Machine learning force fields (MLFFs) have gained popularity in recent years as they provide a cost-effective alternative to ab initio molecular dynamics (MD) simulations. Despite a small error on the test set, MLFFs inherently suffer from generalization and robustness issues during MD simulations. To alleviate these issues, we propose global force metrics and fine-grained metrics from element and conformation aspects to systematically measure MLFFs for every atom and every conformation of molecules. We selected three state-of-the-art MLFFs (ET, NequIP, and ViSNet) and comprehensively evaluated on aspirin, Ac-Ala3-NHMe, and Chignolin MD datasets with the number of atoms ranging from 21 to 166. Driven by the trained MLFFs on these molecules, we performed MD simulations from different initial conformations, analyzed the relationship between the force metrics and the stability of simulation trajectories, and investigated the reason for collapsed simulations. Finally, the performance of MLFFs and the stability of MD simulations can be further improved guided by the proposed force metrics for model training, specifically training MLFF models with these force metrics as loss functions, fine-tuning by reweighting samples in the original dataset, and continued training by recruiting additional unexplored data.
REFERENCES
1.
J.
Behler
and M.
Parrinello
, “Generalized neural-network representation of high-dimensional potential-energy surfaces
,” Phys. Rev. Lett.
98
, 146401
(2007
).2.
L.
Zhang
, J.
Han
, H.
Wang
, R.
Car
, and E.
Weinan
, “Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics
,” Phys. Rev. Lett.
120
, 143001
(2018
).3.
L.
Zhang
, J.
Han
, H.
Wang
, W.
Saidi
, R.
Car
, and E.
Weinan
, “End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems
,” in Advances in Neural Information Processing Systems
, edited by S.
Bengio
, H.
Wallach
, H.
Larochelle
, K.
Grauman
, N.
Cesa-Bianchi
, and R.
Garnett
(Curran Associates, Inc.
, 2018
), Vol. 31
.4.
A.
Kabylda
, V.
Vassilev-Galindo
, S.
Chmiela
, I.
Poltavsky
, and A.
Tkatchenko
, “Towards linearly scaling and chemically accurate global machine learning force fields for large molecules
,” arXiv:2209.03985 (2022
).5.
B. J.
Alder
and T. E.
Wainwright
, “Studies in molecular dynamics. I. General method
,” J. Chem. Phys.
31
, 459
–466
(1959
).6.
R.
Car
and M.
Parrinello
, “Unified approach for molecular dynamics and density-functional theory
,” Phys. Rev. Lett.
55
, 2471
(1985
).7.
A. P.
Bartók
, M. C.
Payne
, R.
Kondor
, and G.
Csányi
, “Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons
,” Phys. Rev. Lett.
104
, 136403
(2010
).8.
R.
Drautz
, “Atomic cluster expansion for accurate and transferable interatomic potentials
,” Phys. Rev. B
99
, 014104
(2019
).9.
K. T.
Schütt
, F.
Arbabzadah
, S.
Chmiela
, K. R.
Müller
, and A.
Tkatchenko
, “Quantum-chemical insights from deep tensor neural networks
,” Nat. Commun.
8
, 13890
(2017
).10.
K.
Schütt
, P.-J.
Kindermans
, H.
Sauceda
, S.
Chmiela
, A.
Tkatchenko
, and K.-R.
Müller
, “SchNet: A continuous-filter convolutional neural network for modeling quantum interactions
,” in Proceedings of the 31st International Conference on Neural Information Processing Systems
(Curran Associates Inc.
, 2017
), pp. 992
–1002
.11.
K. T.
Schütt
, H. E.
Sauceda
, P.-J.
Kindermans
, A.
Tkatchenko
, and K.-R.
Müller
, “SchNet—A deep learning architecture for molecules and materials
,” J. Chem. Phys.
148
, 241722
(2018
).12.
J.
Gasteiger
, J.
Groß
, and S.
Günnemann
, “Directional message passing for molecular graphs
,” in International Conference on Learning Representations
, 2019
.13.
J.
Klicpera
, S.
Giri
, J. T.
Margraf
, and S.
Günnemann
, “Fast and uncertainty-aware directional message passing for non-equilibrium molecules
,” in NeurIPS-W
, 2020
.14.
K.
Schütt
, O.
Unke
, and M.
