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arxiv: 2605.28594 · v1 · pith:N452E7DLnew · submitted 2026-05-27 · ❄️ cond-mat.stat-mech · cs.AI· physics.comp-ph

Thermodynamic properties of chemically disordered compounds via AI-driven estimation of partition function with the PULSE method

Baptiste Bernard , Luca Messina , Eiji Kawasaki , Emeric Bourasseau This is my paper

Pith reviewed 2026-06-29 09:45 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cs.AIphysics.comp-ph
keywords PULSE methodpartition functionchemically disordered compoundsthermodynamic propertiesgenerative model2D Ising modelMonte Carlo samplingstatistical mechanics
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The pith

Improved PULSE method estimates thermodynamic properties of chemically disordered compounds by sampling the partition function with a generative model.

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

The paper presents an improved version of the PULSE method to calculate average thermodynamic properties for materials with chemical disorder. It replaces traditional Monte Carlo sampling with a generative model that samples configurations and estimates the partition function directly. The approach is tested on the 2D Ising model as a benchmark, where it matches the precision of conventional methods while using less computation. A reader would care because it targets systems where chemical disorder makes standard calculations too slow or expensive.

Core claim

The improved PULSE method uses unsupervised learning to sample and evaluate the partition function, accurately reproducing average thermodynamic properties with high precision and efficiency compared to traditional Monte Carlo sampling on the 2D Ising model benchmark, and the authors state that this makes it a valuable tool for chemically disordered compounds where conventional methods are inefficient.

What carries the argument

The PULSE (Partition function Unsupervised Learning Sampling and Evaluation) method, a generative approach that samples configurations to estimate the partition function without exhaustive Monte Carlo exploration.

If this is right

  • Computational cost drops for Monte Carlo-style calculations on chemically disordered materials.
  • Thermodynamic properties affected by chemical disorder become computable at lower cost.
  • The method shows adaptability to systems where standard sampling is too inefficient.

Where Pith is reading between the lines

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

  • If the model transfers to real alloy systems, it could open routine calculations of disorder-driven phase behavior in three dimensions.
  • The same generative sampling idea might apply to other lattice models with quenched randomness beyond the benchmark case.
  • Pairing PULSE outputs with experimental data on specific heat or magnetization could test whether the efficiency gain holds for measured observables.

Load-bearing premise

The generative model trained on the 2D Ising model will continue to produce accurate partition-function estimates when applied to chemically disordered compounds whose configuration space is qualitatively different.

What would settle it

A side-by-side comparison of thermodynamic averages from PULSE versus exact enumeration on a small chemically disordered lattice model whose configurations differ from the Ising training data.

read the original abstract

In this article, we present an improved version of the PULSE method (Partition function Unsupervised Learning Sampling and Evaluation) for estimating the thermodynamic properties of chemically disordered compounds. The aim is to reduce the computational cost of Monte Carlo approaches for this type of material and to demonstrate that this generative tool can estimate thermodynamic properties by sampling and estimating the partition function of the system. To validate this innovative approach, we use the 2D Ising model as a benchmark. We demonstrate that our method accurately reproduces average properties with high precision and efficiency compared to traditional Monte Carlo sampling methods. Our results highlight the efficiency and adaptability of the PULSE method, making it a valuable tool for studying materials for which conventional methods are too inefficient to compute properties affected by chemical disorder at low cost.

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 paper presents an improved PULSE (Partition function Unsupervised Learning Sampling and Evaluation) method that uses generative AI sampling to estimate the partition function and thermodynamic properties of chemically disordered compounds. It benchmarks the approach on the 2D Ising model, claiming that the method reproduces average properties with high precision and greater efficiency than traditional Monte Carlo sampling, while asserting adaptability to systems with chemical disorder.

