Simultaneous learning of several materials properties from incomplete databases with multi-task SISSO

Abstract

The identification of descriptors of materials properties and functions that capture the underlying physical mechanisms is a critical goal in data-driven materials science. Only such descriptors will enable a trustful and efficient scanning of materials spaces and possibly the discovery of new materials. Recently, the sure-independence screening and sparsifying operator (SISSO) has been introduced and was successfully applied to a number of materials-science problems. SISSO is a compressed sensing based methodology yielding predictive models that are expressed in form of analytical formulas, built from simple physical properties. These formulas are systematically selected from an immense number (billions or more) of candidates. In this work, we describe a powerful extension of the methodology to a 'multi-task learning' approach, which identifies a single descriptor capturing multiple target materials properties at the same time. This approach is specifically suited for a heterogeneous materials database with scarce or partial data, e.g. in which not all properties are reported for all materials in the training set. As showcase examples, we address the construction of materials properties maps for the relative stability of octet-binary compounds, considering several crystal phases simultaneously, and the metal/insulator classification of binary materials distributed over many crystal prototypes.

From DFT to machine learning: recent approaches to materials science–a review

“…CC BY 3.0 sensing methods for feature selection [194,196]. The implementation of this methodology, called sure independence screening and sparsifying operator (SISSO) [202,443] is presented in table 3. As proof of concept, the methodology was applied to quantitative predict the crystal structure of binary compound semiconductors between zinc blende (ZB) or rock salt (RS) structures, which have very small energy differences, shown in figure 18.…”

CheKiPEUQ Intro 1: Bayesian Parameter Estimation Considering Uncertainty or Error from both Experiments and Theory**

“…As noted earlier in the manuscript, alternative long‐used methods for preventing overfitting during regression include regularization methods. In particular, the methods of LASSO regression, [22–23] RIDGE regression, [25–26] and SISSO regression [24] add hyperparameters – which are parameters external to the physical model – to bias the solution towards smaller/fewer changes in the parameters relative to their initial best guess (here, the mean‐vector of the prior distribution). In this sense, regularization methods are similar to BPE as BPE is also mathematically equivalent to performing a biased CPE (and in special cases, BPE and regularizations are transformations of each other [21,102] ).…”

“…A significant drawback to that approach is that the best fit can ran result in physically unrealistic parameter values, often due to overfitting. A long‐used approach to avoid overfitting and obtain more physically realistic fits is to use more sophisticated regression with regularization methods (which introduce hyperparameters to prevent overfitting) [1,5,21–26] …”

Preface

“…These approaches can also utilise spectral data, as shown by Kiyohara et al [8] who use forwardfeed neural networks to directly predict six properties of silicon oxides based on simulated core-loss spectra; and can be used to directly visualise multi-dimensional structure/ property relationships, as shown by Sun et al [9] in their study of silver and platinum nanoparticles using unsupervised t-distributed stochastic neighbour embedding and self-organising maps. The introduction of machine learning to materials science has even led to new algorithms more attuned to the unique needs of this domain, as described by Ouyang et al [10] in their paper on the new multi-tasking sure-independence screening and sparsifying operator method designed to handle sparse data sets where not all properties are known for all materials.Most interestingly, we are also seeing a convergence of these methods and the blurring of computational and discipline boundaries. Fowler et al [11] shows how to use data-driven methods to manage the uncertainties in DFT, using a non-Bayesian approach to estimate the uncertainty and identify accurate or inaccurate predictions of the electron density; and Brunton et al [12] review the development of data-driven multiscale methods for predicting the macroscopic properties of heterogeneous microscopic materials, a topic that expands upon work in multi-scale simulation that received the Nobel Prize in Chemistry in 2013.…”

“…These approaches can also utilise spectral data, as shown by Kiyohara et al [8] who use forwardfeed neural networks to directly predict six properties of silicon oxides based on simulated core-loss spectra; and can be used to directly visualise multi-dimensional structure/ property relationships, as shown by Sun et al [9] in their study of silver and platinum nanoparticles using unsupervised t-distributed stochastic neighbour embedding and self-organising maps. The introduction of machine learning to materials science has even led to new algorithms more attuned to the unique needs of this domain, as described by Ouyang et al [10] in their paper on the new multi-tasking sure-independence screening and sparsifying operator method designed to handle sparse data sets where not all properties are known for all materials.…”