Source-linked AI summary
Learning atomic interactions for the thermodynamics of liquid mixtures
Marco Hoffmann, Sebastian Schmitt, Hans Hasse, Fabian Jirasek
TL;DR
Activity coefficients are central to process design, but established group-contribution models have limited molecular resolution and neural-network models can be costly to use in simulations. COGNAC learns neighborhood-dependent atom parameters within the mod. UNIFAC framework; it improves accuracy over HANNA across binary and multicomponent mixtures while retaining reusable parameters and thermodynamic consistency.
Problem
Activity coefficients are needed for process design, but group-contribution models have coarse molecular resolution and neural-network models can be prohibitively expensive for process simulation.
Source: §1 · p. 1Method
COGNAC combines a graph neural network with mod. UNIFAC, learning atom-level geometry and interaction parameters that depend on molecular neighborhoods.
Source: §1 · p. 2Results
COGNAC has lower median MAEsys than HANNA across binary, ternary, and quaternary mixtures, with reported reductions ranging from 13–63% across data types.
Source: §2.1 · p. 5Takeaways & Limitations
For a specified component set, one network evaluation generates a parameter table reusable across compositions and temperatures, and the thermodynamic equations satisfy consistency properties by construction.
Source: §1 · p. 2, §3 · p. 9Electrolytes and polymers are outside COGNAC’s current domain.
Source: §3 · p. 9
Abstract
from arXiv · showhide
Predictive models for activity coefficients, which describe the non-ideality of liquid mixtures, are foundational for process design and optimization. Group-contribution methods, such as UNIFAC, are computationally cheap and well established in process simulators. Modern machine learning models, such as HANNA, offer higher accuracy and broader applicability, but their integration into process simulation is expensive or even infeasible. In this work, we introduce COGNAC, a graph neural network that learns atom-level geometry and interaction parameters that depend on the molecular neighborhood and evaluates them in the UNIFAC framework. Trained on about 820,000 experimental data points, COGNAC achieves significantly higher accuracy than UNIFAC and HANNA for binary and multi-component mixtures, reduces error relative to HANNA by 13-63%, reliably predicts multi-phase equilibria and identifies azeotropes, yields interpretable parameters, and is strictly thermodynamically consistent. COGNAC evaluations run at a cost comparable to UNIFAC, thereby unlocking the potential of machine-learning models for process simulations.
1 Main
COGNAC addresses the limited molecular resolution of group-contribution models and the simulation cost of neural-network thermodynamics by learning neighborhood-dependent atom parameters for the mod. UNIFAC framework. Its parameters are reusable across mixture compositions and temperatures, while the thermodynamic equations retain consistency properties by construction.
1 Main
- Group-contribution methods are computationally inexpensive and widely implemented, but predefined groups coarsely resolve neighborhoods and limit coverage to components with suitable groups and fitted parameters.The coarse grouping can miss effects beyond the nearest neighbors and cannot distinguish some multifunctional molecules and structural isomers.Source: §1 · p. 1
- Neural-network models such as HANNA use molecular structure broadly and can be accurate, but require evaluation at every simulation step, making them prohibitively expensive for process simulation.Quantum-chemistry methods also require expensive calculations per component and have not shown a systematic accuracy advantage over group-contribution methods where both apply.Source: §1 · pp. 1–2
- COGNAC replaces predefined structural groups with atoms whose geometry and interaction parameters depend on molecular neighborhoods, capturing influences between neighboring functional groups.The model combines a graph neural network with the local-composition framework of mod. UNIFAC.Source: §1 · p. 2
- Its message-passing network encodes atoms within four bonds, then predicts atom-level volume and surface-area parameters and pairwise interaction parameters for the unchanged mod. UNIFAC equations.Hydrogens bound to non-carbon atoms are explicit nodes, distinguishing hydrogen-bond donors and acceptors.Source: §1 · p. 2
- COGNAC's equations are smooth and satisfy Gibbs–Duhem consistency, permutation symmetry, and pure-component limits by construction; parameters are generated once per component set and reused without further network evaluations.The same equations cover binary and multicomponent mixtures without extra parameters or a separate multicomponent approximation, and the learned parameters are interpretable.Source: §1 · p. 2
2 Results
COGNAC improves activity-coefficient and phase-equilibrium predictions across binary and multicomponent mixtures, including aqueous systems and azeotropes. Its learned atom-level parameters also support interpretable predictions and batch-distillation simulations at computational costs comparable in order of magnitude to mod. UNIFAC.
