Figure 41.

Learning tensorial properties. The figure shows learning curves for the λ = 0 (top) and λ = 2 (bottom) components of the per-atom polarizability for the QM7b dataset.³⁵² Polarizabilities were calculated using CCSD, and the test set in all cases consists of 1811 molecules. (a, b) Effect of the kernel exponent. Nonlinear (ζ = 2, 4) SA-GPR SOAP kernels yield much better asymptotic learning performance than the linear (ζ = 1) form. A radial cutoff of r_c = 4 Å is used throughout. (c, d) Effect of the environment cutoff radius. Polarizability is a property that depends strongly on long-range correlations, and so a large cutoff distance is usually beneficial. However, a multiscale kernel built by combining kernels with different cutoffs, with weights that are optimized by cross-validation, yields a small but consistent improvement over each of the individual models. Adapted from ref (99).