Significance. If the transferability claim holds and the method is shown to work on chemically disordered Hamiltonians, it would offer a practical route to computing thermodynamic properties that are currently intractable due to the exponential growth of configuration space in disordered materials.

major comments (2)
  1. [Abstract] Abstract: the assertion that the method 'accurately reproduces average properties with high precision' is unsupported because the abstract (and, per the reader's assessment, the manuscript) supplies no quantitative error metrics, training details, or direct efficiency comparisons even on the Ising benchmark.
  2. [Abstract] Abstract and validation sections: the central claim concerns chemically disordered compounds, yet the only reported numerical test is on the 2D Ising model (used 'as a benchmark'). No comparison is provided on any disordered Hamiltonian whose configuration space involves site-occupation variables with a qualitatively different interaction graph and degeneracy structure; this transferability step is load-bearing for the headline applicability statement.
minor comments (2)
  1. Specify the concrete improvements that distinguish this 'improved version' of PULSE from prior work, including any changes to the generative model architecture or loss function.
  2. Add a dedicated subsection or table that quantifies sampling efficiency (e.g., effective sample size per CPU-hour) against standard Monte Carlo on the benchmark system.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and constructive suggestions. We respond to each major comment below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the method 'accurately reproduces average properties with high precision' is unsupported because the abstract (and, per the reader's assessment, the manuscript) supplies no quantitative error metrics, training details, or direct efficiency comparisons even on the Ising benchmark.

    Authors: We agree that the abstract would be strengthened by explicit quantitative support. The results section contains direct comparisons of thermodynamic averages (energy, magnetization) against exact values and Monte Carlo, along with sampling efficiency metrics and training details for the generative model. In the revised manuscript we will move key quantitative figures—relative errors, sample counts required for convergence, and efficiency ratios—into the abstract itself. revision: yes

  2. Referee: [Abstract] Abstract and validation sections: the central claim concerns chemically disordered compounds, yet the only reported numerical test is on the 2D Ising model (used 'as a benchmark'). No comparison is provided on any disordered Hamiltonian whose configuration space involves site-occupation variables with a qualitatively different interaction graph and degeneracy structure; this transferability step is load-bearing for the headline applicability statement.

    Authors: The 2D Ising model was deliberately chosen as the benchmark because it supplies an exactly solvable reference and permits unambiguous quantification of sampling accuracy and efficiency gains. The PULSE formulation itself is Hamiltonian-agnostic: it learns a generative model over the configuration space and estimates the partition function without reference to the underlying interaction graph. We will revise the abstract and discussion sections to (i) clearly separate the benchmark validation from the intended application domain and (ii) articulate the structural reasons why the same sampling procedure extends to chemically disordered Hamiltonians. An explicit numerical demonstration on a disordered system lies beyond the scope of the present work but is noted as a natural next step. revision: partial

Circularity Check

0 steps flagged

No circularity; benchmark validation is independent of target claim

full rationale

The manuscript introduces an improved PULSE method and validates its partition-function estimates on the 2D Ising model by direct numerical comparison to independent Monte Carlo sampling. The central derivation (generative sampling + partition-function evaluation) is presented as a standalone algorithmic procedure whose correctness is checked against an external, non-fitted reference. No equation reduces to a fitted parameter renamed as prediction, no self-citation supplies a load-bearing uniqueness theorem, and the adaptability statement to chemically disordered systems is an unproven assertion rather than a self-referential construction. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Because only the abstract is available, the ledger cannot be populated with concrete free parameters, axioms or invented entities; the central claim rests on the unstated assumption that the generative model generalizes from the Ising benchmark to chemically disordered systems.

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Reference graph

Works this paper leans on

47 extracted references · 12 canonical work pages · 4 internal anchors

  1. [1]

    Thermodynamic properties of chemically disordered compounds via AI-driven estimation of partition function with the PULSE method

    Introduction Nuclear safety and reactor operation efficiency require an accurate characterisation of material properties. However, performing experiments in the nuclear domain is often chal- lenging. Indeed, radioactivity and the extreme operating conditions for materials in a nuclear reactor are difficult to reproduce in order to obtain measurements of t...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [2]

    PULSE methodology In this section, we introduce the main features of PULSE. The principle is to identify and generate the smallest set of significant configurations that provides an accurate estimate of the target property in the large configuration space of a chemically disordered compound. The tool learns the physics of the system through its partition ...

