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REVIEW 4 major objections 5 minor 26 references

Amending CALPHAD databases using a neural network for predicting mixing enthalpy of liquids

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A neural network trained on 91 known binary liquid alloys can predict the mixing enthalpy of unseen binary systems with estimated uncertainty below 1 kJ/mol, and the resulting Redlich-Kister parameters can be written directly into CALPHAD…

desk verdict Useful ML pipeline for filling missing binary liquid Hmix in steel CALPHAD databases, with honest LOOCV, but the <1 kJ/mol uncertainty claim for extrapolated systems is asserted rather than demonstrated. read the letter →

arxiv 2504.18366 v2 pith:WWZWAOFV submitted 2025-04-25 physics.chem-ph cond-mat.dis-nncond-mat.mtrl-sci

Clement Vincely , Amin Reiners-Sakic , Vedant Dave , Erwin Povoden-Karadeniz , Elmar Rueckert , Ronald Schnitzer , David Holec This is my paper · ORCID
classification physics.chem-phcond-mat.dis-nncond-mat.mtrl-sci
keywords CALPHADneuralnetworkmixingenthalpyliquidphaseRedlich-Kisterparametersleave-one-outcross-validationthermodynamicdatabasesmaterialsinformatics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that a neural network can predict the mixing enthalpy of liquid binary alloy systems that were entirely absent from its training data, with an estimated uncertainty below 1 kJ/mol. If true, the approach turns an existing thermodynamic database into a generator of Redlich-Kister parameters for the 140 missing binary combinations among 22 elements, so those parameters can be plugged directly back into CALPHAD databases. The authors argue this can spare substantial experimental calorimetric work on systems such as Fe-Sn, Fe-Sb, and Al-Sb that are becoming relevant due to scrap recycling in steel production. The claim is demonstrated through k-fold cross-validation, leave-one-out cross-validation, and an uncertainty quantification that removes two correlated systems at a time.

What carries the argument

The central object is a neural network regression model mapping a descriptor vector of a binary liquid at a given composition to its mixing enthalpy $H_{\mathrm{mix}}$. The descriptors combine 151 atomic features, 181 composition-based features, plus Miedema and Yang alloy features extracted with Matminer, chosen to encode electronegativity differences, orbital overlaps, and semi-empirical enthalpic trends. The model is trained at a fixed temperature, 1873 K, on 2000 equidistant composition points per binary system extracted from the MatCalc open database with pycalphad, augmented by experimental enthalpy data. Validation uses 10-fold cross-validation and leave-one-system-out cross-validation to test genuine extrapolation; the final predictions are fitted to a fourth-order Redlich-Kister polynomial $H_{\mathrm{mix}} = x_1 x_2 \sum_{k=1}^{4} L_k (x_1 - x_2)^{k-1}$, whose parameters are tabulated for direct insertion into a CALPHAD database file.

What would settle it

Measure the mixing enthalpy of a predicted-but-unseen binary system such as Al-Sn or Al-Sb by high-temperature calorimetry at 1873 K and compare the curve to the model's prediction; if the deviation exceeds the claimed 1 kJ/mol uncertainty at any composition, the central uncertainty claim is falsified for that system.

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Extended reading notes

Core claim

On its own terms, the paper claims that a feedforward neural network, trained on 91 binary liquid-phase systems from an open steel database supplemented with experimental mixing enthalpies, learns composition-dependent interaction behavior well enough to predict mixing enthalpy curves for binary systems it has never seen. The key demonstration is leave-one-out validation: when a whole binary system such as Fe-Cu is quarantined, the network reproduces the CALPHAD curve, including demixing, as long as some other binary containing each element (Fe and Cu) remains in training. The two failures, Fe-Sn and Fe-Sb, occur precisely when no other Sn- or Sb-containing system is available. The paper further reports that a model trained on all data achieves a mean absolute error of 16.52 J/mol on held-out points and R²=0.99, and that uncertainty from removing a second correlated system stays below about 0.5 kJ/mol, leading to the claim that extrapolated predictions for the 140 missing binaries carry errors under 1 kJ/mol.

Load-bearing premise

The central claim rests on the premise that interaction knowledge from binaries containing an element transfers to unseen binaries with that element—a premise the paper shows fails when a quarantined element disappears from training (Fe-Sn and Fe-Sb), so the blanket 1 kJ/mol claim for all 140 missing binaries assumes this transfer works for every element, including sparse As, Sn, and Sb.