Gastegger
, “Equivariant message passing for the prediction of tensorial properties and molecular spectra
,” in International Conference on Machine Learning
(PMLR
, 2021
), pp. 9377
–9388
.15.
J.
Gasteiger
, F.
Becker
, and S.
Günnemann
, “GemNet: Universal directional graph neural networks for molecules
,” in Advances in Neural Information Processing Systems
(Curran Associates Inc.
, 2021
), Vol. 34
, pp. 6790
–6802
.16.
P.
Thölke
and G.
De Fabritiis
, “TorchMD-NET: Equivariant transformers for neural network based molecular potentials
,” arXiv:2202.02541 (2022
).17.
S.
Batzner
, A.
Musaelian
, L.
Sun
, M.
Geiger
, J. P.
Mailoa
, M.
Kornbluth
, N.
Molinari
, T. E.
Smidt
, and B.
Kozinsky
, “E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
,” Nat. Commun.
13
, 2453
(2022
).18.
Y.
Wang
, S.
Li
, X.
He
, M.
Li
, Z.
Wang
, N.
Zheng
, B.
Shao
, T.
Wang
, and T.-Y.
Liu
, “ViSNet: A scalable and accurate geometric deep learning potential for molecular dynamics simulation
,” arXiv:2210.16518 (2022
).19.
X.
Fu
, Z.
Wu
, W.
Wang
, T.
Xie
, S.
Keten
, R.
Gomez-Bombarelli
, and T.
Jaakkola
, “Forces are not enough: Benchmark and critical evaluation for machine learning force fields with molecular simulations
,” arXiv:2210.07237 (2022
).20.
J. D.
Morrow
, J. L.
Gardner
, and V. L.
Deringer
, “How to validate machine-learned interatomic potentials
,” J. Chem. Phys.
158
, 121501
(2023
).21.
S.
Stocker
, J.
Gasteiger
, F.
Becker
, S.
Günnemann
, and J. T.
Margraf
, “How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?
,” Mach. Learn.: Sci. Technol.
3
, 045010
(2022
).22.
A. S.
Christensen
and O. A.
Von Lilienfeld
, “On the role of gradients for machine learning of molecular energies and forces
,” Mach. Learn.: Sci. Technol.
1
, 045018
(2020
).23.
S.
Chmiela
, V.
Vassilev-Galindo
, O. T.
Unke
, A.
Kabylda
, H. E.
Sauceda
, A.
Tkatchenko
, and K.-R.
Müller
, “Accurate global machine learning force fields for molecules with hundreds of atoms
,” Sci. Adv.
9
, eadf0873
(2023
).24.
J.
MacQueen
, “Classification and analysis of multivariate observations
,” in 5th Berkeley Symposium on Math. Statist. Probability
(University of California
, Los Angeles
, 1967
), pp. 281
–297
.25.
H.
Hotelling
, “Analysis of a complex of statistical variables into principal components
,” J. Educ. Psychol.
24
, 417
(1933
).26.
R. T.
McGibbon
, K. A.
Beauchamp
, M. P.
Harrigan
, C.
Klein
, J. M.
Swails
, C. X.
Hernández
, C. R.
Schwantes
, L.-P.
Wang
, T. J.
Lane
, and V. S.
Pande
, “MDTraj: A modern open library for the analysis of molecular dynamics trajectories
,” Biophys. J.
109
, 1528
–1532
(2015
).27.
B.
Settles
, Active Learning Literature Survey. Computer Sciences Technical Report 1648
, University of Wisconsin–Madison
, 2009
.28.
S.
Fujikake
, V. L.
Deringer
, T. H.
Lee
, M.
Krynski
, S. R.
Elliott
, and G.
Csányi
, “Gaussian approximation potential modeling of lithium intercalation in carbon nanostructures
,” J. Chem. Phys.
148
, 241714
(2018
).29.
J.
Vandermause
, S. B.
Torrisi
, S.
Batzner
, Y.
Xie
, L.
Sun
, A. M.
Kolpak
, and B.
Kozinsky
, “On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events
,” npj Comput. Mater.
6
, 20
(2020
).30.
N. V.
Chawla
, “Data mining for imbalanced datasets: An overview
,” Data Min. Knowl. Discov.
875
–886
(2009
).31.
H.
He
and E. A.
Garcia
, “Learning from imbalanced data
,” IEEE Trans. Knowl. Data Eng.
21
, 1263
–1284
(2009
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.