The climbing-image nudged elastic band (CI-NEB) method serves as an indispensable tool for computational chemists, offering insight into minimum-energy reaction paths (MEPs) by delineating both transition states (TSs) and intermediate nonstationary structures along reaction coordinates. However, executing CI-NEB calculations for reactions with extensive reaction coordinate spans necessitates a large number of images to ensure a reliable convergence of the MEPs and TS structures, presenting a computationally demanding optimization challenge, even with mildly costly electronic-structure methods. In this study, we advocate for the utilization of physically inspired prior mean function-based Gaussian processes (GPs) to expedite MEP exploration and TS optimization via the CI-NEB method. By incorporating reliable prior physical approximations into potential energy surface (PES) modeling, we demonstrate enhanced efficiency in multidimensional CI-NEB optimization with surrogate-based optimizers. Our physically informed GP approach not only outperforms traditional nonsurrogate-based optimizers in optimization efficiency but also on-the-fly learns the reaction path valley during optimization, culminating in significant advancements. The surrogate PES derived from our optimization exhibits high accuracy compared to true PES references, aligning with our emphasis on leveraging reliable physical priors for robust and efficient posterior mean learning in GPs. Through a systematic benchmark study encompassing various reaction pathways, including gas-phase, bulk-phase, and interfacial/surface reactions, our physical GPs consistently demonstrate superior efficiency and reliability. For instance, they outperform the popular fast inertial relaxation engine optimizer by approximately a factor of 10, showcasing their versatility and efficacy in exploring reaction mechanisms and surface reaction PESs.

中文翻译：

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物理先验均值函数驱动的高斯过程利用爬升图像微移弹性带搜索最小能量反应路径：气相、界面和体相反应的通用方法


爬升图像微移弹性带 (CI-NEB) 方法是计算化学家不可或缺的工具，通过沿着反应坐标描绘过渡态 (TS) 和中间非平稳结构，提供对最小能量反应路径 (MEP) 的深入了解。然而，对具有广泛反应坐标跨度的反应执行 CI-NEB 计算需要大量图像，以确保 MEP 和 TS 结构的可靠收敛，即使使用成本较低的电子结构方法，也提出了计算要求较高的优化挑战。在本研究中，我们主张利用物理启发的基于先验均值函数的高斯过程 (GP) 通过 CI-NEB 方法加快 MEP 探索和 TS 优化。通过将可靠的先验物理近似融入势能面 (PES) 建模中，我们证明了基于替代优化器的多维 CI-NEB 优化效率的提高。我们的基于物理的 GP 方法不仅在优化效率方面优于传统的基于非代理的优化器，而且还可以在优化过程中动态学习反应路径谷，最终取得重大进步。与真实的 PES 参考相比，从我们的优化中得出的替代 PES 表现出较高的准确性，这与我们强调利用可靠的物理先验在 GP 中实现稳健且高效的后验均值学习相一致。通过涵盖各种反应途径（包括气相、体相和界面/表面反应）的系统基准研究，我们的物理 GP 始终表现出卓越的效率和可靠性。 例如，它们的性能比流行的快速惯性弛豫引擎优化器高出大约 10 倍，展示了它们在探索反应机制和表面反应 PES 方面的多功能性和功效。