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Learning simple heuristic rules for classifying materials based on chemical composition

Andrew Ma, Marin Soljačić

TL;DR

The paper addresses predicting whether materials are topological or metallic from composition alone. It introduces a simple heuristic framework called topogivity and extends it with a periodic-table–based inductive bias, implementing a full element-wise model $g(M;\mathbf{t})$ and a restricted, partition-based model $\eta(M;\boldsymbol{\theta})$ with $g(M;\mathbf{t})=\mathbf{t}\cdot\mathbf{f}(M)$ and $\eta(M;\boldsymbol{\theta})=\boldsymbol{\theta}\cdot\boldsymbol{\nu}(M)$. The key contributions include two tasks (topology and metallicity) evaluated across large training-set sizes, revealing that the restricted model reduces data requirements while preserving interpretability via periodic-table visualizations, whereas the full model gains accuracy with more data. The work demonstrates that simple, interpretable heuristic rules can perform competitively against more complex models in data-limited regimes and provides a framework for incorporating chemistry knowledge into ML for materials discovery. By mapping learned elemental parameters to the periodic table, the approach offers chemical intuition for material classification that can guide data collection and hypothesis formation.

Abstract

In the past decade, there has been a significant interest in the use of machine learning approaches in materials science research. Conventional deep learning approaches that rely on complex, nonlinear models have become increasingly important in computational materials science due to their high predictive accuracy. In contrast to these approaches, we have shown in a recent work that a remarkably simple learned heuristic rule -- based on the concept of topogivity -- can classify whether a material is topological using only its chemical composition. In this paper, we go beyond the topology classification scenario by also studying the use of machine learning to develop simple heuristic rules for classifying whether a material is a metal based on chemical composition. Moreover, we present a framework for incorporating chemistry-informed inductive bias based on the structure of the periodic table. For both the topology classification and the metallicity classification tasks, we empirically characterize the performance of simple heuristic rules fit with and without chemistry-informed inductive bias across a wide range of training set sizes. We find evidence that incorporating chemistry-informed inductive bias can reduce the amount of training data required to reach a given level of test accuracy.

Learning simple heuristic rules for classifying materials based on chemical composition

TL;DR

The paper addresses predicting whether materials are topological or metallic from composition alone. It introduces a simple heuristic framework called topogivity and extends it with a periodic-table–based inductive bias, implementing a full element-wise model and a restricted, partition-based model with and . The key contributions include two tasks (topology and metallicity) evaluated across large training-set sizes, revealing that the restricted model reduces data requirements while preserving interpretability via periodic-table visualizations, whereas the full model gains accuracy with more data. The work demonstrates that simple, interpretable heuristic rules can perform competitively against more complex models in data-limited regimes and provides a framework for incorporating chemistry knowledge into ML for materials discovery. By mapping learned elemental parameters to the periodic table, the approach offers chemical intuition for material classification that can guide data collection and hypothesis formation.

Abstract

In the past decade, there has been a significant interest in the use of machine learning approaches in materials science research. Conventional deep learning approaches that rely on complex, nonlinear models have become increasingly important in computational materials science due to their high predictive accuracy. In contrast to these approaches, we have shown in a recent work that a remarkably simple learned heuristic rule -- based on the concept of topogivity -- can classify whether a material is topological using only its chemical composition. In this paper, we go beyond the topology classification scenario by also studying the use of machine learning to develop simple heuristic rules for classifying whether a material is a metal based on chemical composition. Moreover, we present a framework for incorporating chemistry-informed inductive bias based on the structure of the periodic table. For both the topology classification and the metallicity classification tasks, we empirically characterize the performance of simple heuristic rules fit with and without chemistry-informed inductive bias across a wide range of training set sizes. We find evidence that incorporating chemistry-informed inductive bias can reduce the amount of training data required to reach a given level of test accuracy.
Paper Structure (10 sections, 13 equations, 3 figures)

This paper contains 10 sections, 13 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Modeling Framework
  3. Full Model
  4. Restricted Model
  5. Empirical Results
  6. Description of the Datasets
  7. Model Implementation and Training
  8. Performance Evaluation
  9. Model Visualization
  10. Discussion

Figures (3)

  • Figure 1: Overview of modeling framework. (a) For a given material, the simple heuristic rules predict a binary label using just the element fractions by taking the sign of a weighted average of the parameters of the constituent elements. (b) Both the full model and the restricted model can be understood from this weighted average of parameters perspective -- the full model has a separate parameter for each element whereas the restricted model involves parameter tying so that multiple elements share the same parameter. The parameter tying in the restricted model approach can enable the incorporation of chemistry-informed inductive bias. Each model's approach for diagnosis is illustrated with the example material $\mathrm{Li Ca_2 Mg}$.
  • Figure 2: Performance versus training set size. The top plot and bottom plot respectively correspond to the the topology classification and metallicity classification tasks. For each plot, the mean and standard deviation of the test accuracy is shown for the full model and the restricted model at 25 different training set sizes. These curves were obtained by aggregating results across many iterations of train and test at each training set size (with more iterations for smaller training set sizes). Test set size was fixed at 400 samples.
  • Figure 3: Interpretable visualization of the metallicity classification model. The learned parameters of the full model when fit on the entire metallicity dataset are shown on the periodic table. The values of the parameters are shown numerically and displayed visually via the color of the element. Using this table, one can immediately perform a heuristic diagnosis of whether a material is a metal by looking at the sign of the appropriately weighted average of the material's constituent elements' parameters.