Sugisawa Hiroki, Ida Tomonori, Krems R V
Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada.
Division of Material Chemistry, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan.
J Chem Phys. 2020 Sep 21;153(11):114101. doi: 10.1063/5.0023492.
The goal of the present work is to obtain accurate potential energy surfaces (PESs) for high-dimensional molecular systems with a small number of ab initio calculations in a system-agnostic way. We use probabilistic modeling based on Gaussian processes (GPs). We illustrate that it is possible to build an accurate GP model of a 51-dimensional PES based on 5000 randomly distributed ab initio calculations with a global accuracy of <0.2 kcal/mol. Our approach uses GP models with composite kernels designed to enhance the Bayesian information content and represents the global PES as a sum of a full-dimensional GP and several GP models for molecular fragments of lower dimensionality. We demonstrate the potency of these algorithms by constructing the global PES for the protonated imidazole dimer, a molecular system with 19 atoms. We illustrate that GP models thus constructed can extrapolate the PES from low energies (<10 000 cm), yielding a PES at high energies (>20 000 cm). This opens the prospect for new applications of GPs, such as mapping out phase transitions by extrapolation or accelerating Bayesian optimization, for high-dimensional physics and chemistry problems with a restricted number of inputs, i.e., for high-dimensional problems where obtaining training data is very difficult.
本工作的目标是以一种与系统无关的方式，通过少量的从头算计算获得高维分子系统的精确势能面（PES）。我们使用基于高斯过程（GPs）的概率建模。我们表明，基于5000个随机分布的从头算计算，可以构建一个51维PES的精确GP模型，全局精度<0.2 kcal/mol。我们的方法使用具有复合核的GP模型，旨在增强贝叶斯信息内容，并将全局PES表示为一个全维GP和几个低维分子片段的GP模型之和。我们通过构建质子化咪唑二聚体（一个具有19个原子的分子系统）的全局PES来证明这些算法的有效性。我们表明，这样构建的GP模型可以从低能量（<10000 cm）外推PES，在高能量（>20000 cm）处得到PES。这为GP的新应用开辟了前景，例如通过外推绘制相变或加速贝叶斯优化，用于输入数量有限的高维物理和化学问题，即获取训练数据非常困难的高维问题。
