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Fast Bayesian force fields from active learning and mapped Gaussian processes: application to structural phase transition of stanene

Yu Xie1*, Jonathan Vandermause1*, Lixin Sun1*, Andrea Cepellotti1*, Boris Kozinsky1,2*

1 John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

2 Robert Bosch LLC, Research and Technology Center, Cambridge, Massachusetts 02142, USA

* Corresponding authors emails:,,,,
DOI10.24435/materialscloud:7k-9g [version v1]

Publication date: Aug 03, 2020

How to cite this record

Yu Xie, Jonathan Vandermause, Lixin Sun, Andrea Cepellotti, Boris Kozinsky, Fast Bayesian force fields from active learning and mapped Gaussian processes: application to structural phase transition of stanene, Materials Cloud Archive 2020.90 (2020), doi: 10.24435/materialscloud:7k-9g.


Gaussian process (GP) regression is one promising technique of constructing machine learning force fields with built-in uncertainty quantification, which can be used to monitor the quality of model predictions. A current limitation of existing GP force fields is that the prediction cost grows linearly with the size of the training data set, making accurate GP predictions slow. In this work, we exploit the special structure of the kernel function to construct a mapping of the trained Gaussian process model, including both forces and their uncertainty predictions, onto spline functions of low-dimensional structural features. This method is incorporated in the Bayesian active learning workflow for training of Bayesian force fields. To demonstrate the capabilities of this method, we construct a force field for stanene and perform large scale dynamics simulation of its structural evolution. We provide a fully open-source implementation of our method, as well as the training and testing examples with the stanene dataset.

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File name Size Description
733 Bytes README
94.1 KiB Python code of this method, including building spline interpolations and Bayesian active learning
374.8 KiB The extracted training and testing data of stanene
88.3 MiB Large-scale molecular dynamics simulation of melting process of stanene, including MGP pair style coefficient file, LAMMPS input, data, log and trajectory files
3.4 MiB LAMMPS source code of MGP pair style, also including an executable


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Y. Xie, J. Vandermause, L. Sun, A. Cepellotti, B. Kozinsky, in preparation.
Journal reference (Paper and code on which this method is based)
Software (Code in which the method is implemented)


machine learning molecular dynamics Bayesian inference stanene phase transition