Module for Ab Initio Structure Evolution features

Neural network description of interatomic interactions
Evolutionary optimization of bulk, film, and nanoparticle structures
Analysis of structural properties

General information

MAISE is an open-source C code for parallel execution on Linux platforms. Current version is 2.1.
Input/output files generally follow VASP format.
Evolutionary search is implemented for crystals, films, or clusters.
Evolutionary optimization can be run with DFT (VASP), neural networks (MAISE), or classical potentials (MAISE, LAMMPS).
Neural networks are trained on energy/forces and use Behler-Parrinello symmetry functions.

Development team

Alexey Kolmogorov (developer, 2009-present)
Samad Hajinazar (co-developer, 2014-present)
Ernesto Sandoval (co-developer, 2016-present)

Recent news

Nov 2018 Neural networks are used to accelerate prediction of stable Mg-Ca alloys.
Aug 2018 MAISE and developed NN models are made publically available on Github.
Jan 2017 Stratified construction of NN models for multielement systems is developed.

Select MAISE predictions confirmed in joint experimental studies


A brand-new oP10 crystal structure predicted to be stable for FeB4 and CrB4 under ambient pressure. Both predictions [1a,2a] have been confirmed [3a,4a,5a]. FeB4 appears to be the first superconductor designed fully 'in silico' [1a,2a]: no compound was known at this Fe-B composition, oP10 was not observed before, and the predicted phonon-mediated pairing was not expected for an iron-containing material. The new material was also shown to be superhard. A lot of credit goes to my colleagues in Europe, especially to N. Dubrovinskaia and L. Dubrovinsky, who synthesized and characterized the material in a year-long series of challenging experiments. See APS Viewpoint article for more details.


An unexpectedly complex high-pressure tI56 crystal structure synthesized and solved for the CaB6 compound [6a,7a]. The new phase comprised of unfamiliar 24-boron atom building blocks was successfully quenched down to ambient conditions. The ground state structure was found with our evolutionary search without any structural parameter input, e.g. truly 'from scratch'. The study contains an extensive benchmark of different structure optimization strategies and illustrates the importance of the crossover operation in the evolutionary search for the success in the determination of particularly large systems.

Neural network features


Neural network-based interaction models fitted to ab initio data are generally more transferable than traditional classical potentials.
The group's focus has been on automating the construction of NN models that can be used in unconstrained structure searches.
We have introduced an evolutionary sampling approach to include configurations typically encountered in global searches.
We have also developed a stratified training scheme to fit NN models for compounds, starting from elements and proceeding to binaries and ternaries.

We have made all published NN models publically available on Github:
Mg, Ca, Cu, Pd, Ag, Mg-Ca, Cu-Pd, Cu-Ag, Pd-Ag, Cu-Pd-Ag
We welcome requests to develop NN models for prediction of stable alloys based on Na, Mg, Al, K, Ca, Cu, Pd, Ag, Pt, and Au.
Please contact Alexey Kolmogorov for more information.

Example of a two-layer NN with two inputs, two hidden layers, and an output. NN potentials used in global structure searches generally have 51-10-10-1 architectures per chemical element. The 51 NN inputs represent a given atomic environment, the two hidden layers have 10 neurons each, and the output produces energies, force components, or stress components.
Typically, we use about 10,000 structures per elemental, binary, or ternary reference data set which costs 10,000-30,000 CPU hours to generate. The fitting of NN's free parameters to energy and atomic force data takes about 3,000 CPU hours. We intentionally include structures with high energy to avoid seeing artificial minima in unconstrained structure searches. The resulting NN potentials have ~10 meV/atom accuracy. For simulation of 100-atom structures, NNs are 1,000-10,000 faster than DFT and ~100 slower than empirical potentials.


Evolutionary search features


Evolutionary methods are particularly suited for finding global minima in complex systems with a large number of degrees of freedom.
The EA is based on passing on beneficial traits to future generations via the survival of the fittest.
For compound prediction, atomic positions and unit cell parameters are used as genes that are swapped and mutated to produce offspring.
Efficient performance of EA requires the tuning of many parameters, such as generation size, selection criteria, crossover and mutation.
The following features are currently available for optimization of crystals, films, or clusters:
different evolution and selection options: crossover + mutation, pure mutation, or pure random search
detection and elimination of duplicate structures to avoid stagnation
start from random or predefined structures

The plot below illustrates a typical performance of the evolutionary search:
Search for the ground state for 1:4 and 1:2 Fe-B compoisitions. Each generation has 12 members fully relaxed with VASP.

For the system of about 10 atoms per unit cell the evolutionary search typically locates the ground states in 20-50 generations (240-600 VASP relaxations). In these Fe2B8 and Fe4B8 examples the EA search found brand new ground states noticeably lower in enthalpy than any known configuration listed in the ICSD. Note that the best member is always kept in the generation (green dots) while the population diversity (grey dots) is maintained through detection and elimination of the similar structures.


MAISE predictions confirmed in joint or independent experiments.

[ 1a] New superconducting and semiconducting Fe-B compounds predicted with an ab initio evolutionary search, Phys. Rev. Lett., 105, 217003 (2010)
[ 2a] Possible routes for synthesis of new boron-rich Fe-B and Fe(1-x)CrxB4 compounds, Appl. Phys. Lett., 98, 081901 (2011)
[ 3a] Structure, bonding, and possible superhardness of CrB4, Phys. Rev. B, 85, 144116 (2012)
[ 4a] Discovery of a superhard iron tetraboride superconductor, Phys. Rev. Lett., 111, 157002 (2013)
[ 5a] Viewpoint: Materials Prediction Scores a Hit, Physics 6, 109 (2013)
[ 6a] Pressure-driven evolution of the covalent network in CaB6, Phys. Rev. Lett., 109, 075501 (2012)
[ 7a] Stability and superconductivity of Ca-B phases at ambient and high pressure, Phys. Rev. B, 88, 014107 (2013)
[ 8a] Largest ab initio database for metal borides: prediction and analysis of compounds at ambient and high pressure, CALPHAD 46, 184 (2014)
[ 9a] Discovery of a new layered LiB predicted to be a close analog to the record-breaking MgB2 superconductor, Phys. Rev. B 92, 144110 (2015)
[10a] Prediction of a new NaSn2 phase (recently confirmed) with non-trivial topological properties, Sci. Rep. 6, 28369 (2016)

page updated Feb 2019