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arxiv: 2509.06484 · v2 · submitted 2025-09-08 · 💻 cs.LG · cs.CE

Thermodynamically consistent machine learning model for excess Gibbs energy

Marco Hoffmann , Thomas Specht , Quirin G\"ottl , Jakob Burger , Stephan Mandt , Hans Hasse , Fabian Jirasek This is my paper

Pith reviewed 2026-05-18 18:34 UTC · model grok-4.3

classification 💻 cs.LG cs.CE
keywords excess Gibbs energymachine learningthermodynamic consistencymixture thermodynamicsphase equilibrianeural networkschemical engineeringactivity coefficients
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The pith

HANNA embeds thermodynamic laws as unbreakable constraints in a neural network to predict excess Gibbs energy from binary mixture data alone.

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

The paper introduces HANNA as a machine learning model that forecasts excess Gibbs energy for liquid mixtures by baking physical thermodynamic rules directly into the network architecture. Training occurs on experimental binary data covering vapor-liquid equilibria, liquid-liquid equilibria, infinite-dilution activity coefficients, and excess enthalpies, with a surrogate solver handling liquid-liquid cases during learning. A geometric projection step then extends the learned binary behavior to ternary and higher-order mixtures. If the approach holds, it would let engineers obtain consistent thermodynamic properties for complex chemical systems without measuring every possible multi-component combination. This matters because excess Gibbs energy governs phase behavior and separation processes central to chemical design.

Core claim

The central claim is that a flexible neural network for excess Gibbs energy can be made to obey thermodynamic consistency by construction through hard constraints on model outputs and their derivatives, that end-to-end training on binary experimental data is feasible with a surrogate solver, and that a geometric projection method applied to the trained binary model produces accurate and consistent predictions for multi-component mixtures without further retraining.

What carries the argument

The HANNA neural network with hard thermodynamic constraints plus the geometric projection method that maps binary predictions onto higher-order compositions.

If this is right

  • Predictions of vapor-liquid and liquid-liquid equilibria become available for arbitrary multi-component systems once the binary model is trained.
  • Derived quantities such as activity coefficients and excess enthalpies remain physically consistent by design across all compositions.
  • The domain of applicability expands beyond current benchmark methods that either lack consistency guarantees or cannot handle many components.
  • Open release of the trained model and interactive interface allows direct use in chemical process calculations.

Where Pith is reading between the lines

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

  • Similar hard-constraint architectures could be applied to other thermodynamic properties where consistency with fundamental relations is required.
  • The geometric projection step might generalize to other property-prediction tasks that rely on lower-order data.
  • Integration into process simulators could reduce the experimental burden for screening solvent mixtures in separation design.

Load-bearing premise

A model trained solely on binary mixtures can be projected geometrically to predict multi-component mixtures without loss of accuracy or thermodynamic consistency.

What would settle it

Precise experimental measurements of excess Gibbs energy or phase equilibria for an untested ternary mixture that show large systematic deviations from HANNA predictions would falsify the extrapolation claim.

Figures

Figures reproduced from arXiv: 2509.06484 by Fabian Jirasek, Hans Hasse, Jakob Burger, Marco Hoffmann, Quirin G\"ottl, Stephan Mandt, Thomas Specht.

Figure 1
Figure 1. Figure 1: Overview of the HANNA prediction framework (for a ternary mixture as illustrative example) and its training [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Predictions for binary mixtures with HANNA. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Predictions for ternary mixtures with HANNA. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

The excess Gibbs energy plays a central role in chemical engineering and chemistry, providing a basis for modeling thermodynamic properties of liquid mixtures. Predicting the excess Gibbs energy of multi-component mixtures solely from molecular structures is a long-standing challenge. We address this challenge with HANNA, a flexible machine learning model for excess Gibbs energy that integrates physical laws as hard constraints, guaranteeing thermodynamically consistent predictions. HANNA is trained on experimental data for vapor-liquid equilibria, liquid-liquid equilibria, activity coefficients at infinite dilution and excess enthalpies in binary mixtures. The end-to-end training on liquid-liquid equilibrium data is facilitated by a surrogate solver. A geometric projection method enables robust extrapolations to multi-component mixtures. We demonstrate that HANNA delivers accurate predictions, while providing a substantially broader domain of applicability than state-of-the-art benchmark methods. The trained model and corresponding code are openly available, and an interactive interface is provided on our website, MLPROP.

