Machine Learning and Materials Informatics: Recent Applications and Prospects

• Historical examples include Hume-Rothery rules, Hall-Petch relationships, and group-contribution methods, which established empirical links between material descriptors and properties.Source: Overarching Perspectives · p. 3
• Data-driven materials research has become an essential part of the materials research portfolio, supported by simulations and high-throughput experiments or computations that generate targeted critical data.Source: Overarching Perspectives · p. 3
• Materials informatics learns from past reliable data to identify previously unknown correlations and make rapid property predictions without directly solving governing equations.Source: Overarching Perspectives · pp. 2–3
• Applying models outside the domain of prior data is dangerous, making recognition of out-of-domain cases and prediction-uncertainty quantification central challenges.Source: Overarching Perspectives · p. 3
• The article reviews successful data-driven materials strategies from the last decade and identifies challenges the community should overcome.Source: Overarching Perspectives · p. 3

• Reliable, curated past data or a controlled effort to create it is a prerequisite for applying machine learning to a materials problem.Source: Elements of Machine Learning (Within… · p. 3
• A materials-property dataset defines inputs as materials and targets as measured or computed properties, enabling prediction of a new material’s property.Source: Elements of Machine Learning (Within… · p. 4
• Fingerprinting reduces each material to a numerical representation, a domain-expertise-intensive step that makes quantitative prediction possible.Source: Elements of Machine Learning (Within… · p. 4
• Learning establishes a numerical mapping from fingerprints to continuous or discrete target properties using algorithms such as regression, trees, or neural networks.Source: Elements of Machine Learning (Within… · pp. 4–5
• Cross-validation and testing on unseen data are essential for checking generalization and avoiding overfitting.Source: Elements of Machine Learning (Within… · p. 5
• The broader machine-learning process includes organized dataset creation, fingerprinting, learning, and progressive targeted data infusion for adaptive improvement.Source: Elements of Machine Learning (Within… · p. 5

• Fingerprint design depends on the problem and prediction goals, with granularity varying according to required accuracy and the desired level of understanding.Source: Hierarchy of Fingerprints or Descriptors · p. 5
• Finer fingerprints generally offer greater expected accuracy but require more labor and data and provide less conceptual learning.Source: Hierarchy of Fingerprints or Descriptors · p. 6
• Coarser fingerprints are generally appropriate for rapid initial screening, while finer representations suit accuracy-critical predictions.Source: Hierarchy of Fingerprints or Descriptors · pp. 5–6
• Material fingerprints should remain invariant to rigid translations and rotations so equivalent physical configurations receive equivalent representations.Source: Hierarchy of Fingerprints or Descriptors · p. 6

• Hume-Rothery and Hall-Petch relationships show how coarse descriptors can connect composition or grain size with materials behavior.Modern machine learning extends this knowledge-discovery strategy to multivariate and highly nonlinear dependencies.Source: Examples of learning based on… · p. 6
• LASSO-based workflows generate large nonlinear descriptor spaces, select critical features, and build surrogate models for intrinsic electrical breakdown fields.The workflow includes cross-validation and testing after feature generation and down-selection.Source: Examples of learning based on… · pp. 6, 8
• The breakdown-field model screened perovskites and identified boron-containing compounds predicted to have intrinsic breakdown strengths of ∼1 GV/m, later confirmed by first-principles computations.The benchmark began with 82 binary octet insulators, while four new cases were outside the original dataset.Source: Examples of learning based on… · p. 8
• Descriptor-based classification predicted preferred crystal structures, including an 86% correct-structure probability for 2,105 experimentally known AxBy examples.The model searched 1.7 × 10^5 nonlinear descriptors and reduced them to three optimal descriptors.Source: Examples of learning based on… · p. 8
• A related proof of concept predicted 12 novel gallide candidates, which were synthesized and confirmed as Heusler compounds.The candidates had formulae MRu2Ga and RuM2Ga, with M = Ti, V, Cr, Mn, Fe, or Co.Source: Examples of learning based on… · p. 9
• Gross-level descriptors have also supported surrogate models for band gaps, formation enthalpies, free energies, defect energetics, melting temperatures, mechanical properties, thermal conductivity, and catalytic activity.Source: Examples of learning based on… · p. 9

