Kai Sundmacher

Edgar Ivan Sanchez Medina, Steffen Linke, Martin Stoll et al.

The accurate prediction of physicochemical properties of chemical compounds in mixtures (such as the activity coefficient at infinite dilution $γ_{ij}^\infty$) is essential for developing novel and more sustainable chemical processes. In this work, we analyze the performance of previously-proposed GNN-based models for the prediction of $γ_{ij}^\infty$, and compare them with several mechanistic models in a series of 9 isothermal studies. Moreover, we develop the Gibbs-Helmholtz Graph Neural Network (GH-GNN) model for predicting $\ln γ_{ij}^\infty$ of molecular systems at different temperatures. Our method combines the simplicity of a Gibbs-Helmholtz-derived expression with a series of graph neural networks that incorporate explicit molecular and intermolecular descriptors for capturing dispersion and hydrogen bonding effects. We have trained this model using experimentally determined $\ln γ_{ij}^\infty$ data of 40,219 binary-systems involving 1032 solutes and 866 solvents, overall showing superior performance compared to the popular UNIFAC-Dortmund model. We analyze the performance of GH-GNN for continuous and discrete inter/extrapolation and give indications for the model's applicability domain and expected accuracy. In general, GH-GNN is able to produce accurate predictions for extrapolated binary-systems if at least 25 systems with the same combination of solute-solvent chemical classes are contained in the training set and a similarity indicator above 0.35 is also present. This model and its applicability domain recommendations have been made open-source at https://github.com/edgarsmdn/GH-GNN.

Alexander Klimek, Christoph Plate, Sebastian Sager et al.

This study presents a multi-objective optimization framework for sustainable aviation fuel (SAF) production, integrating artificial neural networks (ANNs) within a mixed-integer quadratically constrained programming (MIQCP) formulation. By embedding data-driven surrogate models into the mathematical optimization structure, the proposed methodology addresses key limitations of conventional superstructure-based approaches, enabling simultaneous optimization of discrete process choices and continuous operating parameters. The framework captures variable input and output stream compositions, facilitating the joint optimization of target product composition and system design. Application to Fischer-Tropsch (FT) kerosene production demonstrates that cost-minimizing configurations under unconstrained CO2 emissions are dominated by the fossil-based autothermal reforming (ATR) route. Imposing carbon emission constraints necessitates the integration of biomass gasification and direct air capture coupled with carbon sequestration (DAC-CS), resulting in substantially reduced net emissions but higher production costs. At the zero-emission limit, hybrid configurations combining ATR and biomass gasification achieve the lowest costs (~2.38 \$/kg-kerosene), followed closely by biomass gasification-only (~2.43 \$/kg), both of which outperform the ATR-only pathway with DAC-CS (~2.65 \$/kg). In contrast, DAC-only systems relying exclusively on atmospheric CO2 and water electrolysis are prohibitively expensive (~10.8 \$/kg). The results highlight the critical role of the embedded ANNs: optimal process conditions, such as FT reactor pressure and gasification temperature, adapt to changing circumstances, consistently outperforming fixed setups and achieving up to 20% cost savings.

Edgar Ivan Sanchez Medina, Kai Sundmacher

Predictive thermodynamic models are crucial for the early stages of product and process design. In this paper the performance of Graph Neural Networks (GNNs) embedded into a relatively simple excess Gibbs energy model, the extended Margules model, for predicting vapor-liquid equilibrium is analyzed. By comparing its performance against the established UNIFAC-Dortmund model it has been shown that GNNs embedded in Margules achieves an overall lower accuracy. However, higher accuracy is observed in the case of various types of binary mixtures. Moreover, since group contribution methods, like UNIFAC, are limited due to feasibility of molecular fragmentation or availability of parameters, the GNN in Margules model offers an alternative for VLE estimation. The findings establish a baseline for the predictive accuracy that simple excess Gibbs energy models combined with GNNs trained solely on infinite dilution data can achieve.

Christoph Plate, Mirko Hahn, Alexander Klimek et al.

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the number of layers. We survey and propose different approaches to analyze and improve the run time behavior of mixed-integer programming solvers in this context. Among them are clipped variants and regularization techniques applied during training as well as optimization-based bound tightening and a novel scaling for given ReLU networks. We numerically compare these approaches for three benchmark problems from the literature. We use the number of linear regions, the percentage of stable neurons, and overall computational effort as indicators. As a major takeaway we observe and quantify a trade-off between the often desired redundancy of neural network models versus the computational costs for solving related optimization problems.

Ion Victor Gosea, Luisa Peterson, Pawan Goyal et al.

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning dynamical systems from time-domain data. The application in our study is carbon dioxide methanation, an important reaction within the Power-to-X framework, to demonstrate its potential. The numerical results show the ability of the reduced-order models constructed with operator inference to provide a reduced yet accurate surrogate solution. This represents an important milestone towards the implementation of fast and reliable digital twin architectures.

Sahil Sethi, Kai Sundmacher, Caroline Ganzer

Ionic liquids (ILs) have emerged as versatile replacements for traditional solvents because their physicochemical properties can be precisely tailored to various applications. However, accurately predicting key thermophysical properties remains challenging due to the vast chemical design space and the limited availability of experimental data. In this study, we present a data-driven transfer learning framework that leverages a neural recommender system (NRS) to enable reliable property prediction for ILs using sparse experimental datasets. The approach involves a two-stage process: first, pre-training NRS models on COSMO-RS-based simulated data at fixed temperature and pressure to learn property-specific structural embeddings for cations and anions; and second, fine-tuning simple feedforward neural networks using these embeddings with experimental data at varying temperatures and pressures. In this work, five essential IL properties are considered: density, viscosity, surface tension, heat capacity, and melting point. The framework supports both within-property and cross-property knowledge transfer. Notably, pre-trained models for density, viscosity, and heat capacity are used to fine-tune models for all five target properties, achieving improved performance by a substantial margin for four of them. The model exhibits robust extrapolation to previously unseen ILs. Moreover, the final trained models enable property prediction for over 700,000 IL combinations, offering a scalable solution for IL screening in process design. This work highlights the effectiveness of combining simulated data and transfer learning to overcome sparsity in the experimental data.