2.1 Prediction of phase equilibria and excess properties
- Binary median MAEsys are 13–32% lower than HANNA’s across data types, while ternary errors are 17–49% lower; COGNAC is also at least as accurate as mod. UNIFAC for ternary data.For quaternary mixtures, median errors are 27–63% lower than HANNA’s and 9–18% lower than mod. UNIFAC’s on systems all three models describe.Source: Figure 2 · p. 4, §2.1 · p. 5
- COGNAC’s aqueous-system median error rises 31% when hydrogen atoms are treated implicitly, compared with 1.7% for non-aqueous systems.Aqueous mixtures worsen in all eleven tested combinations of mixture order and data type in this ablation.Source: §2.1 · p. 5
- Among 1,368 structural-isomer pairs with measured ln γ∞ differences of at least 0.15, COGNAC reproduces the experimental order in 84.5% of cases.Mod. UNIFAC predicts identical activity coefficients for isomers with identical group counts by construction.Source: §2.1 · p. 5
2.2 Prediction of azeotropes and residue curve maps
- COGNAC correctly classifies 92.5% of 25,894 azeotrope data points, versus 90.9% for HANNA; for ternary data, accuracies are 83.2% and 64.7%, respectively.The models are similar for binary azeotropes; COGNAC recovers 2 of 58 measured double azeotropes, compared with 36 for HANNA and 28 for mod. UNIFAC.Source: §2.2 · pp. 6–7, Figure 3 · p. 6
- For correctly classified azeotropes, median composition deviations are 0.020 (binary) and 0.022 mol mol−1 (ternary) for COGNAC, versus 0.024 and 0.056 mol mol−1 for HANNA.Mod. UNIFAC’s corresponding deviations are 0.019 and 0.025 mol mol−1; its parameters were fitted to the DDB azeotropic data.Source: §2.2 · p. 7
- COGNAC predicts the measured azeotrope types in the acetone + chloroform + hexane example and maps three distillation regions for a mixture outside mod. UNIFAC’s scope.For the two ternary examples, predicted azeotrope compositions deviate by at most 0.028 and 0.018 mol mol−1 in any mole fraction, and pressures by 2.0% and 1.8%, respectively.Source: Figure 3 · p. 6, §2.2 · p. 7
2.3 Model interpretability
- COGNAC learns atom-level geometry parameters regularized toward COSMO cavity data; for 45,488 held-out molecules, average volume and surface-area deviations are 11.0 Å3 and 14.1 Å2.Learned exchange energies vary with molecular neighborhood: the hydroxyl group’s influence on carbon–water-oxygen interactions extends about two bonds.Source: §2.3 · p. 7, Figure 4 · p. 8
2.4 Application in process simulation
- In batch distillation of ternary and five-component mixtures, COGNAC predictions agree well with plant data and require 1.9 and 2.4 times mod. UNIFAC’s integration-step time, respectively.The comparison excludes compilation time for generated residual functions.Source: §2.4 · p. 8, Figure 5 · p. 9
3 Discussion
COGNAC attributes the accuracy gap between group-contribution and modern machine-learning models to rigid predefined groups, replacing them with neighborhood-dependent atomic parameters in unchanged mod. UNIFAC equations. It reports improved accuracy and process-simulation efficiency while retaining thermodynamic consistency, with electrolytes and polymers outside its current domain.
3 Discussion
- COGNAC is more accurate than HANNA across binary, ternary, and quaternary mixture data types, including aqueous mixtures and azeotrope predictions.The discussion attributes the accuracy gap to rigid predefined groups rather than the local-composition equations.Source: §3 · p. 9
- A single network evaluation produces a parameter table valid across temperatures and compositions, and process simulations run within about a factor of two of mod. UNIFAC.The model is also reported to run two orders of magnitude faster than the HANNA ensemble.Source: §3 · p. 9
- Learned geometry parameters are regularized against COSMO cavities, while interaction parameters align with chemical intuition, making COGNAC more interpretable than black-box ML and standard mod. UNIFAC.In standard mod. UNIFAC, effects such as hydrogen bonding are only implicitly represented in group parameters.Source: §3 · p. 9
- COGNAC covers molecules and ionic liquids built from the dataset’s twelve elements, but electrolytes and polymers remain outside its current domain.The discussion says extensions for long-range electrostatic interactions and free-volume effects are possible.Source: §3 · p. 9
- Trained models and code are open source, and users can download system-specific parameter tables for direct process-simulator implementation.The MLPROP interface also calculates activity coefficients, excess enthalpies, and phase equilibria with COGNAC.Source: §3 · p. 9
4.1 Equation framework
COGNAC computes activity coefficients by combining mod. UNIFAC’s combinatorial and residual framework with learned atom-level geometry and interaction parameters. Its unchanged equations use atom-level surface areas and pair interactions to calculate molecular contributions directly.
