Gaussian process regression for nonparametric force fields

Student thesis: Doctoral ThesisDoctor of Philosophy


The recent years have seen a surge in the development of machine learning algorithms in different areas of scientific research. In the field of simulation of materials, the development of machine learning force fields to carry out fast and accurate molecular dynamics simulations has been attracting a lot of interest ever since the early manuscripts of Blank et al. in 1995, Brown et al. in 1996, and the pioneering work of Behler and Parrinello in 2007. Machine learning force fields are trained using reference data coming from expensive ab initio simulations and try to approximate these accurate methods without recurring to any ad hoc fitting procedure in a computationally efficient way. In this thesis, we present the work done on the development of algorithms that employ Gaussian process regression to build machine learning force fields. We specifically design Gaussian process force fields that use explicitly 2-body, 3-body, and simplified many-body descriptors of local atomic environments. Furthermore, we develop an algorithm to map such Gaussian process force fields into nonparametric classical force fields. This rather general “mapping” procedure removes the inefficient computational scaling of Gaussian process regression methods and yields, without meaningful accuracy losses, force fields that are as fast as classical parametric force fields. All the algorithms and numerical procedures discussed in this thesis are available as a Python package, named “MFF”, which I have coauthored. This package is freely available at, and fully documented. To benchmark the speed and accuracy of the MFF package, we test it on bulk metals (Fe, Ni) and semiconductors (C, Si). We also address the problem of developing machine learning force fields for metallic nanoparticles such as Ni, Au and AgAu. Nanoparticles display very complex energetic landscapes, and accurate force fields that are not fitted on bulk properties are highly desirable to predict structural transitions and phase changes. We build force fields for a set of five isomers of Ni19, and carry out classical molecular dynamics simulations for a total of ∼ 200 ns, a time scale not reachable via ab initio methods, but indeed easily accessible using our mapped machine learning force fields. Subsequently, we discuss the development of machine learning force fields that are accurate for nanoparticles with varying numbers of atoms and analyse small Ni nanoparticles containing 13 to 20 atoms, and larger Au nanoparticles containing 147, 309 and 561 atoms. For the smaller Ni nanoparticles, machine learning force fields are not transferable between particle sizes, reinforcing the belief that “every atom counts” in small nanoparticles. For larger Au nanoparticles, force fields trained on Au147 data well predict forces in the two bigger Au nanoparticles; this result paves the way towards the development of machine learning force fields which are accurate for nanoparticles that contain too many atoms to be effectively simulated using quantum methods.
Date of Award1 Jun 2020
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorFrancesca Baletto (Supervisor), Nicola Bonini (Supervisor) & Alessandro De Vita (Supervisor)

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