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-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
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.