Alchemical and structural distribution based representation for universal quantum machine learning

Abstract

We introduce a representation of any atom in any chemical environment for the automatized generation of universal kernel ridge regression-based quantum machine learning (QML) models of electronic properties, trained throughout chemical compound space. The representation is based on Gaussian distribution functions, scaled by power laws and explicitly accounting for structural as well as elemental degrees of freedom. The elemental components help us to lower the QML model's learning curve, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training. This point is demonstrated for the prediction of covalent binding in single, double, and triple bonds among main-group elements as well as for atomization energies in organic molecules. We present numerical evidence that resulting QML energy models, after training on a few thousand random training instances, reach chemical accuracy for out-of-sample compounds. Compound datasets studied include thousands of structurally and compositionally diverse organic molecules, non-covalently bonded protein side-chains, (HO)-clusters, and crystalline solids. Learning curves for QML models also indicate competitive predictive power for various other electronic ground state properties of organic molecules, calculated with hybrid density functional theory, including polarizability, heat-capacity, HOMO-LUMO eigenvalues and gap, zero point vibrational energy, dipole moment, and highest vibrational fundamental frequency.

High-dimensional potential energy surfaces for molecular simulations: from empiricism to machine learning

“…For example, after training on 50 000 structures, both the PhysNet neural network architecture [103] and KRR based on the FCHL2019 descriptor [62] achieve a mean absolute error of ≈0.3 kcal mol −1 for predicting the energy of unseen molecules. When the FCHL2018 [61] descriptor is used in the kernel model, the same accuracy is reached after training on just 20 000 structures. However, FCHL2018 descriptors are computationally expensive and therefore difficult to apply to larger training set sizes [62].…”

“…a vector of internal coordinates, a molecular descriptor like the Coulomb matrix [50], descriptors for atomic environments, e.g. symmetry functions [59], SOAP [60] or FCHL [61,62], or a representation of crystal structure [63][64][65]). The representer theorem [66] for a functional relation y=f (x) states that f (x) can always be approximated as a linear combination…”

Representations and descriptors unifying the study of molecular and bulk systems

“…Interested readers are referred to Reference for an overview in a chemical context. Such feature spaces can be equivalently built: From radial and spherical harmonic expansion of smoothed atomic densities via atom‐centered Gaussians, that is, the Smooth Overlap of Atomic Integrals representation, Through the arbitrary nonlinear combination of two‐ and three‐body descriptors, as in the case of Beheler‐Parrinello symmetry functions, Chebychev polynomial expansion of radial and angular distribution functions, and scaled Gaussian basis functions, or From functions of n‐body kernels …”

Chemical machine learning with kernels: The impact of loss functions

“…In addition, several chemical environment representations have been proposed in order to improve prediction accuracy. Some of the notable recent development include, Coulomb matrices, Bag of Bonds, representations based on Fourier series of atomic radial distribution functions, forces on atom, interatomic many body expansions and alchemical and structural distribution, constant size descriptors, and references therein. The resulting machine learning frameworks often use a kernel ridge regression or neural networks with impressive prediction performance.…”

“…Recently, there is a great deal of interest in the materials design using machine learning at quantum chemistry level with existing DFT data. [3][4][5][6][7][8][9][10][11][12][13][14][15] This research approach has been supported with strong preliminary evidence that we can simulate relatively large systems with thousands of atoms with accurate prediction performance.…”