stat.APMar 23, 2026

Data Curation for Machine Learning Interatomic Potentials by Determinantal Point Processes

Authors: Joanna Zou, Youssef Marzouk

Organizations: Computational Science & Engineering Massachusetts Institute of Technology Cambridge, MA, 02139, USA

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Abstract

The development of machine learning interatomic potentials faces a critical computational bottleneck with the generation and labeling of useful training datasets. We present a novel application of determinantal point processes (DPPs) to the task of selecting informative subsets of atomic configurations to label with reference energies and forces from costly quantum mechanical methods. Through experiments with hafnium oxide data, we show that DPPs are competitive with existing approaches to constructing compact but diverse training sets by utilizing kernels of molecular descriptors, leading to improved accuracy and robustness in machine learning representations of molecular systems. Our work identifies promising directions to employ DPPs for unsupervised training data curation with heterogeneous or multimodal data, or in online active learning schemes for iterative data augmentation during molecular dynamics simulation.

Figures & tables

Figure 1: Sample subsets drawn with each method from a MD trajectory of alanine dipeptide.
Figure 2: RMSE and R2R^{2} values of energy predictions on the validation set by the MLIP trained on set size NN . The center point denotes the median value and rangebars denote the 25th to 75th percentile over 100 trials.
Figure 3: Distribution of energies and force amplitudes of 1160 selected configurations.
Figure 4: Relative error in energy predictions on the test set by an MLIP trained on a 1160-element set. Errors in Hf 2 , Hf, O 2 , and O have been truncated to visualize the main mass of the distribution.
Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

AlgorithmPrimary ReferenceSimilarity MetricSubset SizeType
SRS–NoneVariableProbabilistic
kk -means clusteringHuan et al. (2017)Euclidean distance in descriptor spaceVariableProbabilistic
MaxVolPodryabinkin and Shapeev (2017)Fisher information matrixFixedDeterministic
Entropy max.Karabin and Perez (2020)Entropy functionVariableDeterministic
fixed-size DPPThis workPSD kernelVariableProbabilistic
Appendix
Table 1: Review of data subselection algorithms for ML-IPs in literature.
indexMP IDsetno. configurationsno. Hfno. O
1–HfO 2 figshare20523672
2352HfO 2 EOS 1D30048
3550893HfO 2 EOS 1D13112
4550893HfO 2 EOS 6D2762012
5–HfO gas12911
6–HfO EOS 1D1496911
Appendix
Table 2: Training/validation set of hafnium dioxide (HfO 2 ) and hafnium monoxide (HfO) configurations.
indexMP IDsetno. configurationsno. Hfno. O
1–Hf 2 gas6320
2103Hf 2 EOS 1D20220
3103Hf 2 EOS 3D937720
4103Hf 2 EOS 6D1720520
5100Hf EOS 1D20110
6100Hf 1D primitive20110
Appendix
Table 3: Test set of hafnium (Hf) and oxygen (O) configurations.
Figure 5: RMSE and R2R^{2} values of energy predictions on the validation set by the hafnium MLIP for training set size NN . The center point denotes the median value and rangebars denote the interquartile range (25th to 75th percentile) over 100 trials.
Figure 6: Distribution of energies and force amplitudes of 400 configurations selected by each algorithm.
Figure 7: Representation from simulation datasets 1-6 (Table 3 ) in the 800-element subsets selected by DPPs and kk -means, with the uniform rate from SRS as reference.
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