Editorial extensions

If this is right

  • All 140 missing binary liquid systems among the 22 considered elements become available as fitted Redlich-Kister parameters, so a CALPHAD database can be amended without new calorimetric measurements.
  • Systems relevant to scrap recycling, such as Fe-Sn, Fe-Sb, Fe-As, Al-Sn, and Al-Sb, receive a first thermodynamic description at 1873 K, useful for initial phase-stability screening.
  • The same workflow can be extended to temperature-dependent training data, since the constant-temperature restriction is presented as a proof of concept rather than a fundamental limit.
  • The predicted parameters are formatted to be read directly into existing thermodynamic database files, making the output usable by standard CALPHAD software.
  • If the uncertainty claim holds, the model provides quantitatively reliable interpolation across the binary composition matrix, complementing prior work on ternary extrapolation from known binaries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's own LOOCV failures for Fe-Sn and Fe-Sb imply that the 140 'missing' predictions should be stratified by how many correlated binaries exist for the involved elements; binaries pairing two sparse elements (e.g., As-Sn, As-Sb, Sn-Sb) are the least supported, and a calorimetric spot-check on one of them would be the sharpest test of the 1 kJ/mol claim.
  • Because the descriptor set includes Miedema and Yang features that already encode semi-empirical estimates of mixing enthalpy, part of the apparent predictive accuracy may be inherited from those physics-informed features rather than learned from the thermodynamic database; ablating those features and retraining would separate the two contributions.
  • The uncertainty-quantification procedure suggests a natural active-learning loop: remove the binary whose removal most degrades predictions for a target system, run an experiment there, add it to the training set, and repeat to build a complete 22-element matrix with minimal calorimetric effort.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a neural-network model trained on CALPHAD-derived and experimental liquid-phase mixing-enthalpy data for 91 binary systems of 22 elements at 1873 K, using Matminer elemental and composition features. The authors report a 10-fold cross-validated MAE of 16.52 J/mol, a leave-one-system-out test on Fe-X binaries, and an uncertainty analysis that removes a primary and one correlated secondary system. They then use the model to predict Hmix for all missing binaries, extract Redlich-Kister parameters, and claim that the uncertainty of the predicted mixing enthalpy is below 1 kJ/mol, so that the parameters can be reintegrated into a CALPHAD database.

Significance. If the extrapolation claim were fully supported, this would be a valuable tool for augmenting CALPHAD databases with first-pass descriptions of unassessed binary systems, especially for tramp elements relevant to steel recycling. The paper has genuine strengths: the LOOCV protocol is the right kind of test for unseen systems; the authors openly report the Fe-Sn and Fe-Sb failures; the data and code are shared through a Zenodo repository; and the Redlich-Kister extraction addresses practical use by the CALPHAD community. However, the evidence as presented supports a more limited claim than the abstract makes: reliable extrapolation is demonstrated only for systems whose elements appear elsewhere in the training set, and the sub-1 kJ/mol uncertainty bound is asserted for systems that were not tested against any held-out data.