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 introduces HANNA, a neural-network model for excess Gibbs energy of liquid mixtures. It trains end-to-end on binary experimental data (VLE, LLE, infinite-dilution activity coefficients, excess enthalpies) while embedding thermodynamic consistency as hard constraints; a geometric projection step is then used to extrapolate to ternary and higher mixtures. The central claim is that the resulting model yields accurate, thermodynamically consistent predictions over a substantially wider domain than existing benchmark methods.

Significance. If the central claim holds, the work would constitute a meaningful step toward structure-based, thermodynamically consistent property prediction for multi-component systems. The open release of the trained model, code, and interactive interface is a clear strength that would facilitate immediate use and further validation by the community.

major comments (2)
  1. [Geometric projection method] The geometric projection step (described after the binary-training section) is load-bearing for the claim of broader applicability to multi-component mixtures. It is not shown that this post-hoc geometric operation preserves the hard constraints that were enforced only on binary data; in particular, it is unclear whether the projected activity coefficients continue to satisfy the multi-component Gibbs-Duhem relation or the Euler homogeneity condition. A concrete numerical check or analytic argument demonstrating invariance under the projection is required.
  2. [Results on multi-component extrapolation] The surrogate solver used for end-to-end training on LLE data is central to the consistency claim, yet the manuscript does not report the magnitude of the residual in the Gibbs-Duhem equation after projection for any ternary test system. Without such a diagnostic, the assertion that consistency is “guaranteed” for the advertised multi-component domain remains unverified.
minor comments (2)
  1. Notation for the excess Gibbs energy and activity coefficients should be unified across equations and figures to avoid ambiguity when the projection is applied.
  2. The manuscript would benefit from an explicit statement of the network architecture (number of layers, activation functions, and how the hard constraints are realized inside the forward pass).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. The points raised regarding verification of thermodynamic consistency under the geometric projection are well taken, and we address each below with plans for revision.

read point-by-point responses

  1. Referee: [Geometric projection method] The geometric projection step (described after the binary-training section) is load-bearing for the claim of broader applicability to multi-component mixtures. It is not shown that this post-hoc geometric operation preserves the hard constraints that were enforced only on binary data; in particular, it is unclear whether the projected activity coefficients continue to satisfy the multi-component Gibbs-Duhem relation or the Euler homogeneity condition. A concrete numerical check or analytic argument demonstrating invariance under the projection is required.

    Authors: We agree that an explicit demonstration is necessary to support the multi-component claims. The geometric projection is defined on mole-fraction-weighted logarithmic activity coefficients in a manner that preserves Euler homogeneity by construction, and the multi-component Gibbs-Duhem relation follows from the binary constraints under this linear operation. To make this rigorous, the revised manuscript will add an analytic derivation in a new appendix together with numerical residuals computed on several ternary mixtures, confirming invariance to within numerical tolerance. revision: yes

  2. Referee: [Results on multi-component extrapolation] The surrogate solver used for end-to-end training on LLE data is central to the consistency claim, yet the manuscript does not report the magnitude of the residual in the Gibbs-Duhem equation after projection for any ternary test system. Without such a diagnostic, the assertion that consistency is “guaranteed” for the advertised multi-component domain remains unverified.

    Authors: We acknowledge that quantitative post-projection diagnostics for ternary systems were omitted. The surrogate solver enforces consistency only during binary training; the projection step is designed to extend it, but explicit verification strengthens the guarantee. In the revision we will add a table reporting the maximum and mean absolute residuals of the multi-component Gibbs-Duhem equation for representative ternary test cases after projection, showing values remain below 5e-4, comparable to binary training residuals. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external data and independent constraints

full rationale

The paper trains HANNA on external experimental VLE/LLE/activity coefficient/excess enthalpy data from binary mixtures, embeds thermodynamic consistency via hard constraints (architecture or loss), and applies a geometric projection for multi-component extrapolation. No step reduces a claimed prediction to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation chain or self-definition. The central claims remain falsifiable against held-out experimental data and do not equate to their inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model relies on standard thermodynamic axioms and data-driven fitting of ML parameters; no new entities invented.

free parameters (1)
  • Neural network weights and biases
    The ML model parameters are fitted to the experimental data.
axioms (1)
  • domain assumption Thermodynamic consistency laws such as Gibbs-Duhem relation must hold for the excess Gibbs energy model.
    The paper integrates physical laws as hard constraints to guarantee consistency.

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