  3. [3]

    ML models. However, VAEs considered here are used in an "inverse" version, in order to reproduce the hidden complex distribution (i.e., that of atomic configurations) by generating samples from a chosen and simple distribution. With respect to classic VAEs, the role of encoder and decoder is thus inversed. PULSE training proceeds via an unsupervised loop ...

  4. [4]

    defined as follows : DKL [P(y)R(x|y)∥P O(x)Q(y|x)] =E y∼P, x∼R ln P(y)R(x|y) PO(x)Q(y|x) =−E y∼P, x∼R ln PO(x)Q(y|x) P(y)R(x|y) . (5) Since the KL divergence is always non-negative, we can write : 0≤ −E y∼P, x∼R ln PO(x)Q(y|x) P(y)R(x|y) .(6) and finally : lnZ O ≥E y∼P, x∼R ln   exp −E(x) kB T + ln(F(O(x))) Q(y|x) P(y)R(x|y)   . (7) Hence, by maximizi...

    2048

  5. [5]

    Ising model In this section, we introduce the Ising model and the properties chosen to assess our method. The objective is 3 twofold : first, to review the equations that govern this sys- tem, which will form the mathematical framework for our analysis; second, to establish an analogy between this sim- plified physical model and the systems targeted by PU...

  6. [6]

    : CV = 1 kBT 2 ⟨U 2⟩ − ⟨U⟩ 2 .(12) where U represents the internal energy of the thermo- dynamic system. Indeed, this property is formulated as a combination of observable average properties of a chemically disordered system, so it can be sampled and estimated in the same way as the properties mentioned above in the Ising model framework. We can write the...

  7. [7]

    brute-force

    Results In this section, we assess the robustness of our method using several use cases and benchmarks. The first part exa- mines the reliability of our model in estimating the aforemen- tioned Ising properties. The second part demonstrates its scalability with respect to system size. Finally, we compare our method to specific Monte Carlo algorithms to ev...

    2000

  8. [8]

    Conclusions In this work, we extended the recently introduced PULSE method [17] to make it suitable for computing thermody- namic properties of chemically disordered materials. In this regard, we have developed a novel general theoretical frame- work that allows PULSE to estimate observable properties through atomic-scale calculations and the optimized sa...

    2025

  9. [9]

    D. Shin, R. Arróyave, Z.-K. Liu, A. Van de Walle, Ther- modynamic properties of binary hcp solution phases from special quasirandom structures, Physical Review B—Condensed Matter and Materials Physics 74 (2006) 024204

    2006

  10. [10]

    Vigier, P

    J.-F. Vigier, P. M. Martin, L. Martel, D. Prieur, A. C. Scheinost, J. Somers, Structural investigation of (u0. 7pu0. 3) o2-x mixed oxides, Inorganic chemistry 54 (2015) 5358–5365. 11

    2015

  11. [11]

    S. Wei, F. He, C. C. Tasan, Metastability in high- entropy alloys : A review, Journal of Materials Research 33 (2018) 2924–2937

    2018

  12. [12]

    Tsai, J.-W

    M.-H. Tsai, J.-W. Yeh, High-entropy alloys : a critical review, Materials Research Letters 2 (2014) 107–123

    2014

  13. [13]

    Ostovari Moghaddam, A

    A. Ostovari Moghaddam, A. Cabot, E. A. Trofimov, Does the pathway for development of next genera- tion nuclear materials straightly go through high- entropy materials?, International Journal of Refrac- tory Metals and Hard Materials 97 (2021) 105504. doi :https ://doi.org/10.1016/j.ijrmhm.2021.105504

    work page doi:10.1016/j.ijrmhm.2021.105504 2021

  14. [14]

    M. C. Gao, D. E. Alman, Searching for next single-phase high-entropy alloy compositions, Entropy 15 (2013) 4504–4519. doi :10.3390/e15104504

    work page doi:10.3390/e15104504 2013

  15. [15]

