Compressive sensing as a paradigm for building physics models

Abstract

The widely-accepted intuition that the important properties of solids are determined by a few key variables underpins many methods in physics. Though this reductionist paradigm is applicable in many physical problems, its utility can be limited because the intuition for identifying the key variables often does not exist or is difficult to develop. Machine learning algorithms (genetic programming, neural networks, Bayesian methods, etc.) attempt to eliminate the a priori need for such intuition but often do so with increased computational burden and human time. A recentlydeveloped technique in the field of signal processing, compressive sensing (CS), provides a simple, general, and efficient way of finding the key descriptive variables. CS is a new paradigm for model building-we show that its models are more physical and predict more accurately than current state-of-the-art approaches, and can be constructed at a fraction of the computational cost and user effort.

Efficient determination of alloy ground-state structures

“…A combination of DFT calculation and the cluster expansion (CE) method [14][15][16] is also useful for alloys. Recent progress in combining the CE method with DFT calculations [17][18][19][20][21][22][23][24][25][26][27][28] has enabled us to evaluate the ground-state structures and phase stability accurately. Although it is impossible to find structures beyond a given crystal lattice using the ordinary CE method, many yet-unobserved structures have been discovered within alloy configurations on the crystal lattice.…”

Theory-Guided Machine Learning in Materials Science

“…Once features have been extracted, there might then be some downselection to test only the most important features. Ghiringhelli et al (2015) successfully used feature extraction in combination with LASSO-based compressive sensing (Nelson et al, 2013) to generate descriptors for the energy difference between zinc blende or wurtzite and rock salt structure for 68 octet binary compounds.…”

“…In materials science, for example, researchers have used LASSO (least absolute shrinkage and selection operator) to construct power series (e.g., cluster) expansions of the partition function for alloys faster than prior genetic algorithms by orders of magnitude (Nelson et al, 2013). Tree-based models are being used to optimize 3D printed part density (Kamath, 2016), predict faults in steel plates (Halawani, 2014), and select dopants for ceria water splitting (Botu et al, 2016).…”

“…Researchers are seeking connections in materials datasets to find new compounds (Hautier et al, 2010), make performance predictions (Klanner et al, 2004), accelerate computational model development (Nelson et al, 2013), and gain new insights from characterization techniques (Belianinov et al, 2015a,b). Although great strides have been made, the field of materials informatics is set to experience an even greater explosion of data with more complex models being developed and increasing emphasis on national and global initiatives related to the materials genome (National Science and Technology Council, 2011;Featherston and O'Sullivan, 2014).…”

On the Compressive Spectral Method

“…For example, in [13], L 1 -regularized least squares was used to sparsely approximate the Fourier coefficients in multiscale dynamic PDEs (and in this work we expand that approach). In [21,22,23], eigenfunctions with compact support were constructed to efficiently solve problems in quantum mechanics. Also, in [24], an L 1 nonlinear least squares model was used to sparsely recover coefficients of a second order ODE which are related to constructing intrinsic mode functions.…”