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arxiv: 2606.21467 · v1 · pith:XWVD44COnew · submitted 2026-06-19 · ❄️ cond-mat.mtrl-sci

Machine learning metallic glass critical cooling rates through elemental and molecular simulation based featurization

Lane E. Schultz , Benjamin Afflerbach , Paul M. Voyles , Dane Morgan This is my paper

Pith reviewed 2026-06-26 13:53 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords metallic glassescritical cooling ratemachine learningmolecular dynamicsVoronoi polyhedraconvex hull energyheat capacityideal entropy
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The pith

A machine learning model predicts critical cooling rates for metallic glasses using one elemental entropy feature and three simulation-derived features, achieving R² of 0.78.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a machine learning approach to predict critical cooling rates needed to form metallic glasses, comparing simple elemental property features against more involved properties extracted from molecular dynamics simulations. It tests features across 34 alloys spanning 20 chemical systems and identifies the strongest model as one that combines an ideal entropy value based on alloy stoichiometry with three computed quantities: energy above the convex hull, change in heat capacity, and the fraction of icosahedra-like Voronoi polyhedra. Models are evaluated with a strict cross-validation that holds out entire chemical systems, yielding R² of 0.78 and mean absolute error of 0.76 in log10(K/s) units. Shapley analysis shows the features exert physically reasonable effects on the predictions. The same workflow is presented as extensible to other material properties across diverse compositions.

Core claim

The best-performing model for critical cooling rates is learned from one elemental-property feature (ideal entropy from stoichiometry) and three features from molecular dynamics simulations (energy above the convex hull, heat-capacity change, and fraction of icosahedra-like Voronoi polyhedra), reaching R² = 0.78 and MAE = 0.76 log10(K/s) under repeated leave-one-chemical-system-out cross-validation across 34 alloys from 20 systems.

What carries the argument

Machine learning regression trained on ideal entropy together with three molecular-dynamics-derived descriptors (energy above convex hull, heat capacity change, icosahedra Voronoi fraction).

If this is right

  • The same feature-extraction and modeling pipeline can be applied to high-throughput screening of other material properties for alloys of varying compositions.
  • Shapley additive explanations confirm that the selected features influence predictions in directions consistent with known physical roles in glass formation.
  • The cross-validation protocol that excludes entire chemical systems provides a realistic estimate of performance on new alloy families.
  • Combining one cheap elemental descriptor with a small number of simulation descriptors yields better accuracy than either class of features alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the simulation features remain reliable, the model could be used to rank candidate alloys for glass-forming ability before any experiment is performed.
  • The emphasis on icosahedral order and energy above the hull suggests that local structural motifs and thermodynamic stability are key drivers captured by the simulations.
  • Extending the approach to additional simulation observables, such as diffusion constants or elastic moduli, might further reduce prediction error for new chemical systems.

Load-bearing premise

Features taken from ab initio, machine-learning-potential, and empirical-potential simulations are accurate enough and comparable to one another to serve as reliable inputs for experimental critical cooling rates across many chemical systems.

What would settle it

Measure the experimental critical cooling rate for an alloy outside the training chemical systems and check whether the model's prediction falls within 0.76 log10(K/s) of that measured value.

Figures

Figures reproduced from arXiv: 2606.21467 by Benjamin Afflerbach, Dane Morgan, Lane E. Schultz, Paul M. Voyles.

Figure 1
Figure 1. Figure 1: Potential energy, self-diffusion, and viscosity for [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Potential energy (Fig. 2a), self-diffusion (Fig. 2b), and viscosity (Fig. 2c) versus [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The SHAP values for XGBoost is shown for [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: RMSE/σy as a function included features sorted with SHAP values for XGBoost models are shown. Assessing models with Xbest yields an RMSE/σy (R2 ) of 0.46 (0.78). The associated parity plot is shown in [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The parity plot using Xbest for the 34 compositions that had MLPs are shown. The model appears to predict Rc across chemical systems well. The lowest RMSE/σy obtained from the shuffling feature selection procedure (see the end of Sec. 2.10) is about 1.36 (see Supplemental Materials) and is significantly higher than the 0.46 17 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
read the original abstract

