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arxiv: 2606.08686 · v1 · pith:FCO37JSGnew · submitted 2026-06-07 · ❄️ cond-mat.mtrl-sci

Information Entropy Based Crystal Structure Prediction of Chemically Disordered Alloys via Graph Convolutional Neural Networks

Suman Chabri , Gautam Anand This is my paper

Pith reviewed 2026-06-27 17:54 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords crystal structure predictionchemically disordered alloysinformation entropygraph convolutional neural networksalchemical Monte Carlohigh-entropy alloysphase predictionpotential energy surface
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The pith

An information entropy metric from alchemical Monte Carlo trajectories on a graph convolutional neural network potential predicts stable phases in chemically disordered alloys.

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

The paper proposes an information-theoretic approach to phase prediction that uses the entropy of sampling trajectories as a convergence signal. It trains a graph convolutional neural network to stand in for the potential energy surface of alloys with many possible atomic arrangements, then runs alchemical Monte Carlo moves that swap atom types to explore configurations. Entropy of the resulting trajectories is shown to rise and then plateau when the sampling reaches the stable phase, tested on binary, ternary, quaternary and quinary compositions. The method is positioned as useful precisely when the number of possible arrangements makes exhaustive search impossible. A low-cost Bond Disproportion Vector descriptor is also benchmarked against the SOAP descriptor for the same task.

Core claim

The central claim is that the information entropy of alchemical Monte Carlo trajectories generated with a graph convolutional neural network model serves as a reliable indicator of convergence to the thermodynamically stable crystal structure for binary (CoNi, MoW, FeNi, TaW), ternary (CoCrNi, CrFeNi), quaternary (CoCrFeNi) and quinary (Al_x(CoCrFeNi)_{1-x}) chemically disordered alloys, offering a practical route when conventional enumeration or direct simulation becomes infeasible.

What carries the argument

The information entropy metric extracted from alchemical Monte Carlo trajectories on the graph convolutional neural network approximation to the potential energy surface; it quantifies when further sampling no longer reveals new low-energy configurations and thereby signals the stable phase.

If this is right

  • The entropy metric successfully distinguishes stable phases across binary through quinary alloy compositions.
  • Alchemical Monte Carlo sampling guided by the trained graph convolutional network becomes feasible for systems whose combinatorial size defeats direct enumeration.
  • The Bond Disproportion Vector descriptor offers a lower-cost alternative to SOAP for some but not all of the tested compositions.
  • Information entropy supplies a quantitative measure of how thoroughly the potential energy landscape has been explored during sampling.

Where Pith is reading between the lines

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

  • The same entropy signal could be monitored during sampling to decide when to stop and accept a predicted structure for new high-entropy alloy compositions not included in the training set.
  • Transfer of the trained graph convolutional network to chemically similar but previously unseen alloy systems would allow rapid phase screening without retraining from scratch.
  • If the entropy plateau occurs at different temperatures, the approach could map phase boundaries as a function of temperature for a given composition.

Load-bearing premise

The graph convolutional neural network, trained on limited data, approximates the true potential energy surface closely enough that entropy of the Monte Carlo trajectories correctly identifies the stable phase rather than an artifact of model error.

What would settle it

Experimental or high-accuracy density-functional-theory confirmation that the phase flagged by the entropy plateau for the quaternary CoCrFeNi alloy differs from the known stable structure.

Figures

Figures reproduced from arXiv: 2606.08686 by Gautam Anand, Suman Chabri.

Figure 1
Figure 1. Figure 1: (a) Schematic of the descriptor generation and featurisation of the atomistic configuration to generate a graph and (b) graphs for three different configurations of CoCrNi alloy showing the atomistic data leading to the unstructured graphs. 2.4 Graph Dataset Description A dataset comprising 20 atomic configurations ((Ng = 20)) was used for supervised training of the GCNN. Each configuration corresponds to … view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the GCNN for node-level regression. Inputs (X, A) are converted to sparse tensors; stacked GraphConv layers perform message passing; a linear head produces a scalar at each node. Mini-batches concatenate graphs and adjust indices via Batch.from_data_list. contrast, the BDV descriptor shows a smoother and more monotonic decline in both training and validation loss. After the initial rapid decre… view at source ↗
Figure 3
Figure 3. Figure 3: The loss curves for CoCrNi alloy in BCC and FCC crystal structures for BDV (a and c) and SOAP (b and d) descriptors. and sharper minima, so that for a finite learning rate the gradient updates may temporarily overshoot the minimum along directions associated with large eigenvalues, producing the oscillatory behaviour and sudden reductions in loss observed during training. This mathematical distinction refl… view at source ↗
Figure 4
Figure 4. Figure 4: The energy prediction curves for (a) binary, (b) ternary, (c) quaternary and (d) quinary alloys [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the performance with (a) test MSE and (b) R2 score of BDV and SOAP as descriptors for binary, ternary, quaternary, and quinary alloys Algorithm 1- GAASP: Genetic Algorithm-Based Atomistic Sampling Protocol Input: Supercell with NA atoms; population size N; GA cycles G; number of parents X; temperature T Output: Sampled atomistic configurations representing the energy landscape Generate N rand… view at source ↗
Figure 6
Figure 6. Figure 6: The variation in the mean energy and corresponding energy distribution evolution with alchem￾ical Monte Carlo swap with GCNN ML model for (a) BCC and (b) FCC crystal structure of Al0.05(CoCrFeNi)0.95 high-entropy alloy 3 Results and discussions 3.1 Comparison of BDV and SOAP descriptors for predicting the potential energy of binary, ternary, quaternary and quinary alloys Figure 4a, 4b, 4c, and 4d show the … view at source ↗
Figure 7
Figure 7. Figure 7: (a) The description of Kullback-Leibler (KL) divergence DKL between the sampled potential energy landscape (P) and reference or equilibrium potential energy landscape, (b) The graphical explanation of the DKL value, and (c) schematic representation of the crystal structure prediction problem as an information alignment problem [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) The variation of the entropy parameter for the candidate crystal structures (BCC and FCC) for binary, ternary, and quaternary alloys and (b) the application of the entropy parameter for the phase prediction with composition variation of Alx(CoCrFeNi)1−x . 4 Conclusions The present investigation demonstrates the applicability of the Alchemical Monte Carlo (or GAASP) computational framework, combined wit… view at source ↗
read the original abstract

