Table 1 CV space coverage, atomic energy (E-) and atomic force (F-) RMSEs, as well as position (Pos.) and uncertainty (Unc.) auto-correlation times (ACTs) for alanine dipeptide experiments conducted with posterior-based uncertainties

Experiment	CV space cov.	E-RMSE	F-RMSE	Pos. ACT^a	Unc. ACT^a
random sel. (300 K)	0.58 ± 0.03	34.09 ± 6.29	0.191 ± 0.019	–	–
random sel. (600 K)	0.76 ± 0.04	31.44 ± 4.77	0.143 ± 0.015	–	–
random sel. (1200 K)	0.95 ± 0.01	19.83 ± 4.62	0.116 ± 0.017	–	–
unbiased MD (300 K)	0.58 ± 0.03	30.29 ± 5.47	0.149 ± 0.019	2.07 ± 0.11	327.11 ± 8.69
unbiased MD (600 K)	0.89 ± 0.00	26.03 ± 2.23	0.116 ± 0.012	1.23 ± 0.02	257.88 ± 22.01
unbiased MD (1200 K)	0.97 ± 0.01	1.47 ± 0.09	0.055 ± 0.002	0.74 ± 0.02	21.41 ± 4.91
biased MD (300 K, τ = 0.25, w. H)	0.87 ± 0.02	5.09 ± 5.40	0.082 ± 0.016	2.08 ± 0.13	19.38 ± 7.42
biased MD (300 K, τ = 0.25, w/o. H)	0.94 ± 0.01	1.97 ± 0.88	0.071 ± 0.003	0.69 ± 0.04	52.79 ± 19.40

^aACTs computed for experiments with the random selection (random sel.) strategy are excluded from the analysis because different approaches may introduce systematic biases, making the comparison unreliable.
E- and F-RMSEs are reported for MLIPs obtained at the end of each experiment, while CV space coverage and ACTs are computed using the entire trajectory obtained throughout the experiment. E-RMSE is given in meV atom⁻¹, while F-RMSE is in eV Å⁻¹. All E-RMSE and F-RMSE values are computed for the test data set obtained from a long MD trajectory at 1200 K; see Methods. ACTs are provided in ps. For biased MD, we compare two cases: one with (w.) biasing hydrogen atoms and one without (w/o.). We also compare biased and unbiased MD with experiments that involve the random selection (random sel.) strategy for acquiring training data. The best performance is highlighted in bold, and the second-best performance is underlined.

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