GPR_calculator: An On-the-Fly Surrogate Model to Accelerate Massive Nudged Elastic Band Calculations

TL;DR

GPR_calculator tackles the high computational cost of Nudged Elastic Band calculations by introducing an on-the-fly Gaussian Process Regression surrogate that learns during simulations and quantifies uncertainty to decide when to invoke expensive electronic structure calculations. The method integrates a rotation-invariant SO(3) structural descriptor with kernel-based GP regression to predict energies and forces, updating the model as needed to maintain accuracy. Benchmark applications on surface diffusion and dissociation show consistent energy profiles with DFT while achieving $3$-$10$× speedups, demonstrating substantial efficiency gains without compromising reliability. The work highlights practical integration with ASE, parallelization strategies, and potential extensibility to other electronic structure codes, making it a scalable tool for accelerated catalysis and materials science investigations.

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 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 expensive electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the power 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.

Figures (7)

• Figure 1: The list of available modules in the GPR_calculator package and their corresponding outputs. The modules with accerlation are also highlighted in light blue boxes.
• Figure 2: The workflow of NEB-GPR calculation. (a) In a NEB run, each image's energy and forces are predicted by the GPR calculator until the NEB calculation converges. (b) The GPR calculator use either GP model or the base calculator to yield the energy and forces. If the base calculator is called, the GP model is updated with the new image's energy and forces.
• Figure 3: The simulated Au diffusion on Al(100) surface from the EMT and GPR calculators with different energy tolerances. The number of EMT/GPR calculations required for convergence is shown in parentheses.
• Figure 4: The simulated MEP of Pd$_4$'s dissociation on the MgO(100) surface from both the GPR and pure VASP calculators. The representative structures along the transition path are also shown in the inset.
• Figure 5: The simulated MEP of H$_2$S's dissociation on the Pd(100) surface from both the GPR and pure VASP calculators. The representative structures along the transition path are also shown in the inset.