Table 1 RMS errors in the predicted energies/forces for the individual Ta-V-Cr-W in-distribution subsystems.

Subsystem	MTP^a	GM-NN^b	EAM^a
TaV	1.94/0.050	1.54/0.029	32.0/0.404
TaCr	3.26/0.057	2.98/0.038	43.6/0.343
TaW	2.72/0.038	2.99/0.025	44.8/0.248
VCr	2.29/0.036	2.82/0.025	44.8/0.270
VW	2.50/0.037	2.00/0.023	21.3/0.292
CrW	4.35/0.041	2.87/0.029	23.4/0.248
TaVCr	2.43/0.054	1.97/0.045	34.1/0.313
TaVW	1.67/0.043	1.70/0.034	39.6/0.321
TaCrW	2.08/0.051	2.19/0.039	23.6/0.327
VCrW	1.37/0.040	1.94/0.031	19.4/0.314
TaVCrW (0 K)	2.09/0.049	2.16/0.037	50.8/0.488
TaVCrW (2500 K)	2.40/0.156	2.67/0.179	59.4/0.521
Overall	2.43/0.054	2.32/0.043	37.14/0.443

The results are provided for the MTP, GM-NN, and EAM models. Atomic energies are given in meV/atom, while forces are given in eV/Å. The best training result is written in boldface.
^aThe results for MTP and EAM are obtained by averaging over ten splits of the original data set, except for the deformed structures. The latter were obtained for all models trained on the whole data set (training + test).
^bFor GM-NN models, 500 structures were selected randomly from the respective training set to prevent overfitting using the early stopping technique⁵⁴. Thus, GM-NN models were trained on 500 structures less than MTP and EAM. This procedure was repeated ten times for each of the original data splits and resulted in averaging over 100 splits in total. For the deformed structures, the results are averaged over ten splits.
^cBinary structures are strained along the [100] direction and used as a part of the validation set. For different binaries, the strains are chosen based on certain accommodation rules (see ‘Methods’ section). The strains can vary up to 4.71%.

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