Table 2 Atomic energy (E-), atomic force (F-), and stress (S-) RMSEs, as well as position (Pos.) and uncertainty (Unc.) auto-correlation times (ACTs) for MIL-53(Al) experiments conducted with posterior-based uncertainties

Experiment	E-RMSE	F-RMSE	S-RMSE	Pos. ACT^a	Unc. ACT^a
T = 600 K
random sel. (0 MPa)	1.62 ± 0.52	0.062 ± 0.002	145.3 ± 35.49	–	–
random sel. (250 MPa)	0.84 ± 0.09	0.057 ± 0.001	63.8 ± 15.82	–	–
unbiased MD (0 MPa)	1.17 ± 0.36	0.058 ± 0.002	90.81 ± 32.82	10.60 ± 9.54	88.05 ± 2.53
unbiased MD (250 MPa)	0.57 ± 0.05	0.052 ± 0.001	42.72 ± 1.37	2.08 ± 0.58	66.32 ± 2.02
Metadynamics (0 MPa)	0.58 ± 0.10	0.058 ± 0.002	74.83 ± 11.89	–	–
biased MD (0 MPa, τ = 0.5)	0.57 ± 0.08	0.051 ± 0.001	36.60 ± 1.46	2.75 ± 0.46	44.87 ± 14.08
T = 300 K
random sel. (0 MPa)	1.04 ± 0.26	0.058 ± 0.001	70.49 ± 6.61	–	–
random sel. (250 MPa)	0.58 ± 0.08	0.055 ± 0.002	52.19 ± 2.22	–	–
unbiased MD (0 MPa)	0.88 ± 0.20	0.056 ± 0.001	58.57 ± 5.94	3.45 ± 4.06	99.25 ± 10.34
unbiased MD (250 MPa)	0.48 ± 0.01	0.054 ± 0.000	39.88 ± 1.76	1.86 ± 0.14	54.56 ± 4.82
biased MD (0 MPa, τ = 0.5)	0.49 ± 0.09	0.052 ± 0.001	33.89 ± 3.06	42.92 ± 14.18	26.89 ± 8.94

^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-, F-, and S-RMSEs are reported for MLIPs obtained at the end of each experiment, while ACTs are computed using the entire trajectory sampled throughout the experiment. E-RMSE is given in meV atom⁻¹, F-RMSE in eV Å⁻¹, and S-RMSE in MPa. All E-RMSE, F-RMSE, and S-RMSE values are computed for the test data set obtained based on first principles MD trajectories at 600 K; see ref. ⁴¹. ACTs are provided in ps. 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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