4.1 Equation framework
- COGNAC separates each activity coefficient into a combinatorial contribution for molecular size and shape and a residual contribution for molecular-site interactions, which contains the excess enthalpy.Both contributions use learned molecular representations.Source: §4.1 · p. 10
- The combinatorial term adopts mod. UNIFAC’s expression with coordination number z = 10 and an empirical 3/4 exponent; replacing the corrected volume recovers original UNIFAC.Molecular volume and surface area are sums of the contributions from all graph nodes, including explicit polar hydrogens.Source: §4.1 · p. 10
- The model learns each atom’s volume and surface-area parameters from its type and molecular neighborhood; non-carbon-bound hydrogens are explicit nodes, while carbon-bound hydrogen contributions are absorbed into carbon parameters.These parameters are summed over component graph nodes to obtain molecular volume and surface area.Source: §4.1 · p. 10
- Atom-level surface-area fractions and pairwise Boltzmann factors feed the closed-form UNIFAC residual expression, which COGNAC uses unchanged with atoms replacing structural groups.The molecular residual contribution sums differences between atom residual coefficients in the mixture and pure-component reference state.Source: §4.1 · pp. 10–11
- For each atom pair, COGNAC predicts temperature-independent coefficients for a quadratic temperature dependence of symmetric exchange energy, ensuring equal reverse-pair energies and zero like-pair exchange energy.These coefficients are atom-pair analogues of mod. UNIFAC’s tabulated group interaction parameters.Source: §4.1 · p. 11
- The framework takes atom-level volume and surface-area parameters plus temperature-dependent pair exchange energies as inputs, and its residual term is direct, differentiable, and cheap to evaluate.The equations also apply to mixtures with any number of components.Source: §4.1 · p. 11
4.2 Molecular graphs
Each molecule is represented as a graph with heavy atoms and selected explicit hydrogens as nodes. This representation keeps carbon-bound hydrogens implicit while resolving polar hydrogens as distinct sites.
4.2 Molecular graphs
- The graph includes every heavy atom and each hydrogen not bonded to carbon as a node, while carbon-bound hydrogens are encoded on their parent carbon.This keeps apolar molecular graphs compact while representing polar hydrogens explicitly.Source: §4.2 · p. 11
- Explicit donor hydrogens and acceptor atoms can form distinct pair-interaction sites, allowing the model to represent hydrogen bonding directly.Water is represented by three nodes; alcohols, carboxylic acids, and amines expose donor hydrogens as separate sites.Source: §4.2 · p. 11
- Edges encode covalent bonds, and atom and bond features encode chemical and structural information, including bond type, conjugation, and ring membership.Atom features include atomic number, total degree, formal charge, hybridization, aromaticity, and implicit-hydrogen count.Source: §4.2 · p. 11
4.3 Local message passing encoder
The encoder embeds categorical atom and bond features, then refines atom states through four message-passing layers. Each final atom embedding represents its chemical identity and molecular neighborhood up to four bonds away.
4.3 Local message passing encoder
- Categorical atom and bond features are mapped to learned 256-dimensional vectors, summed per feature type, and layer-normalized to initialize atom and bond states.The learned embedding tables have one 256-dimensional row per feature category.Source: §4.3 · p. 12
- Four message-passing layers update each atom by aggregating messages from covalently bonded neighbors and applying a residual connection.Messages use the central-atom state, neighbor state, and bond embedding; bond embeddings remain static across layers.Source: §4.3 · p. 12
- The final atom state encodes the atom’s chemical identity and molecular neighborhood within four bonds.The encoder processes each component’s molecular graph separately.Source: §4.3 · p. 12
4.4 Atom-level volume and surface area
A shared neural-network head predicts positive effective cavity volume and surface area for each atom. Summing atom-level contributions yields molecular structural parameters, while geometry regularization grounds predictions in COSMO cavity values.