• Fragment-level descriptors encode finer structural detail than gross properties by representing materials through molecular or chemical building blocks.Their origins include cheminformatics, QSAR/QSPR, and polymer group-contribution methods.Source: Examples of learning based on… · pp. 9–10
• Hundreds of polymers assembled from seven chemically allowed basic units were evaluated with DFT for dielectric constant and band gap prediction.The study included van der Waals interactions and fingerprinted the polymers for machine-learning modeling.Source: Examples of learning based on… · p. 10
• Kernel ridge regression uses distances in fingerprint space between a new polymer and training examples to predict its property.The workflow is illustrated for surrogate predictions of key dielectric polymer properties and implemented in the Polymer Genome application.Source: Figure 4 · p. 11
• Polymer properties that are difficult to compute or measure, including band gap, dielectric constant, glass transition temperature, and dielectric loss, can be learned and predicted.Source: Examples of learning based on… · p. 12
• Fragment-based representations extend beyond polymers to predicting compositions and likely crystal structures of AxByOz ternary oxides.The probabilistic model combines crystal-structure type with elemental composition information.Source: Examples of learning based on… · p. 12

• Fine-level fingerprints encode precise atomic configurations for learning potential energies, structural phases, motifs, and atomic forces.Such models can support accelerated atomistic computation and efficient on-the-fly characterization.Source: Examples of learning based on… · p. 12
• Chemical accuracy means errors below 1 kcal/mol for potential energies and reaction enthalpies, or below 0.05 eV/˚A for atomic forces.These thresholds are important for reliable molecular dynamics and precise structural-phase identification.Source: Examples of learning based on… · p. 12
• Machine-learning surrogates trained on atomic configuration-to-property data can be several orders of magnitude faster than DFT while retaining quantum-mechanical and chemical accuracy.They also address the limited transferability of traditional semi-empirical force fields when adequate reference DFT data are available.Source: Examples of learning based on… · p. 13
• Fine-level fingerprinting schemes must be invariant to translations, rotations, and exchange of like atoms, while remaining continuous and differentiable under small positional changes.Proposed approaches include symmetry functions, bispectra, Coulomb matrices, and SOAP.Source: Examples of learning based on… · p. 13
• Machine-learning force fields map fingerprints to materials properties using neural networks, kernel ridge regression, or Gaussian process regression.Behler-type schemes and Gaussian approximation potentials have demonstrated chemical accuracy, versatility, and efficiency.Source: Examples of learning based on… · pp. 13–14
• Direct atomic-force learning determines total potential energy by integrating forces along a reaction coordinate or molecular-dynamics trajectory.The approach assigns forces uniquely to individual atoms.Source: Examples of learning based on… · p. 14
• Fine-level fingerprints also support structure refinement, phase-diagram construction from XRD spectra, and classification of atomic environments.Examples include Bayesian/MCMC refinement and SOAP-based dimensionality reduction for silicon.Source: Examples of learning based on… · p. 14, Figure 5 · p. 15

Adaptive design and uncertainty

• Predicted uncertainty can reveal whether a new case lies inside or outside the training-data domain and distinguish interpolation from extrapolation.Uncertainty quantification also supports decisions about which new materials to add during iterative learning.Source: Quantifying the uncertainties of… · p. 16, Adaptive learning and design · p. 16
• Adaptive design improves models by balancing exploration of new material systems against exploitation of currently promising candidates.The goal is to select the next material or question that improves the model or target-material search.Source: Adaptive learning and design · pp. 16–17, Figure 6 · p. 17

Advanced learning targets

• Vectorial targets such as electronic or vibrational densities of states are better learned as complete functions rather than as independent scalar values.The approach seeks to capture the target function simultaneously across energy or frequency.Source: Other algorithms · p. 18

Multi-fidelity learning

• Multi-fidelity learning combines properties computed at different cost and accuracy levels rather than requiring low-fidelity values for every material.This addresses combinatorial searches across large chemical and configurational spaces, where exhaustive low-fidelity computation can be demanding.Source: Figure 6 · p. 17, Other algorithms · p. 18

Inverse design

• Inverse design seeks materials with desired properties, but converting predicted fingerprints into physically and chemically meaningful materials remains a major hurdle.Proposed strategies constrain fingerprints to realizable materials or iteratively search material populations with genetic algorithms or simulated annealing.Source: Other algorithms · pp. 18–19

When to use machine learning

• Machine learning requires reliable past data and is most appropriate for properties costly to measure or compute, complex phenomena, or settings with unknown governing equations.Problem selection should precede adoption of machine-learning methods.Source: Decisions on when to use machine… · p. 19