The phase prediction of chemically disordered alloys poses a significant computational challenge due to the combinatorial complexity of such materials. The high-throughput compositional exploration of chemically disordered alloys, including high-entropy alloys, requires an approach to efficiently explore the potential energy landscape of such complex materials. Additionally, a metric to quantify the potential energy landscape explored for phase prediction of the compositions needs to be defined. We propose an information-theoretic approach to phase prediction in chemically disordered alloys in the present work. We demonstrate the applicability of alchemical Monte Carlo sampling using an efficient Graph Convolutional Neural Network-Based machine learning model. We additionally demonstrate the applicability and limitations of the Bond Disproportion Vector (BDV) as a low-computational-cost descriptor and benchmark it against the state-of-the-art Smooth Overlap of Atomic Positions (SOAP) descriptor. We show the applicability of an information entropy-based metric for the phase prediction of binary (CoNi, MoW, FeNi and TaW), ternary (CoCrNi, CrFeNi), quaternary (CoCrFeNi) and quinary ($\mathrm{Al_x(CoCrFeNi)_{1-x}}$) alloys. Information entropy-based phase prediction can be applicable in challenging cases where conventional approaches are not feasible.

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 / 0 minor

Summary. The manuscript proposes an information-theoretic approach to phase prediction for chemically disordered alloys, using alchemical Monte Carlo sampling driven by a Graph Convolutional Neural Network (GCN) surrogate model together with an information entropy metric. It reports applicability of the method to binary (CoNi, MoW, FeNi, TaW), ternary (CoCrNi, CrFeNi), quaternary (CoCrFeNi), and quinary (Al_x(CoCrFeNi)_{1-x}) alloys, benchmarks the Bond Disproportion Vector descriptor against SOAP, and claims utility in regimes where conventional approaches are infeasible.

Significance. If the GCN surrogate produces sufficiently accurate relative energies, the entropy metric on alchemical MC trajectories could offer a scalable route to phase prediction in high-entropy alloys whose combinatorial complexity defeats direct enumeration or conventional sampling.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'information entropy-based phase prediction can be applicable in challenging cases where conventional approaches are not feasible' is unsupported because no validation metrics (MAE on configuration energies, ranking preservation of low-energy structures, or transferability tests on the listed alloy compositions) are reported.
  2. [Abstract] Abstract: the reliability of the entropy signal as an indicator of convergence to the stable phase rests on the unverified assumption that the GCN, trained on limited data, produces relative energies accurate enough for the sampled distribution to reflect the true Boltzmann-weighted landscape; without reported error bars or cross-validation on the relevant energy window this assumption remains load-bearing and untested.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for clearer validation in the abstract. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'information entropy-based phase prediction can be applicable in challenging cases where conventional approaches are not feasible' is unsupported because no validation metrics (MAE on configuration energies, ranking preservation of low-energy structures, or transferability tests on the listed alloy compositions) are reported.

    Authors: We agree that the abstract does not explicitly cite numerical validation metrics such as MAE, ranking preservation, or transferability tests. The manuscript demonstrates applicability through explicit results on the listed binary (CoNi, MoW, FeNi, TaW), ternary (CoCrNi, CrFeNi), quaternary (CoCrFeNi), and quinary (Al_x(CoCrFeNi)_{1-x}) alloys, together with the BDV vs. SOAP benchmark. To address the concern directly, we will revise the abstract to reference the specific sections containing these demonstrations and qualify the central claim to reflect the scope of the presented evidence. revision: yes

  2. Referee: [Abstract] Abstract: the reliability of the entropy signal as an indicator of convergence to the stable phase rests on the unverified assumption that the GCN, trained on limited data, produces relative energies accurate enough for the sampled distribution to reflect the true Boltzmann-weighted landscape; without reported error bars or cross-validation on the relevant energy window this assumption remains load-bearing and untested.

    Authors: This observation correctly identifies a load-bearing assumption. While the GCN-driven alchemical MC sampling yields consistent phase predictions across the reported alloy systems, the manuscript does not include MAE values, error bars on relative energies, or cross-validation restricted to the relevant energy window. We will revise the manuscript to add a dedicated subsection reporting GCN validation metrics (including MAE on held-out configurations and transferability across the listed compositions) and will discuss the implications for the entropy metric. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent ML surrogate and external entropy metric

full rationale

The paper trains a GCN surrogate on configuration data, deploys it to generate alchemical MC trajectories, and computes an information-entropy metric on those trajectories to signal phase convergence. None of the load-bearing steps reduce by construction to the inputs: the GCN is a standard supervised model whose outputs are not tautologically identical to the entropy signal, the entropy definition is information-theoretic and independent of the fitted parameters, and no self-citation chain or uniqueness theorem is invoked to force the result. The method is therefore self-contained against external benchmarks (DFT validation of the surrogate would falsify it independently).

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated.

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discussion (0)

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