4.4 Atom-level volume and surface area
- A shared two-output MLP predicts positive effective cavity volume and surface area for each atom from its final embedding.Softplus activations and a small positive constant keep both quantities strictly positive.Source: §4.4 · p. 12
- Predicted geometries are regularized against COSMO cavity values, with surface area constrained per atom and volume constrained per molecule.Implicit carbon-bound hydrogen areas are folded into the parent carbon, while explicit polar hydrogens retain their own areas.Source: §4.4 · p. 12
- Molecular structural parameters are obtained by summing the atom-level contributions over the molecular graph.The reference is a single CH2 group in an infinitely long polyethylene molecule, using effective cavity values from COSMO results in the CHAOS database.Source: §4.4 · p. 12
4.5 Pairwise atom exchange energies
A permutation-invariant interaction head predicts three temperature-independent coefficients for each atom pair, which define exchange energies with the quadratic temperature dependence of mod. UNIFAC. The model evaluates atom pairs across the mixture and isolated components, with a sign regularizer for hydrogen-bond interactions.
4.5 Pairwise atom exchange energies
- The interaction head predicts three coefficients from a symmetric pairwise feature vector, producing symmetric interaction parameters for each atom pair.Temperature is not an input to the head; it enters through the interaction polynomial.Source: §4.5 · pp. 12–13
- The exchange energy uses a quadratic temperature dependence, and the exchanged coefficients are converted from the reduced basis to the published mod. UNIFAC basis.The exchange subtraction is applied separately to all three coefficient channels before conversion.Source: §4.5 · p. 13
- The exported interaction matrix is symmetric and has zero diagonal exchange coefficients, although atoms with different molecular neighborhoods can have nonzero interactions even when both are CH2 groups.The diagonal coefficients satisfy aaa = baa = caa = 0.Source: §4.5 · p. 13
- The reduced basis keeps the three output channels on a shared scale for stable training, while zero-initialized temperature-dependent channels let the model develop temperature dependence where data require it.In the original basis, output-channel gradient magnitudes can differ by up to five orders of magnitude.Source: §4.5 · p. 13
- The model evaluates every atom pair in the mixture, including self-pairs, and evaluates each isolated component to obtain pure-component reference terms.The mixture calculation includes pairs within and between components.Source: §4.5 · p. 13
- A regularizer encourages negative exchange energies for donor-hydrogen–acceptor interactions because the model can otherwise distribute the interaction across attached atoms.Other learned interactions are determined from experimental data alone.Source: §4.5 · p. 13
4.6 Data processing and splitting
The authors curate and preprocess Dortmund Data Bank thermodynamic data, then use system-wise binary cross-validation and separate ternary and quaternary evaluations. Data-specific filters and manual review determine which observations enter the processing and evaluation sets.
4.6 Data processing and splitting
- Data from the Dortmund Data Bank are unified, converted to SI units as needed, assigned consistent component order, and represented with canonical SMILES.The binary data provide all training data; ternary and quaternary data are used only for evaluation.Source: §4.6 · pp. 13–14
- VLE and HPV processing removes pure-component edges and derives pure-component vapor pressures from measured points or temperature-valid Antoine parameters.For isobaric sets with a reported pure-component point, the Antoine equation is recalibrated to that measurement; data above 10 bar are excluded because vapor ideality is assumed.Source: §4.6 · p. 14
- VLE rows with liquid and vapor compositions and vapor pressures yield activity coefficients, while rows missing vapor composition retain total pressure as a TPX target.Rows lacking pressure information are dropped.Source: §4.6 · p. 14
- LLE data retain reported coexisting-phase compositions, order them consistently when both are reported, and exclude pressures above 50 bar.Atmospheric pressure is assumed when pressure is unreported.Source: §4.6 · p. 14
- SLE activity coefficients are calculated only on manually identified liquidus branches where a pure-component solid is in equilibrium with the liquid.The branch-specific formula uses averaged reported melting temperatures and fusion enthalpies; other SLE data are dropped.Source: §4.6 · p. 14
- Binary data are visually reviewed mixture by mixture; inconsistent sets and outliers are rejected, while insufficiently reviewable observations remain labeled unreviewed.Review thresholds are at least five points for SLE, HE, and LLE and ten for VLE and ACT.Source: §4.6 · pp. 14–15
- 822,780 data points from 48,432 binary systems form the binary pool, while ternary and quaternary data are reserved for evaluation.The binary pool includes accepted and unreviewed data, excluding rejected observations.Source: §4.6 · p. 15
- Binary cross-validation assigns whole systems to ten folds, stratifies data types, and produces one out-of-fold prediction per system; multicomponent evaluation uses DDB observations with specified exclusions.For ternary and quaternary evaluations, the full-data model is trained on nine binary folds and validated on the tenth; the stated ablation protocols follow the binary cross-validation and, for hydrogen ablation, the ternary full-data setup.Source: §4.6 · p. 15
4.7 Model training
COGNAC is trained jointly on multiple thermodynamic data types using losses tailored to their measured observables and a differentiable treatment of liquid–liquid phase splits. Regularizers constrain learned geometry and hydrogen-bond interactions, alongside a fixed optimization schedule.
