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Cited by 147Machine Learning in Materials ScienceAdvanced Chemical Physics StudiesModel Reduction and Neural Networks

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Active learning of reactive Bayesian force fields applied to heterogeneous catalysis dynamics of H/Pt

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Vandermause, Jonathan, Xie, Yu, Lim, Jin Soo, Owen, Cameron J., Kozinsky, Boris·2022·Nature Communications
DOI 10.1038/s41467-022-32294-0PMC PMC9440250

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Abstract

Atomistic modeling of chemically reactive systems has so far relied on either expensive ab initio methods or bond-order force fields requiring arduous parametrization. Here, we describe a Bayesian active learning framework for autonomous “on-the-fly” training of fast and accurate reactive many-body force fields during molecular dynamics simulations. At each time-step, predictive uncertainties of a sparse Gaussian process are evaluated to automatically determine whether additional ab initio training data are needed. We introduce a general method for mapping trained kernel models onto equivalent polynomial models whose prediction cost is much lower and independent of the training set size. As a demonstration, we perform direct two-phase simulations of heterogeneous H 2 turnover on the Pt(111) catalyst surface at chemical accuracy. The model trains itself in three days and performs at twice the speed of a ReaxFF model, while maintaining much higher fidelity to DFT and excellent agreement with experiment.

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Fig. 1 On-the-fly training and acceleration of many-body Bayesian force fields (BFF). a At each time-step of the MD simulation, local energies, forces, and stresses are computed with the SGP model. If the uncertainty on a local energy exceeds the chosen threshold ΔDFT, a DFT calculation is performed and the model is updated. b Mapping of local environments ρi onto multielement descriptors derived from the atomic cluster expansion. The environment is first mapped onto an equivariant descriptor ci, products of which are used to compute the rotationally invariant descriptor di that serves as an input to the model. c Mapping of a ξ = 2 SGP force field onto an equivalent quadratic model. The prediction cost of the SGP scales linearly with the number of sparse environments NS, while the cost of the corresponding polynomial model is independent of NS.
Fig. 1 On-the-fly training and acceleration of many-body Bayesian force fields (BFF). a At each time-step of the MD simulation, local energies, forces, and stresses are computed with the SGP model. If the uncertainty on a local energy exceeds the chosen threshold ΔDFT, a DFT calculation is performed and the model is updated. b Mapping of local environments ρi onto multielement descriptors derived from the atomic cluster expansion. The environment is first mapped onto an equivariant descriptor ci, products of which are used to compute the rotationally invariant descriptor di that serves as an input to the model. c Mapping of a ξ = 2 SGP force field onto an equivalent quadratic model. The prediction cost of the SGP scales linearly with the number of sparse environments NS, while the cost of the corresponding polynomial model is independent of NS.CC BY · PubMed Central
Fig. 2 On-the-fly training of the reactive SGP force field for H/Pt. a Snapshots of four independent training simulations (left to right): gas-phase H2; bulk Pt; (111) facet of the Pt surface; and H2 interaction with the Pt(111) slab. b Energy versus time during the H/Pt(111) training simulation, with the SGP predictions in green and DFT evaluations shown as black dots. The inset is a zoom-in of the model predictions during the first recombination event observed at t ≈ 0.3 ps. c Snapshots of the first recombination event. Atoms are colored by the uncertainty of the local energy prediction, with red corresponding to the prediction threshold ΔDFT.
Fig. 2 On-the-fly training of the reactive SGP force field for H/Pt. a Snapshots of four independent training simulations (left to right): gas-phase H2; bulk Pt; (111) facet of the Pt surface; and H2 interaction with the Pt(111) slab. b Energy versus time during the H/Pt(111) training simulation, with the SGP predictions in green and DFT evaluations shown as black dots. The inset is a zoom-in of the model predictions during the first recombination event observed at t ≈ 0.3 ps. c Snapshots of the first recombination event. Atoms are colored by the uncertainty of the local energy prediction, with red corresponding to the prediction threshold ΔDFT.CC BY · PubMed Central
Fig. 3 Validation of the H/Pt SGP force field. In each plot, shaded regions indicate 99% confidence regions of the SGP model. a Energy versus volume of bulk Pt. b Energy versus H–H bond distance of a single H2 molecule. c Energy versus intermolecular distance of two H2 molecules oriented perpendicular (blue) and parallel (green) to each other. d Surface energies of Pt for (111), (110), (100), and (211) facets. e H adsorption energies at different binding sites and Pt facets.
Fig. 3 Validation of the H/Pt SGP force field. In each plot, shaded regions indicate 99% confidence regions of the SGP model. a Energy versus volume of bulk Pt. b Energy versus H–H bond distance of a single H2 molecule. c Energy versus intermolecular distance of two H2 molecules oriented perpendicular (blue) and parallel (green) to each other. d Surface energies of Pt for (111), (110), (100), and (211) facets. e H adsorption energies at different binding sites and Pt facets.CC BY · PubMed Central
Fig. 4 Reactive MD simulation of H/Pt(111) with the mapped SGP force field. a Snapshot from a 500 ps simulation at 900 K. The system is a six-layer slab model of a 12 × 12 unit cell of Pt(111) with H2 reactive events occurring at both sides of the slab. b Cumulative number of dissociation and recombination events observed at 450 K (dark blue), 600 K (light blue), 750 K (orange), and 900 K (red). The reaction rate is estimated from the slope of each curve after an initial equilibration period of 200ps. c Arrhenius plot of the reaction rate versus inverse temperature. An apparent activation energy of 0.25(2) eV is obtained, in good agreement with the experimental values of 0.21–0.24 eV55,56.
Fig. 4 Reactive MD simulation of H/Pt(111) with the mapped SGP force field. a Snapshot from a 500 ps simulation at 900 K. The system is a six-layer slab model of a 12 × 12 unit cell of Pt(111) with H2 reactive events occurring at both sides of the slab. b Cumulative number of dissociation and recombination events observed at 450 K (dark blue), 600 K (light blue), 750 K (orange), and 900 K (red). The reaction rate is estimated from the slope of each curve after an initial equilibration period of 200ps. c Arrhenius plot of the reaction rate versus inverse temperature. An apparent activation energy of 0.25(2) eV is obtained, in good agreement with the experimental values of 0.21–0.24 eV55,56.CC BY · PubMed Central

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  1. Bishop, C. M. Pattern Recognition and Machine Learning (Springer, 2006).

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Metadata

Authors
Vandermause, J., Xie, Y., Lim, J. S., Owen, C. J., & Kozinsky, B.
Affiliations
Harvard University (US)
Corresponding author
  • Vandermause, Jonathan
  • Kozinsky, Boris
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2022-09-02
Volume
13
Issue
1
Pages
5183-5183
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-022-32294-0
PMC
PMC9440250
OpenAlex
W4294316513
Cited by
147
References
73
Citations by year
2026: 25 · 2025: 45 · 2024: 41 · 2023: 32 · 2022: 3
FWCI
8.50
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • Research Square (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Robert Bosch
  • National Science Foundation (1808162, DGE1745303)
  • U.S. Department of Energy (DE-SC0020128, DE-SC0012573)
Topics
  • Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
Keywords
reactive force field, Bayesian active learning, heterogeneous catalysis, polynomial surrogate models

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