major comments (4)
  1. [Sec. 3.1 and Fig. 3] The headline MAE of 16.52 J/mol is reported for the best of 10 folds in a point-level k-fold split, so every binary system appears in the training set. This metric cannot support the abstract's claim that the model predicts mixing enthalpy for systems not present in the training dataset. The paper should either report metrics from the LOOCV as the primary out-of-system measure or clearly label the k-fold result as an interpolation test.
  2. [Sec. 3.2 and Sec. 3.4, Fig. 7] The LOOCV is performed only on Fe-X systems, and it fails outright for Fe-Sn and Fe-Sb because no other Sn- or Sb-containing system remains in training. Yet the final deliverable includes missing binaries such as Al-Sn and Al-Sb, where the only training information about Sn or Sb is the single Fe-Sn or Fe-Sb system. The paper does not provide a held-out test for this regime, so the transferability that is load-bearing for those predictions is not demonstrated. At minimum, the abstract and Sec. 3.4 should be reworded to state that reliable extrapolation is conditional on the element being represented elsewhere in the training set.
  3. [Sec. 3.3 and abstract] The uncertainty quantification removes a primary and one correlated secondary system and compares the resulting predictions with CALPHAD values from the same database family used for training. This measures internal consistency of the database, not physical accuracy, and it is shown only for Cu-based systems with many Fe-Z training systems. The abstract's statement that 'the estimated uncertainty of the model is below 1 kJ/mol for the predicted mixing enthalpy' is therefore not supported for the genuinely extrapolated predictions. The paper should either provide a validated error estimate for missing systems (e.g., against experimental data for at least a few held-out systems) or replace the uncertainty claim with a clearly labeled consistency measure.
  4. [Sec. 3.4, final paragraph] The authors concede that As-X, Sn-X, and Sb-X systems 'seem to perform relatively worse' and then state 'we believe' that extrapolated errors will be below 1 kJ/mol. This is an explicit admission that the central uncertainty claim is not demonstrated for the systems that matter most for the proposed application. The manuscript should either provide quantitative evidence for the error on such systems or remove the unqualified sub-1 kJ/mol claim from the abstract and summary.
minor comments (5)
  1. [Abstract] The phrase 'amended with several direct experimental reports' is vague; the paper should specify which systems and how many experimental data points were added.
  2. [Eq. (1)] The Redlich-Kister expansion is written with indices k=1...n, whereas the CALPHAD convention typically starts at k=0; this may confuse readers comparing with standard database files.
  3. [Fig. 6 caption] The caption abbreviates RMSE as 'RSME'; please correct the typo.
  4. [Sec. 2.1 and Fig. 1] The heatmap uses green and red fields, but the caption does not state the color convention explicitly; please add a legend or explicit sentence.
  5. [Sec. 2.4 and Table 1] The precision of the tabulated RK parameters is much higher than the claimed physical accuracy; the footnote is helpful but could be strengthened by adding an explicit statement of the implied uncertainty in the parameter values.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model is trained on external CALPHAD/experimental Hmix data and tested on genuinely held-out systems, while the weaker 1 kJ/mol extrapolated-uncertainty claim is an explicit belief, not a circular derivation.

full rationale

The paper's derivation chain is: extract Hmix values from an external open CALPHAD database plus literature experiments, featurize with Matminer element- and composition-based descriptors, train a neural network to predict Hmix, then fit Redlich-Kister polynomials to the NN output. The target quantity for unseen binaries is not used to construct the features (Miedema and Yang descriptors are derived from elemental properties, not from the target Hmix values), and for quarantined systems the target values are withheld during training. The LOOCV in Sec. 3.2 is a genuine held-out-system test, and its failures for Fe-Sn and Fe-Sb, explicitly attributed to the disappearance of Sn/Sb from the training set, show the test is not vacuous. The uncertainty quantification in Sec. 3.3 compares predictions with CALPHAD values from the same database family used for training, so it measures internal consistency rather than physical accuracy; however, the paper does not present this comparison as a formal derivation of the extrapolated error bound. In Sec. 3.4 the authors explicitly say 'we believe that even for the extrapolated predictions, the difference in error between the true mixing enthalpy and the predicted mixing enthalpy should be less than 1 kJ/mol', and they also flag that As-X, Sn-X, and Sb-X systems 'seem to perform relatively worse'. That is an honest limitation and a correctness/robustness risk, not a circular step. Self-citations such as the MatCalc database [10] are data sources, not load-bearing uniqueness arguments, and no equation is defined in terms of the quantity it claims to predict; no fitted parameter is renamed as a prediction. Therefore no definitional or constructional circularity is present.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the transferability of binary interaction knowledge across elements, on the accuracy of the underlying CALPHAD assessments, on the completeness of the chosen descriptors, and on the adequacy of a 4th-order RK form. No new physical entities are introduced; the only fitted quantities are the NN weights and hyperparameters, plus the extracted RK coefficients.

