A Gaussian process regression adaptive density guided approach for potential energy surface construction

Abstract

Note: This paper is part of the JCP Special Topic on Machine Learning Meets Chemical Physics.

Choosing the right molecular machine learning potential

“…One is to solve the overdetermined system of linear equations including derivatives of MLP as in so-called "operator quantum machine learning" with FCHL 44,95 (analogous to including derivatives in the loss function of NNs). Another one is explicitly including either or both covariances between functions and function derivatives in the system of linear equations 91 as was done using many potentials, such as GDML, 58 sGDML, 20,96 RKHS+F, 67 GPR with either XYZ 12,54 or internal coordinates, 15,17,57 FCHL, 44 and GAP (Gaussian approximation potential). 42 Explicit inclusion of covariances between function derivatives greatly increases the accuracy of MLPs, but the computational cost rapidly grows as the number of linear equations to solve increases with the number of force components in a molecule.…”

“…Other global descriptors used in MLPs 15,17,40,[55][56][57] are internal coordinates, which are also traditional molecular representations in computational chemistry. They satisfy rotational and translational invariance, but their construction is not unique.…”

MLatom 2: An Integrative Platform for Atomistic Machine Learning

“…MLatom uses the very computationally efficient Cholesky decomposition by default. Bunch-Kaufman and LU decomposition approaches are also available, which are sometimes necessary when Cholesky decomposition fails [47]. The solution of the above system of equations also requires calculation of the kernel matrix of size N tr 2 , which can become very large and no longer fit in the available computer memory.…”

“…Note that the derivative information can also be included in the training data for KRR, which usually requires implementing higher-order derivatives of the kernel functions [26,37,39,[47][48][49][50]. Such implementations in MLatom are currently underway and will be released in the near future.…”

Gaussian process models of potential energy surfaces with boundary optimization

“…This approach proceeds by training a statistical technique on a relatively small set of data from ab initio calculations on the PES of interest, known as the training set. Many such techniques have been employed to predict the energy in these algorithms, including neural networks [9][10][11][12][13] , moment tensors [14][15][16] and Gaussian processes [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] (GPs).…”