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How important is microstructural feature selection for data-driven structure-property mapping?

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Abstract

Data-driven approaches now allow for systematic mapping of microstructure to properties. In particular, we now have diverse approaches to “featurize” microstructures, creating a large pool of machine-readable descriptors for subsequent structure-property analysis. We explore three questions in this work: (a) Can a small subset of features be selected to train a good structure-property predictive model? (b) Is this subset agnostic to the choice of feature selection algorithm? And (c) can the addition of expert-identified features improve model performance? Using a canonical dataset, we answer in the affirmative for all three questions.

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Data availability

The source code for analysis are available in github: https://github.com/owodolab/FeatureEngineeringOPV.

Notes

  1. We use the words “features” and “descriptors” interchangeably.

  2. P3HT:PCBM is poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-[6,6]C61.

  3. Expert-enriched features are scaled through standardization (or Z-score normalization) before the feature engineering step to eliminate bias toward the subset with highest variance.

  4. Completeness is difficult to confirm even for hypothesis-driven selection approaches.

  5. Results in Supplementary Information additionally report the normalized mean absolute errors (NMAEs) for fivefold validation and prediction.

  6. Here, we use the monomial function of order two. See Supplementary Information for more results.

Abbreviations

\(\mathcal {X}\) :

Raw dataset with microstructures

\(\widehat{d_i}\) :

Salient feature

\(\widehat{d}\) :

Vector of salient features

\(\widehat{d}^E\) :

Vector of salient features derived by the expert

\(\widehat{d}^{\prime \text {mRMR}}\) :

Vector of salient features derived using the mRMR method from \(d^{\prime }\)

\(\widehat{d}^{\text {FS}}\) :

Vector of salient features derived via forward selection from d.

\(\widehat{d}^{\text {mRMR}}\) :

Vector of salient features derived using the mRMR method from d.

\(\widehat{d}^{\text {RF}}\) :

Vector of salient features derived via random forest method from d.

\(\widehat{f}\) :

Salient features derived via PCA from f

\(\widehat{f}^{\prime }\) :

Salient features derived via PCA from \(f^{\prime }\)

\(\widehat{x}\) :

Salient features derived via PCA from X

\(\widetilde{d}\) :

Vector of monomial-augmented salient features

\(\widetilde{d}^{\prime \text {mRMR}}\) :

Vector of monomial-augmented \(\widehat{d}^{\prime \text {mRMR}}\)

\(\widetilde{d}^{\text {mRMR}}\) :

Vector of monomial-augmented \(\widehat{d}^{\text {mRMR}}\)

\(\widetilde{f}\) :

Monomial-augmented \(\widehat{f}\)

\(\widetilde{f}^{\prime }\) :

Monomial-augmented \(\widehat{f}^{\prime }\)

\(\widetilde{M_4^{\prime }}\) :

SP model mapping \(\widetilde{f}^{\prime }\) to \(J_{\text{sc}}\)

\(\widetilde{M_4}\) :

SP model mapping \(\widetilde{f}\) to \(J_{\text{sc}}\)

\(\widetilde{M}_1\) :

SP model mapping \(\widetilde{d}^{\prime \text {mRMR}}\) to \(J_{\text{sc}}\)

\(A\) :

Influence coefficients capturing the SP map

\(d\) :

Vector of descriptors

\(d^{\prime }\) :

Expert-enriched vector of descriptors

\(d_i\) :

Descriptor/feature

\(F_i\) :

Autocorrelation array of microstructure \(X_i\)

\(F\) :

Function mapping the salient features to property

\(F_i^{\prime }\) :

Array of microstructure \(X_i\) auto-correlation with state enriched by the expert knowledge

\(J_{\text{sc}}\) :

The short circuit current (\(\text{A/m}^2\))

\(m(s)\) :

A state of the microstructure at the location s in X

\(M_1\) :

SP model mapping \(\hat{d}^{{{\text{mRMR}}}}\) to \(J_{\text{sc}}\)

\(M_1^{\prime }\) :

SP model mapping \(\widehat{d}^{\prime \text {mRMR}}\) to \(J_{\text{sc}}\)

\(M_2\) :

SP model mapping \(\widehat{d}^{\text {FS}}\) to \(J_{\text{sc}}\)

\(M_2^{\prime }\) :

SP model mapping \(\widehat{d}^{\prime \text {FS}}\) to \(J_{\text{sc}}\)

\(M_3\) :

SP model mapping \(\widehat{d}^{\text {RF}}\) to \(J_{\text{sc}}\)

\(M_3^{\prime }\) :

SP model mapping \(\widehat{d}^{\prime \text {RF}}\) to \(J_{\text{sc}}\)

\(M_4\) :

SP model mapping the salient features derived using low dimensional embedding of f.

\(M_4^{\prime }\) :

SP model mapping the salient features derived using low dimensional embedding of \(f^{\prime }\)

\(M_5\) :

SP model mapping \(\widehat{x}\) to \(J_{\text{sc}}\)

\(M_E\) :

SP model derived by the expert

\(N\) :

Total number of microstructures in \(\mathcal {X}\)

\(P\) :

Material property of interest, here \(J_{\text{sc}}\)

\({\text{PC}}_{i}\) :

Principal component

\(q\) :

Order of monomial functions

\(\text{RL0}\) :

Representation layer zero: raw data

\(\text{RL1}\) :

Representation layer one: input features

\(\text{RL2}\) :

Representation layer two: salient features

\(X\) :

Microstructure data point in \(\mathcal {X}\)

\(\mathcal{X}^f\) :

Dataset featurized using machine-derived approach

\(\mathcal{X}^{f\prime }\) :

Dataset featurized using machine-derived approach and enriched with expert knowledge

\(S\) :

Size of salient features vector

\(\widetilde{S}\) :

Size of salient extended features vector

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Acknowledgments

This work was supported by National Science Foundation (1906344 and 1910539). BG acknowledges support from the ONR MURI ONR N00014-19-12453. OW and HL acknowledge the support provided by the Center for Computational Research at the University at Buffalo. BY and SK acknowledge support from NIST 70NANB18H039 (program manager Dr. James Warren).

Author information

Authors and Affiliations

  1. Materials Design and Innovation Department, University at Buffalo, Buffalo , NY, USA

    Hao Liu & Olga Wodo

  2. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Berkay Yucel & Surya R. Kalidindi

  3. School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Surya R. Kalidindi

  4. Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Daniel Wheeler

  5. Mechanical Engineering Department, Iowa State University, Ames , IA, USA

    Baskar Ganapathysubramanian

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  1. Hao Liu
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Correspondence to Olga Wodo.

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Liu, H., Yucel, B., Wheeler, D. et al. How important is microstructural feature selection for data-driven structure-property mapping?. MRS Communications 12, 95–103 (2022). https://doi.org/10.1557/s43579-021-00147-4

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