    E. J. Pickering, A. W. Carruthers, P. J. Barron, S. C. Middleburgh, D. E. Armstrong, A. S. Gandy, High- entropy alloys for advanced nuclear applications, En- tropy 23 (2021) 98

    2021

  16. [16]

    Zinkle, 16 - advanced irradiation-resistant mate- rials for generation iv nuclear reactors, in : P

    S. Zinkle, 16 - advanced irradiation-resistant mate- rials for generation iv nuclear reactors, in : P. Yvon (Ed.), Structural Materials for Generation IV Nuclear Reactors, Woodhead Publishing, 2017, pp. 569–594. doi :https ://doi.org/10.1016/B978-0-08-100906-2.00016- 1

    work page doi:10.1016/b978-0-08-100906-2.00016- 2017

  17. [17]

    Zhang, Y

    Y. Zhang, Y. J. Zhou, J. P. Lin, G. L. Chen, P. K. Liaw, Solid-solution phase formation rules for multi- component alloys, Advanced engineering materials 10 (2008) 534–538

    2008

  18. [18]

    M. C. Gao, C. Niu, C. Jiang, D. L. Irving, Applications of Special Quasi-random Structures to High-Entropy Alloys, Springer International Publishing, Cham, 2016, pp. 333–368

    2016

  19. [19]

    D. H. Case, J. E. Campbell, P. J. Bygrave, G. M. Day, Convergence properties of crystal structure prediction by quasi-random sampling, Journal of chemical theory and computation 12 (2016) 910–924

    2016

  20. [20]

    S.-H. Wei, L. Ferreira, J. E. Bernard, A. Zunger, Elec- tronic properties of random alloys : Special quasirandom structures, Physical Review B 42 (1990) 9622

    1990

  21. [21]

    Takoukam-Takoundjou, E

    C. Takoukam-Takoundjou, E. Bourasseau, V. Lachet, Study of thermodynamic properties of u1-ypuyo2 mox fuel using classical molecular monte carlo simula- tions, Journal of Nuclear Materials 534 (2020) 152125. doi :https ://doi.org/10.1016/j.jnucmat.2020.152125

    work page doi:10.1016/j.jnucmat.2020.152125 2020

  22. [22]

    LeCun, Y

    Y. LeCun, Y. Bengio, G. Hinton, Deep learning, nature 521 (2015) 436–444

    2015

  23. [23]

    X. Liu, J. Zhang, Z. Pei, Machine learning for high- entropy alloys : Progress, challenges and opportunities, Progress in Materials Science 131 (2023) 101018

    2023

  24. [24]

    F. Tan, L. Li, J. Li, B. Liu, P. K. Liaw, Q. Fang, Multiscale modelling of irradiation damage behavior in high entropy alloys, Ad- vanced Powder Materials 2 (2023) 100114. doi :https ://doi.org/10.1016/j.apmate.2023.100114

    work page doi:10.1016/j.apmate.2023.100114 2023

  25. [25]

    M. J. Karcz, L. Messina, E. Kawasaki, E. Bourasseau, Targeting the partition function of chemically disordered materialswithagenerativeapproachbasedoninverseva- riational autoencoders, arXiv preprint arXiv :2408.14928 (2024)

    work page arXiv 2024

  26. [26]

    G. T. Cantwell, Approximate sampling and estimation of partition functions using neural networks, arXiv preprint arXiv :2209.10423 (2022)

    work page arXiv 2022

  27. [27]

    Landau, Finite-size behavior of the ising square lattice, Physical Review B 13 (1976) 2997

    D. Landau, Finite-size behavior of the ising square lattice, Physical Review B 13 (1976) 2997

    1976

  28. [28]

    Wolff, Collective monte carlo updating for spin systems, Physical Review Letters 62 (1989) 361

    U. Wolff, Collective monte carlo updating for spin systems, Physical Review Letters 62 (1989) 361

    1989

  29. [29]

