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.

中文翻译：

---

基于不确定性的机器学习-DFT 混合框架，用于加速几何优化。


几何优化是化学、物理和材料科学领域用于计算仿真的重要工具。开发更高效、更可靠的算法来减少力评估的数量，可以加速计算建模和材料发现。在这里，我们提出了一个基于 delta 方法的神经网络密度泛函理论 （DFT） 混合优化器，以提高几何优化的计算效率。与以前的主动学习方法相比，我们的算法增加了两个关键功能：一种改进的 delta 方法，该方法结合了力信息以提高不确定性估计的效率，以及一种基于从神经网络计算的 Hessian 矩阵的准牛顿方法;后者提高了临界点附近优化的稳定性。我们使用包括块状金属、金属表面、金属氢化物和氧化物簇在内的系统，根据常用的优化算法对优化器进行了基准测试。结果表明，我们的优化器在所有测试系统中有效地将 DFT force 调用次数减少了 2-3 倍。