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Machine learning with force-field inspired descriptors for materials: fast screening and mapping energy landscape

Kamal Choudhary, Brian DeCost, Francesca Tavazza

arXiv:1805.07325v2cond-mat.mtrl-sci

TL;DR

Chemical-only descriptors do not distinguish structural prototypes with the same composition. The paper introduces chemo-structural descriptors for materials learning and reports high accuracy on a relatively small multicomponent-materials dataset, alongside demonstrations of materials screening and energy-landscape investigation.

  • Problem

    Chemical-only descriptors do not represent structural information needed to distinguish prototypes with the same composition.

    Source: §I · p. 2

  • Method

    The paper introduces a complete set of chemo-structural descriptors and applies machine learning to material properties.

    Source: §I · p. 2, §VI · p. 18

  • Results

    The authors report very high accuracy on a relatively small multicomponent-materials dataset and demonstrate screening exfoliable semiconductors with specific requirements.

    Source: §VI · p. 18

  • Takeaways & Limitations

    Integration with an evolutionary search algorithm opens a route to accelerated investigation of high-dimensional structure and energy landscapes.

    Source: §VI · p. 19

Abstract

from arXiv · show

We present a complete set of chemo-structural descriptors to significantly extend the applicability of machine-learning (ML) in material screening and mapping energy landscape for multicomponent systems. These new descriptors allow differentiating between structural prototypes, which is not possible using the commonly used chemical-only descriptors. Specifically, we demonstrate that the combination of pairwise radial, nearest neighbor, bond-angle, dihedral-angle and core-charge distributions plays an important role in predicting formation energies, bandgaps, static refractive indices, magnetic properties, and modulus of elasticity for three-dimensional (3D) materials as well as exfoliation energies of two-dimensional (2D) layered materials. The training data consists of 24549 bulk and 616 monolayer materials taken from JARVIS-DFT database. We obtained very accurate ML models using gradient boosting algorithm. Then we use the trained models to discover exfoliable 2D-layered materials satisfying specific property requirements. Additionally, we integrate our formation energy ML model with a genetic algorithm for structure search to verify if the ML model reproduces the DFT convex hull. This verification establishes a more stringent evaluation metric for the ML model than what commonly used in data sciences. Our learnt model is publicly available on the JARVIS-ML website (https://www.ctcms.nist.gov/jarvisml ) property predictions of generalized materials.

I. INTRODUCTION

Chemical-only descriptors cannot distinguish structural prototypes with the same composition, motivating descriptors that encode both chemistry and structure. The paper introduces CFID and applies it to material-property prediction and energy-landscape mapping.

I. INTRODUCTION

  • Chemical descriptors alone cannot model different structure prototypes with the same composition because they omit structural information, including bond and dihedral angles.Source: §I · p. 2
  • The study trains two classification and twelve regression models, screens 2D layered materials, and combines a formation-energy model with a genetic algorithm for structure search.Source: §I · pp. 2–3
  • The machine-learning convex hull is reported to agree closely with the DFT convex hull, offering a less expensive route to map multicomponent energy landscapes.Source: §I · p. 3

II. CLASSICAL FORCE-FIELD INSPIRED DESCRIPTORS (CFID)

  • CFID combines radial and nearest-neighbor distributions, bond-angle and dihedral distributions, chemical features, and average atomic radial-charge descriptors.Source: §II · p. 3
  • The descriptors assume interactions matter through four-body terms, with higher-order contributions treated as negligible.Source: §II · p. 3
  • The combined chemical and structural representation has 1,557 descriptors and is independent of primitive, conventional, or supercell representation.The authors contrast this with methods such as the Coulomb matrix, which require a primitive structure.Source: §II · p. 4

III. TRAINING DATA AND ALGORITHM

The study trains gradient-boosted decision-tree models on a broad JARVIS-DFT materials dataset, using chemo-structural descriptors for classification and regression. The section also describes the dataset’s composition, visualization, and model-selection procedure.

