GPR_calculator: An on-the-fly surrogate model to accelerate massive nudged elastic band calculations

Abstract

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate computationally expensive electronic structure calculations. The key idea is to dynamically train a GPR model during the simulation that can accurately predict energies and forces with uncertainty quantification. When the uncertainty is high, the costly electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the effectiveness of GPR_calculator, we demonstrate its application in Nudged Elastic Band (NEB) simulations of surface diffusion and reactions, achieving 3-10 times acceleration compared to pure ab initio calculations. The source code is available at https://github.com/MaterSim/GPR_calculator.

Program summary

Program Title: GPR_calculator

CPC Library link to program files: https://doi.org/10.17632/vyhpdf9fkh.1

Licensing provisions: MIT [1]

Programming language:: Python 3 & C++

Nature of problem: Many atomistic simulations—such as geometry optimization, barrier calculations, molecular dynamics, and equation-of-state simulations—require sampling a large number of atomic configurations in a compact phase space. While Density Functional Theory (DFT) provides good accuracy and relatively scalable performance for systems with fewer than hundreds of atoms, it can become prohibitively expensive for massive simulations. This is particularly evident in energy barrier calculations for surface diffusion or reaction studies, where hundreds or thousands of energy and force evaluations are needed.

Solution method: The GPR_calculator is an On-the-Fly Atomistic Calculator based on Gaussian Process Regression (GPR), designed as an add-on module that can be used with the popular Atomic Simulation Environment (ASE). It is essentially a hybrid approach that consists of: (i) a base calculator to provide ground truth reference energy and forces for the given input structure, and (ii) a surrogate model serving as the less expensive approximation trained on-the-fly. When the uncertainty of the GPR prediction exceeds a user-defined threshold, the base calculator is invoked to obtain accurate results and update the GPR model. This adaptive approach ensures accuracy while significantly reducing computational cost.

References

• [1]
  https://opensource.org/licenses/MIT