Uncertainty Based Machine Learning-DFT Hybrid Framework for Accelerating Geometry Optimization

Geometry optimization is an important tool used for computational simulations in the fields of chemistry, physics, and material science. Developing more efficient and reliable algorithms to reduce the number of force evaluations would lead to accelerated computational modeling and materials discovery. Here, we present a delta method-based neural network-density functional theory (DFT) hybrid optimizer to improve the computational efficiency of geometry optimization. Compared to previous active learning approaches, our algorithm adds two key features: a modified delta method incorporating force information to enhance efficiency in uncertainty estimation, and a quasi-Newton approach based upon a Hessian matrix calculated from the neural network; the later improving stability of optimization near critical points. We benchmarked our optimizer against commonly used optimization algorithms using systems including bulk metal, metal surface, metal hydride, and an oxide cluster. The results demonstrate that our optimizer effectively reduces the number of DFT force calls by 2-3 times in all test systems.