. Ga-Au-Ca System New AuCaGa3 (39 meV/atom below the hull) New Au5CaGa (24 meV/atom below the hull) New Au3Ca (28 meV/atom below the hull)

14 ● Different objective functions can be applied for CSP search such as similarity to an experimental X-ray diffraction (XRD) pattern. ● Our test search successfully find a crystal structure with XRD pattern close to the target one. Composition ratio can be restricted according to a XRF measurement. ● Crystal structures corresponding to a XRD pattern can be reproduced numerically without using database. Discussion target result Reconstructed crystal structure 2θ[degree] Intensity This is a collaborative study with Gen Tamaki in a summer internship 2023 Ref: Lee et al., Nat. Comp. Mat. 2023

15 ● We developed a CSP system without database using GA and universal NNP “PFP”, and showed that PFP has high enough accuracy to search known and new stable crystal structures. ● Our system can reproduce ternary phase diagram in 10-20 hours with 10 NVIDIA V100 GPUs. ● We propose a novel sampling algorithm by extending NSGA-III algorithm, which enables an efficient search of whole composition ratio. Mutation and crossover operations of GA are implemented to handle variable atom number. ● The objective function can be set to other variables such as XRD similarity and search crystal structures matching experimental data. Next Steps ● Improving the reproducibility of MP phase diagram. ● Applying CSP to 4 or 5 element system. ● Finite temperature and finite pressure. ● Utilizing meta-stable structures. ● Checking other databases. Summary Newly found TiW2N4