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

The role of computational modeling approaches has become increasingly important in the design of catalysts. Developing reliable computational models requires a fundamental understanding of catalytic surface reactions, particularly the relevant elementary steps and their associated kinetics such as activation barriers and reaction rates. A widely used approach to study surface reactions is the identification of the minimum energy pathway (MEP), typically computed using the nudged elastic band (NEB) method. In the NEB method, the MEP is initialized as a discrete chain of configurations (images) connecting two local minima. Usually 5-10 images are employed, and their positions iteratively adjusted during the optimization. Converging to the desired MEP often requires hundreds of steps, translating to hundreds of energy and force evaluations per image using electronic structure methods—most commonly density functional theory (DFT). Each electronic structure evaluation typically takes tens or even hundreds of CPU minutes, making NEB calculations very computationally demanding. To address this computational bottleneck, we introduce a GPR_calculator, a package based on Python and C++ languages to build an on-the-fly surrogate model Gaussian Process Regression (GPR) to approximate the expensive electronic structure calculations. The GPR model dynamically trains during simulations, predicting energies and forces with uncertainty quantification. When uncertainty is high, electronic structure calculations are performed to obtain ground truth data to update the GPR model. We demonstrate the effectiveness of the GPR_calculator, on several catalytic surface reactions, achieving 3-5 times acceleration compared to conventional NEB calculations that rely solely on DFT. The source code is available at https://github.com/MasterSim/GPR_calculator.