Department of Chemistry , Yale University , P.O. Box 208107, New Haven , Connecticut 06520-8107 , United States.
Energy Sciences Institute , Yale University , P.O. Box 27394, West Haven , Connecticut 06516-7394 , United States.
J Chem Theory Comput. 2018 Jun 12;14(6):3351-3362. doi: 10.1021/acs.jctc.8b00124. Epub 2018 May 2.
We introduce the so-called "Classical Optimal Control Optimization" (COCO) method for global energy minimization based on the implementation of the diffeomorphic modulation under observable-response-preserving homotopy (DMORPH) gradient algorithm. A probe particle with time-dependent mass m( t;β) and dipole μ( r, t;β) is evolved classically on the potential energy surface V( r) coupled to an electric field E( t;β), as described by the time-dependent density of states represented on a grid, or otherwise as a linear combination of Gaussians generated by the k-means clustering algorithm. Control parameters β defining m( t;β), μ( r, t;β), and E( t;β) are optimized by following the gradients of the energy with respect to β, adapting them to steer the particle toward the global minimum energy configuration. We find that the resulting COCO algorithm is capable of resolving near-degenerate states separated by large energy barriers and successfully locates the global minima of golf potentials on flat and rugged surfaces, previously explored for testing quantum annealing methodologies and the quantum optimal control optimization (QuOCO) method. Preliminary results show successful energy minimization of multidimensional Lennard-Jones clusters. Beyond the analysis of energy minimization in the specific model systems investigated, we anticipate COCO should be valuable for solving minimization problems in general, including optimization of parameters in applications to machine learning and molecular structure determination.
我们引入了所谓的“经典最优控制优化”（COCO）方法，用于基于可观测响应保持同伦（DMORPH）梯度算法的实现进行全局能量最小化。具有时变质量 m(t;β)和偶极矩 μ(r, t;β)的探针粒子在势能表面 V(r)上经典演化，与电场 E(t;β)耦合，如通过在网格上表示的时变态密度或通过 k-均值聚类算法生成的高斯线的线性组合来描述。通过跟随能量相对于β的梯度来优化定义 m(t;β)、μ(r, t;β)和 E(t;β)的控制参数β，将它们适应于引导粒子朝向全局最小能量配置。我们发现，所得的 COCO 算法能够解析由大能量势垒分隔的近简并态，并成功定位在平坦和崎岖表面上的高尔夫势的全局最小值，这些表面以前曾用于测试量子退火方法和量子最优控制优化（QuOCO）方法。初步结果表明多维 Lennard-Jones 团簇的能量最小化成功。除了分析所研究的特定模型系统中的能量最小化之外，我们预计 COCO 应该对解决一般的最小化问题有用，包括机器学习和分子结构确定应用中的参数优化。