Training data

  • The dataset contains 24,549 bulk and 616 monolayer 2D materials, with compositions from unary to senary and reported shares of 1.5% unary, 26% binary, 56% ternary, 13% quaternary, 2% quinary and 1% senary.It covers 201 space groups and seven crystal systems.Source: §III · p. 5

Data visualization

  • The t-SNE visualization shows a dispersed dataset without bias toward one material type, while materials with similar chemical descriptors tend to share crystal structures.The plotted marker colors encode crystal system; formation energies are concentrated around -4 to 2 eV/atom.Source: §III · p. 5

Algorithm and targets

  • The authors use GBDT for two classification tasks and twelve independent regression models, including bandgap and dielectric-constant data from OPT and MBJ calculations.The dataset also includes bulk and shear moduli and exfoliation energies for 2D layered materials.Source: §III · pp. 5–6

Model selection

  • Models use a 90:10 train-test split, five-fold cross-validation on the training set, and early stopping before further hyperparameter optimization.The independent test set is not used for training or hyperparameter optimization.Source: §III · p. 7

Learning curves

  • At similar data sizes, the MBJ bandgap model has higher MAEs than the OPT bandgap model.The comparison is shown in the supplementary learning curves.Source: §III · p. 7

IV. MODEL PERFORMANCE AND INTERPRETATIONS

The paper evaluates CFID descriptors on material classification and property prediction tasks. Metal/insulator and magnetic/non-magnetic classification achieve ROC areas of 0.95 and 0.96, respectively.

Classification

  • The authors evaluate CFID on metal/insulator and magnetic/non-magnetic classification, measuring performance by area under the ROC curve..Source: §IV · p. 8
  • ROC areas are 0.95 for metal/insulator classification and 0.96 for magnetic/non-magnetic classification.The two values correspond, respectively, to Fig. 2c and Fig. 2d.Source: §IV · p. 8
  • For bandgap classification, materials are labeled metallic when Eg=0 and non-metallic when Eg>0; the paper also applies classification to magnetic status..Source: §IV · p. 9

MAECFID-DFT MAEDFT-Exp MADDFT

The supplied comparison row reports a sample count and several values, but does not provide enough context to assign each value to a metric or comparison.

Comparison row

  • The reported row lists 24,549 entries alongside 0.12, 0.136, and 0.809; their metric assignments are not stated in the passage..Source: Formation energy · p. 9
  • The row includes the value 0.12, without identifying its metric or comparator in the passage..Source: Formation energy · p. 9
  • The row includes 0.136, without identifying its metric or comparator in the passage..Source: Formation energy · p. 9

Formation energy

The supplied formation-energy table fragments include a bulk-modulus entry and several numerical values, but do not identify the metric assignments for all values.

(meV/atom)

  • The fragment labels Bulk modulus (GPa) and reports 10,954 data points..Source: (meV/atom) · p. 9
  • The bulk-modulus fragment lists 10.5, without further metric labeling in the passage..Source: (meV/atom) · p. 9
  • The same fragment includes the range 8.5–10.0, without specifying its meaning in the passage..Source: (meV/atom) · p. 9
  • A second fragment reports 10,954 data points and the value 9.5, without identifying the associated metric..Source: Shear modulus · p. 9
  • The second fragment also lists 10.0 and the citation, without specifying their relationship in the passage..Source: Shear modulus · p. 9
  • The second fragment includes the value 23.26, without identifying its metric in the passage..Source: Shear modulus · p. 9

(GPa)

Adding structural descriptors improves formation-energy model accuracy, while descriptor-importance analysis identifies different feature groups as informative for different properties. The models are reported for multiple material properties and as tools for screening and energy-landscape exploration, with limits on direct MAE comparisons between ML and DFT.

