Ti-2021-08-04-all-icsd

The current structure dataset comprises 13531 structures generated from unique ICSD prototype structures composed of single elements with zero oxidation state. A more detailed procedure is found in Phys. Rev. B 99, 214108 (2019). The procedure to estimate interatomic potentials from the dataset is found in Phys. Rev. B 99, 214108 (2019) and Phys. Rev. B 102, 174104 (2020).

Improvement from **-dataset-10000-all-icsd

• More robust for structures with a small interatomic distance

• More robust for structures with a large interatomic distance

• More complex potential models are included.

• MLPs are estimated without using DFT stress tensors.

• MLPs are estimated by using small regression weights for energetically unstable structures.

Predictions using Pareto optimal MLPs

The cohesive energy and volume are obtained by performing a local structure optimization from the DFT equilibrium structure. In addition, the DFT equilibrium structure is obtained by optimizing a prototype structure included in ICSD, and the prototype is used as the structure legend in the figure. Therefore, the structure type of the converged structure is sometimes different from that shown in the legend even if the potential energy surface predicted by MLP is almost the same as the true one.

The other properties predicted by each Pareto optimal MLP are available from column Predictions in the following table.

Ti-2021-08-04-all-icsd shows large prediction errors. They should be carefully used. Such an MLP is often accurate for reasonable structures, but it is not accurate for unrealistic structures.

Pareto optimals

Name	Time [ms] (1core/36cores)	RMSE [meV/atom]/[eV/A]	Predictions	Files
pair-14	0.017 / 0.038	40.739 / 0.3140	–	–
pair-27	0.018 / 0.005	37.078 / 0.2923	–	–
pair-28	0.027 / 0.007	36.943 / 0.2927	–	–
pair-18	0.033 / 0.017	34.786 / 0.2987	–	–
pair-31	0.050 / 0.007	33.826 / 0.2810	–	–
pair-32	0.051 / 0.010	32.626 / 0.2806	–	–
pair-33	0.069 / 0.012	31.965 / 0.2819	–	–
pair-37	0.136 / 0.018	27.536 / 0.2664	–	–
pair-38	0.171 / 0.022	27.317 / 0.2658	–	–
gtinv-300	0.228 / 0.023	11.732 / 0.1654	–	–
gtinv-235	0.281 / 0.023	11.266 / 0.1593	–	–
gtinv-312	0.472 / 0.036	8.8905 / 0.1570	predictions	mlp.lammps input log
gtinv-190	0.523 / 0.038	8.5320 / 0.1488	predictions	mlp.lammps input log
gtinv-301	0.743 / 0.062	7.6462 / 0.1472	predictions	mlp.lammps input log
gtinv-236	0.804 / 0.059	7.3916 / 0.1408	predictions	mlp.lammps input log
gtinv-171	0.818 / 0.060	7.3368 / 0.1412	predictions	mlp.lammps input log
gtinv-172	1.152 / 0.075	5.9662 / 0.1281	predictions	mlp.lammps input log
gtinv-237	1.177 / 0.073	5.9225 / 0.1275	predictions	mlp.lammps input log
gtinv-173	1.686 / 0.115	5.8945 / 0.1330	predictions	mlp.lammps input log
gtinv-174	1.973 / 0.134	5.0020 / 0.1228	predictions	mlp.lammps input log
gtinv-239	2.057 / 0.133	4.9880 / 0.1222	predictions	mlp.lammps input log
gtinv-197	2.819 / 0.158	4.9723 / 0.1231	predictions	mlp.lammps input log
gtinv-262	2.839 / 0.166	4.8880 / 0.1225	predictions	mlp.lammps input log
gtinv-194	3.908 / 0.240	4.4188 / 0.1147	predictions	mlp.lammps input log
gtinv-264	5.489 / 0.315	4.3144 / 0.1165	predictions	mlp.lammps input log
gtinv-224	14.066 / 0.687	4.0217 / 0.1123	predictions	mlp.lammps input log
gtinv-294	17.107 / 0.825	3.9952 / 0.1144	predictions	mlp.lammps input log

Column “Time” shows the time required to compute the energy and forces for 1 MD step and 1 atom, which is estimated from a simulation of 10 runs for a structure with 284 atoms using a workstation with Intel(R) Xeon(R) CPU E5-2695 v4 @ 2.10GHz. Note that the MLPs should be carefully used for extreme structures. The MLPs often return meaningless values for them.

• All Pareto optimal MLPs are available here.