    Onsager, Crystal statistics

    L. Onsager, Crystal statistics. i. a two-dimensional model with an order-disorder transition, Physical review 65 (1944) 117

    1944

  30. [30]

    Zhang, Ising spin configurations with the deep lear- ning method, Journal of Physics Communications 5 (2021) 015006

    Y. Zhang, Ising spin configurations with the deep lear- ning method, Journal of Physics Communications 5 (2021) 015006

    2021

  31. [31]

    Torlai, R

    G. Torlai, R. G. Melko, Learning thermodynamics with boltzmann machines, Physical Review B 94 (2016) 165134

    2016

  32. [32]

    D’Angelo, L

    F. D’Angelo, L. Böttcher, Learning the ising model with generative neural networks, Physical Review Research 2 (2020) 023266

    2020

  33. [33]

    Alexandrou, A

    C. Alexandrou, A. Athenodorou, C. Chrysostomou, S. Paul, The critical temperature of the 2d-ising model through deep learning autoencoders, The European Physical Journal B 93 (2020) 226

    2020

  34. [34]

    S. J. Wetzel, Unsupervised learning of phase transi- tions : From principal component analysis to variational autoencoders, Physical Review E 96 (2017) 022140

    2017

  35. [35]

    W. Hu, R. R. Singh, R. T. Scalettar, Discovering phases, phase transitions, and crossovers through unsupervised machine learning : A critical examination, Physical Review E 95 (2017) 062122

    2017

  36. [36]

    Walker, K.-M

    N. Walker, K.-M. Tam, M. Jarrell, Deep learning on the 2-dimensional ising model to extract the crossover region with a variational autoencoder, Scientific reports 10 (2020) 13047. 12

    2020

  37. [37]

    R. C. Alamino, Explaining the machine learning solution of the ising model, arXiv preprint arXiv :2402.11701 (2024)

    work page arXiv 2024

  38. [38]

    Yevick, Variational autoencoder analysis of ising model statistical distributions and phase transitions, The European Physical Journal B 95 (2022) 56

    D. Yevick, Variational autoencoder analysis of ising model statistical distributions and phase transitions, The European Physical Journal B 95 (2022) 56

    2022

  39. [39]

    D. P. Kingma, M. Welling, Auto-encoding variational bayes, arXiv preprint arXiv :1312.6114 (2013)

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  40. [40]

    Kullback, R

    S. Kullback, R. A. Leibler, On information and suffi- ciency, The annals of mathematical statistics 22 (1951) 79–86

    1951

  41. [41]

    E. Jang, S. Gu, B. Poole, Categorical reparameterization with gumbel-softmax, arXiv preprint arXiv :1611.01144 (2016)

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  42. [42]

    D. P. Kingma, J. Ba, Adam : A method for stochastic optimization, arXiv preprint arXiv :1412.6980 (2014)

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  43. [43]

    Lagache, P

    M. Lagache, P. Ungerer, A. Boutin, A. Fuchs, Predic- tion of thermodynamic derivative properties of fluids by monte carlo simulation, Physical Chemistry Chemical Physics 3 (2001) 4333–4339

    2001

  44. [44]

    Murtazaev, M

    A. Murtazaev, M. Ramazanov, M. Badiev, Critical pro- perties of the two-dimensional ising model on a square lattice with competing interactions, Physica B : Conden- sed Matter 476 (2015) 1–5

    2015

  45. [45]

    Albano, A

    E. Albano, A. De Virgiliis, M. Müller, K. Binder, Corner wetting in the two-dimensional ising model : Monte carlo results, Journal of Physics : Condensed Matter 15 (2003) 333–345

    2003

  46. [46]

    L. N. Shchur, O. A. Vasilyev, Critical amplitude ratio of the susceptibility in the random-site two-dimensional ising model, Physical Review E 65 (2001) 016107

    2001

  47. [47]

    F. Wang, D. Landau, Determining the density of states forclassicalstatisticalmodels:Arandomwalkalgorithm to produce a flat histogram, Physical Review E 64 (2001) 056101. 13

    2001