Wavelet scattering networks for atomistic systems with extrapolation of material properties

Abstract

The dream of machine learning in materials science is for a model to learn the underlying physics of an atomic system, allowing it to move beyond the interpolation of the training set to the prediction of properties that were not present in the original training data. In addition to advances in machine learning architectures and training techniques, achieving this ambitious goal requires a method to convert a 3D atomic system into a feature representation that preserves rotational and translational symmetries, smoothness under small perturbations, and invariance under re-ordering. The atomic orbital wavelet scattering transform preserves these symmetries by construction and has achieved great success as a featurization method for machine learning energy prediction. Both in small molecules and in the bulk amorphous LiαSi system, machine learning models using wavelet scattering coefficients as features have demonstrated a comparable accuracy to density functional theory at a small fraction of the computational cost. In this work, we test the generalizability of our LiαSi energy predictor to properties that were not included in the training set, such as elastic constants and migration barriers. We demonstrate that statistical feature selection methods can reduce over-fitting and lead to remarkable accuracy in these extrapolation tasks.

Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

“…Wavelet scattering transforms [94][95][96][97][98][99][100] (WST) use a convolutional wavelet frame representation to describe variations of (local) atomic density at different scales and orientations. Integrating non-linear functions of the wavelet coefficients yields invariant features, where second-and higher-order features couple two or more length scales.…”

“…Integrating non-linear functions of the wavelet coefficients yields invariant features, where second-and higher-order features couple two or more length scales. Variations use different wavelets (Morlet 94,95 , solid harmonic, or atomic orbital [96][97][98]100 ) and radial basis functions (exponential 96 , Laguerre polynomials 97,100 ).…”

How to quantify fields or textures? A guide to the scattering transform

“…So far, it has been used primarily in audio/visual signal processing (e.g., Andén & Mallat 2011;Bruna & Mallat 2013;Sifre & Mallat 2013;Andén & Mallat 2014). It has already been used in a number of scientific applications: intermittency in turbulence (Bruna et al 2015), quantum chemistry and material science (Hirn et al 2017;Eickenberg et al 2018;Sinz et al 2020), plasma physics (Glinsky et al 2020), geography (Kavalerov et al 2019), astrophysics (Allys et al 2019Saydjari et al 2021;Regaldo-Saint Blancard et al 2020), and cosmology (Cheng et al 2020;Cheng & Ménard 2021). In several of these applications, the scattering transform reached state-of-the-art performance compared to the CNNs in use at the time.…”

Spatially Resolved Potential and Li-Ion Distributions Reveal Performance-Limiting Regions in Solid-State Batteries

“…Point defect calculations were partially automatic using PyCDT and the DefectPhaseDiagram methods in pymatgen. The calculations of LCO and Li m Si were taken from previous work. , Potential maps were constructed following the procedure outlined by Swift and Qi, with more details on and defect calculations for Li 3 PO 4 (Modeling Methods in the Supporting Information).…”