(GPa)

  • Formation-energy MAE decreases as structural descriptors are added to chemical features.The authors describe the lower MAEs as establishing improvement from adding structural descriptors.Source: Figure 3 · p. 10, (GPa) · pp. 14–15
  • ML and DFT MAEs are not directly comparable because their reference data differ: ML is assessed against DFT data, while DFT is assessed against experiment.The authors say the CFID GBDT model fits DFT training data about as well as DFT matches experiment.Source: (GPa) · p. 11
  • The formation-energy model has an MAE of 0.12 eV/atom, in the same range as earlier formation-energy ML models, whose MAEs range from 0.039 to 0.25 eV/atom.Source: (GPa) · pp. 11–12
  • 0.45 to 0.55 is the reported refractive-index MAE range across models and crystallographic directions, with learning curves reaching a plateau at training-set sizes of order 10^3.The other examined quantities required training sets of order 10^4 to achieve high accuracy.Source: (GPa) · p. 12
  • 37 meV/atom is the exfoliation-energy model MAE, which the authors consider reasonable for screening against the 200 meV/atom exfoliability threshold.The bulk and shear modulus models have MAEs comparable to the cited DFT MAE of 10 GPa and prior ML values of 9 GPa and 10 GPa.Source: (GPa) · p. 13
  • Chemical features dominate formation-energy importance, RDF and ADF also contribute, and density, RDF, ADF, and packing fraction matter for formation energy, modulus, and refractive index, unlike bandgap and magnetic moment, which depend mainly on chemical data.Charge descriptors were least important in the formation-energy model; unfilled d- and f-orbital descriptors were important for classifying magnetic versus non-magnetic materials.Source: (GPa) · pp. 13–14

ALGORITHM

The authors apply their formation-energy ML model in genetic-algorithm searches and in staged screening of candidate 2D materials. The searches recover known stable structures and identify additional candidates, while selected predictions are checked with DFT.

ALGORITHM

  • Sequential property filters narrowed candidates to 482, then to 65 materials with fewer than three unique atom types.The filters selected MBJ bandgaps of 1.2–3 eV, negative formation energies, and exfoliation energies below 200 meV/atom.Source: ALGORITHM · p. 15
  • After 5,000 Cu structure evaluations, the ML search found one phase more stable than FCC; DFT identified it as tetragonal and only 0.01 eV/atom higher in energy than FCC.That difference is below the formation-energy model's MAE, which the authors use to validate the approach.Source: ALGORITHM · p. 16
  • The Mo-S search recovered 2H-MoS2 as the most stable structure and also identified MoS29, MoS27, Mo29S, and Mo21S as stable configurations.The paper identifies 2H-MoS2 as the known ground state for this system.Source: ALGORITHM · p. 17
  • The W-S search found 2H-WS2 stable and additional high-W, high-S structures, while the Mo-W-S convex hull demonstrates application to a multicomponent system.The reported W-S structures include W29S, WS20, W22S, W28S, and W21S.Source: ALGORITHM · p. 17
  • The ML-GA search is intended as an inexpensive screening stage; the authors recommend DFT calculations on low-energy structures afterward.They also note that classical force fields can find unphysical metastable structures during GA searches.Source: ALGORITHM · p. 17

VI. CONCLUSIONS

The paper concludes that chemo-structural descriptors support accurate learning across varied material properties, even with relatively small datasets. It also presents ML screening and genetic-algorithm integration as routes to material discovery and energy-landscape investigation.

VI. CONCLUSIONS

  • The models predict a wide variety of material properties with very high accuracy while training on a relatively small dataset for multicomponent systems.The conclusion describes the descriptors as applicable to other physical properties as well.Source: §VI · p. 18
  • ML screening identified exfoliable semiconducting materials with specified requirements, such as energy gap, which the authors say can expedite material discovery.The conclusion frames this application as screening for materials with particular property requirements.Source: §VI · p. 18
  • Integrating the formation-energy model with evolutionary search is presented as a way to investigate high-dimensional structures and energy landscapes.The authors also envision ML as a pre-screening tool for DFT-like applications.Source: §VI · p. 19
  • The model can produce some unphysical structures, which the authors note also occur with classical force fields.They nevertheless state that the present methodology should be preferred to the intensive training process of conventional force fields.Source: §VI · p. 19

Supplementary information: Machine learning with force-field inspired

The supplementary material lists descriptor components and cell-size features, and provides figures on property distributions, model learning curves, and structures from genetic-algorithm searches.

Supplementary information

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