Materials Expert-Artificial Intelligence for Materials Discovery

TL;DR

Here, machine learning was used to capture expert intuition into quantifiable descriptors, revealing hypervalency as a key predictor for topological semimetals.

Abstract

The advent of material databases provides an unprecedented opportunity to uncover predictive descriptors for emergent material properties from vast data space. However, common reliance on high-throughput ab initio data necessarily inherits limitations of such data: mismatch with experiments. On the other hand, experimental decisions are often guided by an expert's intuition honed from experiences that are rarely articulated. We propose using machine learning to "bottle" such operational intuition into quantifiable descriptors using expertly curated measurement-based data. We introduce "Materials Expert-Artificial Intelligence" (ME-AI) to encapsulate and articulate this human intuition. As a first step towards such a program, we focus on the topological semimetal (TSM) among square-net materials as the property inspired by the expert-identified descriptor based on structural information: the tolerance factor. We start by curating a dataset encompassing 12 primary features of 879 square-net materials, using experimental data whenever possible. We then use Dirichlet-based Gaussian process regression using a specialized kernel to reveal composite descriptors for square-net topological semimetals. The ME-AI learned descriptors independently reproduce expert intuition and expand upon it. Specifically, new descriptors point to hypervalency as a critical chemical feature predicting TSM within square-net compounds. Our success with a carefully defined problem points to the "machine bottling human insight" approach as promising for machine learning-aided material discovery.

Figures (8)

• Figure 1: "Materials Expert-Artificial Intelligence" (ME-AI) for topological semimetals in square-net materials. (a): The conceptual framework of ME-AI. (b): Crystal structure of some 2D square-net materials. (c): The square-net structure, where purple atoms are arranged on a dense 2D square lattice of lattice constant $d_{sq}$. The centered square-net has an enlarged lattice of lattice constant $a=\sqrt{2}d_{sq}$ containing two atoms. (d): The 3D square-net structure where the magenta and cyan atoms lie in the out-of-plane directions separated by distances $d_1$ and $d_2$ respectively from the square-net atoms (purple). The tolerance factor $t\equiv d_{sq}/d_{nn}$ where $d_{nn}\equiv\min(d_1,d_2)$ is the out-of-plane nearest neighbor distance. (e): The distribution of tolerance factor ($t$) for the compounds in our data set labeled as TSMs (teal) and trivial (orange) materials, where $t\equiv d_{sq}/d_{nn}$ and $d_{nn}$ is the out-of-plane nearest neighbor distance. We find $t\approx 0.96$ (dashed line) as the value that separates TSMs and trivial materials with maximum accuracy. (f): The Brillouin zone (BZ) of the enlarged lattice is obtained by folding the larger BZ of the dense lattice. (g): The spin degenerate band structure arising from $p_{x}$ (pink) and $p_{y}$ (green) orbitals on the 2D square, folded to the BZ of the enlarged unit cell, and plotted along the path shown in panel (h). Band folding gives rise to two crossings with band inversion (at $\Gamma\rightarrow \text{X}$ and $\text{M}\rightarrow\Gamma$), as well as overlapping bands along the folding edge ($\text{X}\rightarrow\text{M}$). (h): BZ with the nodal line (dashed curve) of points where the bands cross. Also shown is the path for the band diagram in panel (g).
• Figure 2: A flowchart illustration of ME-AI. We first create a preprocessed and labeled data set $\mathcal{D}\equiv (\mathbf{X},\mathbf{y})$ composed of the 12 primary features, $\mathbf{X}=(\mathbf{x}_1,\dots, \mathbf{x}_N)$ with $\mathbf{x}_n\in R^{D}$ where $D=12$, and their class labels $\mathbf{y}=(y_1,\dots,y_N)$ with $y_n\in \{0,1\}$. The subscript $n$ denotes different materials in the total $N$ entries database. After converting the classification task into two independent regression tasks, we set up two GPRs with the shared kernel $\mathbf{K}(\mathbf{x},\mathbf{x}\,')$. The correlation matrix $\mathbf{M}$ inside the kernel couples the different primary features and is designed to have a factor analysis structure $\mathbf{M}=\mathbf{L}^T\mathbf{L}+\mathbf{\Lambda}$, which allows us to learn interaction between different PF's with a limited number of hyperparameters. We train the model with the whole data set by maximizing the log marginal likelihood. This automatically includes regularization. We get the correlations $\mathbf{M}^*$ from the trained model parameters between the primary features. The significance of the coupling between the $m^{\text{th}}$ and $n^{\text{th}}$ primary features is measured by the normalized correlation $\mathbf{C}_{mn}$. This reveals the pairs of significant features that identify the square-net TSMs.
• Figure 3: The main results from the GP model. (a): The normalized-correlation matrix $\boldsymbol{C}_{mn}$, where $m$ and $n$ denote the primary features. Only the lower triangle is shown. The inset shows the distribution of magnitudes of non-diagonal elements, $|\boldsymbol{C}_{mn}|$, with the strongest elements shown in black. These strongest elements: ($d_{sq}$, $d_{nn}$), ($d_{sq}$, $fcc$), ($\chi_{sq}$, $d_{sq}$), ($\chi_{sq}$, $d_{nn}$), and ($\chi_{sq}$, $fcc$) are marked with a star. The values of (b):$d_{sq}/d_{nn}$, (c):$d_{sq}/fcc$, (d):$\chi_{sq}/d_{nn}$, (e):$\chi_{sq}\cdot d_{nn}$, and (f):$\chi_{sq}\cdot fcc$, for the TSM and trivial materials in our dataset. The vertical lines separate TSMs from trivial materials. (g): The periodic table with the new element-specific descriptor $\chi_{sq}\cdot fcc$ color-coded from lowest to highest values from blue to red, respectively. The entries in white font fall in the window of 7 to 11. The red line represents the classical Zintl line, while the blue framed elements are known to form Zintl ions as described by Slabonslabon2013structure
• Figure 4: The scatter plot showing TSM and trivial materials in the 2D descriptor space spanned by the $t$-factor and $\chi_{sq}\cdot fcc$. The TSM (teal) and trivial (orange) materials are separated sharply in this 2D space. (a): The originally labeled TSM (teal) and trivial (orange) materials show some outliers in the clustered regions of TSM and trivial materials. (b): Further analysis enabled us to correct mislabeled materials in our original data set. The dark brown points denote the trivial materials originally classified as TSMs; the bright green point denotes a TSM originally classified as trivial.
• Figure S5: (a)-(d) The distributions of the top 4 principal components (PC's) for the compounds in our data set labeled as TSMs (teal) and trivial (orange) materials. The PC's only reflect the structure of the primary feature set without any information about the labels.