We have developed a machine learning model for critical cooling rates for metallic glasses based on computational properties. We compare results for features derived from easy-to-compute functions of elemental properties to more complex physically motivated properties using ab initio, machine-learning potentials, and empirical potential molecular dynamics methods. The established approach enables property acquisition across a diverse range of alloys. Analysis of various features for 34 alloys from 20 chemical systems shows that the best model for critical cooling rates was learned from one elemental property-based feature and three simulated features. The elemental property-based feature is an ideal entropy value based on alloy stoichiometry. The simulated features were acquired from estimates of energies above the convex hull, changes in heat capacity, and the fraction of icosahedra-like Voronoi polyhedra. Models were assessed through a demanding cross validation test based on repeatedly leaving out full chemical systems as test sets and had an $R^2$ of 0.78 and a mean average error of 0.76 in units of $[log_{10}(K/s)]$. We demonstrate with Shapley additive explanation analysis that the most impactful features have physically reasonable influence on model predictions. The established methodology can be applied to other high-throughput studies of material properties of diverse compositions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a machine learning model for predicting critical cooling rates of metallic glasses. It compares elemental-property features (including an ideal entropy based on alloy stoichiometry) against simulation-derived features obtained from ab initio calculations, machine-learning potentials, and empirical-potential molecular dynamics. The best model combines the entropy feature with three simulation quantities (energies above the convex hull, changes in heat capacity, and the fraction of icosahedra-like Voronoi polyhedra). On a set of 34 alloys spanning 20 chemical systems, a leave-one-chemical-system-out cross-validation yields R² = 0.78 and MAE = 0.76 in units of log10(K/s). SHAP analysis is used to confirm that the dominant features exert physically reasonable influence on the predictions.

Significance. If the reported performance holds under the grouped cross-validation protocol, the work supplies a practical route to estimate a technologically relevant but experimentally demanding quantity (critical cooling rate) from a small set of physically motivated computational descriptors. The leave-one-chemical-system-out validation is a clear methodological strength because it enforces generalization across distinct chemistries rather than within them. The explicit physical motivation of the chosen features together with the SHAP interpretability analysis further strengthens the contribution and supports extensibility to other high-throughput materials problems.

major comments (2)
  1. [Methods] Methods: The manuscript provides no description of how the three simulation-derived features (energies above the convex hull, heat-capacity changes, and icosahedra fractions) obtained from ab initio, machine-learning-potential, and empirical-potential molecular-dynamics runs were standardized or scaled to ensure numerical comparability before being combined in the regression model. This detail is load-bearing for the validity of the reported R² = 0.78 and MAE = 0.76.
  2. [Results] Results: The cross-validation performance metrics (R² = 0.78, MAE = 0.76) are reported without error bars, standard deviations across folds, or any uncertainty quantification, which limits assessment of the stability of the quoted figures under the leave-one-chemical-system-out protocol.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'mean average error' should be replaced by the conventional term 'mean absolute error' for clarity.
  2. The manuscript would benefit from an explicit statement of the regression algorithm (e.g., random forest, gradient boosting) and any hyperparameter selection procedure used to obtain the final model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the constructive major comments. We address each point below and will revise the manuscript to incorporate the requested clarifications and additional reporting.

read point-by-point responses

  1. Referee: [Methods] Methods: The manuscript provides no description of how the three simulation-derived features (energies above the convex hull, heat-capacity changes, and icosahedra fractions) obtained from ab initio, machine-learning-potential, and empirical-potential molecular-dynamics runs were standardized or scaled to ensure numerical comparability before being combined in the regression model. This detail is load-bearing for the validity of the reported R² = 0.78 and MAE = 0.76.

    Authors: We agree that an explicit description of feature preprocessing is necessary. All features (elemental and simulation-derived) were standardized to zero mean and unit variance using statistics computed exclusively from the training portion of each leave-one-chemical-system-out fold. This was implemented to ensure numerical comparability without introducing leakage. We will add a dedicated paragraph in the Methods section detailing this procedure, including the exact scaling method and confirmation that it was applied fold-wise. revision: yes

  2. Referee: [Results] Results: The cross-validation performance metrics (R² = 0.78, MAE = 0.76) are reported without error bars, standard deviations across folds, or any uncertainty quantification, which limits assessment of the stability of the quoted figures under the leave-one-chemical-system-out protocol.

    Authors: We acknowledge that reporting variability across folds would improve the assessment of result stability. In the revised manuscript we will add the standard deviation of both R² and MAE computed across the 20 chemical-system folds, together with a brief discussion of the observed variability. This will be presented alongside the mean values already reported. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper applies standard supervised regression (R²=0.78, MAE=0.76 log10(K/s)) to predict experimental critical cooling rates from four externally computed features: one stoichiometry-derived ideal entropy and three simulation-derived quantities (energy above hull, heat capacity change, icosahedral fraction). Validation uses grouped cross-validation that holds out entire chemical systems. No equations, fitted parameters, or self-citations reduce the target to a constructed input; features are obtained independently via ab initio/ML/empirical MD and stoichiometry. The pipeline is self-contained against external benchmarks with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that molecular simulation outputs can be treated as faithful proxies for the physical mechanisms controlling glass formation and that standard ML regression can generalize across chemical systems when trained on only 34 examples.

axioms (2)
  • domain assumption Simulation-derived quantities (energies above hull, heat capacity changes, Voronoi polyhedra fractions) accurately capture the physics relevant to critical cooling rates
    Invoked when the authors select these three features as inputs to the model
  • domain assumption Leave-one-chemical-system-out cross-validation provides a sufficient test of generalization to unseen alloys
    Used to claim model performance of R²=0.78

pith-pipeline@v0.9.1-grok · 5761 in / 1355 out tokens · 42584 ms · 2026-06-26T13:53:38.703386+00:00 · methodology

discussion (0)

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