4.7 Model training
- COGNAC uses a Huber loss across six binary thermodynamic data types, aggregating data-point losses by type and averaging over available targets.The Huber loss is quadratic near zero and linear for large residuals, reducing sensitivity to experimental outliers.Source: §4.7 · p. 15
- TPXY and SLE data directly train activity coefficients, with both terms anchoring the scale of predicted activity coefficients.TPXY supplies both component coefficients, whereas SLE generally supplies the coefficient for only the component in equilibrium with its pure solid.Source: §4.7 · pp. 15–16
- TPX measurements train predicted total pressure using a logarithmic residual, so observations spanning orders of magnitude contribute comparably.These bubble-line measurements lack vapor composition and use an ideal-vapor assumption.Source: §4.7 · p. 16
- Excess-enthalpy training uses the Gibbs–Helmholtz relation and automatic differentiation with respect to temperature to train temperature sensitivity directly.The derivative term back-propagates gradients through the temperature derivative of predicted activity coefficients.Source: §4.7 · p. 16
- LLE phase compositions are obtained from predicted Gibbs energy using a differentiable solver: a convex-envelope grid identifies a gap, then one Newton step refines its endpoints.The model evaluates the Gibbs-energy curve at 401 compositions in a batched call before refinement.Source: §4.7 · pp. 16–17
- The solver-based LLE loss cannot create a phase split, so a curvature hinge term supplies gradients at measured compositions when no split is predicted.The hinge term complements the solver loss and is applied to every LLE point; single-branch observations contribute only the measured-endpoint penalty.Source: §4.7 · p. 17
- Geometry penalties align predicted cavity areas and volumes with available COSMO references, while an explicit-polar-hydrogen prior penalizes repulsive donor–acceptor interactions.COSMO references cover only a subset of training molecules; the hydrogen-bond penalty is active only with explicit polar hydrogens.Source: §4.7 · pp. 17–18
- The total objective sums active data and regularization terms, and models train for 100 AdamW epochs under a one-cycle learning-rate schedule.The reported configuration uses batch size 512, peak learning rate 5 × 10^-4, and fixed final checkpoints rather than selecting the lowest validation loss.Source: §4.7 · p. 18
4.8 Evaluation
Evaluation reports system-wise errors by thermodynamic data type and compares models on shared applicable systems. Binary COGNAC and HANNA results use matched cross-validation folds, while the multicomponent data are not used for training.
4.8 Evaluation
- Errors are system-wise mean absolute errors, summarized by median, mean, and interquartile range, with relative model changes based on the median.Comparisons are restricted to systems all three models can describe; LLE comparisons additionally require all three to predict a phase split for at least one point.Source: §4.8 · p. 18
- HANNA is retrained on COGNAC’s data and folds, whereas mod. UNIFAC is used as published with parameters fitted to DDB data that include benchmark systems.Multicomponent data are never used for training, although some of their binary subsystems occur in binary training data.Source: §4.8 · p. 18
Code availability
The authors provide code and interfaces for using COGNAC and related tools.
Code availability
- COGNAC code and full-binary models are available under the MIT license, alongside an interactive interface, API, MCP connector, Julia implementation, and batch-distillation simulation code.The interface predicts activity coefficients and phase equilibria and returns parameter tables.Source: Code availability · p. 19