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Thermodynamics-Consistent Graph Neural Networks

Jan G. Rittig, Alexander Mitsos

TL;DR

This work proposes excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures and demonstrates high accuracy and thermodynamic consistency of the activity coefficient predictions.

Abstract

We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures. The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy and using thermodynamic relations to obtain activity coefficients. As these are differential, automatic differentiation is applied to learn the activity coefficients in an end-to-end manner. Since the architecture is based on fundamental thermodynamics, we do not require additional loss terms to learn thermodynamic consistency. As the output is a fundamental property, we neither impose thermodynamic modeling limitations and assumptions. We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.

Thermodynamics-Consistent Graph Neural Networks

TL;DR

This work proposes excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures and demonstrates high accuracy and thermodynamic consistency of the activity coefficient predictions.

Abstract

We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures. The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy and using thermodynamic relations to obtain activity coefficients. As these are differential, automatic differentiation is applied to learn the activity coefficients in an end-to-end manner. Since the architecture is based on fundamental thermodynamics, we do not require additional loss terms to learn thermodynamic consistency. As the output is a fundamental property, we neither impose thermodynamic modeling limitations and assumptions. We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.
Paper Structure (7 sections, 6 equations, 3 figures, 2 tables)

This paper contains 7 sections, 6 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods & Modeling
  3. Excess Gibbs Free Energy Graph Neural Networks
  4. Mixture Permutation Invariance
  5. Training and Evaluation
  6. Results & Discussion
  7. Conclusion

Figures (3)

  • Figure 1: Model structure and loss function of our excess Gibbs free energy graph neural network (GE-GNN) for predicting composition-dependent activity coefficients.
  • Figure 2: Activity coefficient predictions, their corresponding gradients with respect to the composition with the associated Gibbs-Duhem deviations, the molar excess Gibbs free energy, and vapor-liquid equilibria for exemplary mixtures by the GE-GNN. The predictions are averaged from the five model runs of the comp-inter split, i.e., an ensemble.
  • Figure 3: Activity coefficient predictions, their corresponding gradients with respect to the composition with the associated Gibbs-Duhem deviations, the molar excess Gibbs free energy, and vapor-liquid equilibria for the exemplary mixture of ethanol/benzene by the (a) GDI-GNN$_\text{xMLP}$ and (b) GE-GNN.