Quantum Machine Learning with Response Operators in Chemical Compound Space

Abstract

The choice of how to represent a chemical compound has a considerable effect on the performance of quantum machine learning (QML) models based on kernel ridge regression (KRR). A carefully constructed representation can lower the prediction error for out-of-sample data by several orders of magnitude with the same training data. This is a particularly desirable effect in data scarce scenarios, such as they are common in first principles based chemical compound space explorations. Unfortunately, representations which result in KRR models with low and steep learning curves for extensive properties, for example, energies, do not necessarily lead to well performing models for response properties. In this chapter we review the recently introduced FCHL18 representation (Faber et al., J Chem Phys 148(24):241717, 2018), in combination with kernel-based QML models to account for response properties by including the corresponding operators in the regression (Christensen et al., J Chem Phys 150(6):064105, 2019). FCHL18 was designed to describe an atom in its chemical environment, allowing to measure distances between elements in the periodic table, and consequently providing a metric for both structural and chemical similarities between compounds. The representation does not decouple the radial and angular degrees of freedom, which makes it well-suited for comparing atomic environments. QML models using FCHL18 display low and steep learning curves for energies of molecules, clusters, and crystals. By contrast, the same QML models exhibit less favorable learning for other properties, such as forces, electronic eigenvalues, or dipole moments. We discuss the use of the electric field differential operator within a kernel-based operator QML (OQML) approach. Using OQML results in the same predictive accuracy for molecular dipole norm, but with approximately 20× less training data, as directly learning the dipole norm with a KRR model.