free parameters (4)
  • NN architecture hyperparameters = not stated in text; in Supplementary Table S1
    Number of layers, neurons, learning rate, and activation were selected by KerasTuner random search on validation loss; the final prediction model depends on these choices.
  • Redlich-Kister order n = 4
    Set uniformly for all systems in Sec. 2.4; this fixes the flexibility of the fitted database parameters and is not selected per system.
  • Temperature = 1873 K
    Fixed reference temperature for all extractions and predictions (Sec. 2.1); the model's validity is restricted to this temperature.
  • Feature set = 332 Matminer descriptors
    The input space is chosen from Matminer's library, including Miedema and Yang features that already encode alloy enthalpy estimates; the model's output is partly shaped by these prior models.
assumptions (5)
  • domain assumption The 91 CALPHAD binary assessments used as ground truth are accurate enough for training and validation.
    Sec. 2.1 and Sec. 3.1: the NN is trained and evaluated against Hmix values extracted via pycalphad from the MatCalc database; if those assessments are wrong, the model learns wrong physics.
  • domain assumption Element-pair interaction knowledge transfers across binaries containing a common element.
    Sec. 3.2 LOOCV: the model is expected to predict quarantined Fe-X systems using other X-Y systems; it explicitly fails for Sn and Sb when no other system contains the element.
  • domain assumption The 332 Matminer features, including Miedema and Yang descriptors, capture the physical determinants of liquid mixing enthalpy.
    Sec. 2.1: these features are used as input; no analysis is provided showing they suffice for all 22 elements.
  • domain assumption A fourth-order Redlich-Kister polynomial adequately represents Hmix(x) for every predicted binary system.
    Sec. 2.4: n=4 is fixed uniformly for all systems; no goodness-of-fit or cross-validation of the RK form is reported.
  • standard math Statistical learning assumptions such as independence and smoothness hold for the extracted data points.
    Sec. 3.1: 10-fold CV randomly splits individual points; the 2000 dense points per system make points within a system highly correlated, so the assumption is violated for the point-level split.

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Pith. "Pith review of Amending CALPHAD databases using a neural network for predicting mixing enthalpy of liquids." pith.science (2026). https://pith.science/paper/WWZWAOFV

@misc{pith2026250418366,
  author       = {Pith},
  title        = {Pith review of: Amending CALPHAD databases using a neural network for predicting mixing enthalpy of liquids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WWZWAOFV}},
  note         = {Machine review of arXiv:2504.18366}
}
read the original abstract

In order to establish the thermodynamic stability of a system, knowledge of its Gibbs free energy is essential. Most often, the Gibbs free energy is predicted within the CALPHAD framework using models employing thermodynamic properties, such as the mixing enthalpy, heat capacity, and activity coefficients. Here, we present a deep-learning approach capable of predicting the mixing enthalpy of liquid phases of binary systems that were not present in the training dataset. Therefore, our model allows for a system-informed enhancement of the thermodynamic description to unknown binary systems based on information present in the available thermodynamic assessment. Thereby, significant experimental efforts in assessing new systems can be spared. We use an open database for steels containing 91 binary systems to generate our initial training (and validation) and amend it with several direct experimental reports. The model is thoroughly tested using different strategies, including a test of its predictive capabilities. The model shows excellent predictive capabilities outside of the training dataset as soon as some data containing species of the predicted system is included in the training dataset. The estimated uncertainty of the model is below 1 kJ/mol for the predicted mixing enthalpy. Subsequently, we used our model to predict the enthalpy of mixing of all binary systems not present in the original database and extracted the Redlich-Kister parameters, which can be readily reintegrated into the thermodynamic database file.

Figures

Figures reproduced from arXiv: 2504.18366 by the authors.

Figure 1
Figure 1. This heatmap provides information on the liquid binary phases in the used, open-source thermo [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The workflow representing the featurization and validation process to construct a NN for extracting [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Overview of the best-performing k-fold model (Fold 7) shown as the density of points representing the difference between predicted and true value (∆Hmix, y-axis) vs. the true value Hmix (x-axis). 3.2. LOOCV validation of the model As a first test of the predictive power of our model when extrapolating to new binary systems, we employed the LOOCV procedure. Here we used the same NN architecture as before, but this ti… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: LOOCV predictions of the mixing enthalpy ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 6
Figure 6. Figure 6: The error metrics of Fold 7 seem to perform significantly well with the lowest mean [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 5
Figure 5. Figure 5: Example of uncertainty quantification for several Cu- [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Performance evaluation of the final NN model (Fold 7) on the systems where input data (thermo [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Predicted mixing enthalpy (Hmix) for all 20 Al-X binary systems. If available in the thermody￾namic database, the CALPHAD results are shown with a solid orange line for reference. We also implemented an in-house Python code to extract the Redlich-Kister parameters from…

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