# Hierarchical Matrix Completion for the Prediction of Properties of Binary Mixtures

arXiv: https://arxiv.org/abs/2410.06060 · HTML: https://mlsanity.com/paper/2410.06060/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Automatic Variational Inference in Stan](https://mlsanity.com/paper/1506.03431/) (2015)
- [Machine Learning in Thermodynamics: Prediction of Activity Coefficients by Matrix Completion](https://mlsanity.com/paper/2001.10675/) (2020)
- [A smile is all you need: Predicting limiting activity coefficients from SMILES with natural language processing](https://mlsanity.com/paper/2206.07048/) (2022)
- [HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction](https://mlsanity.com/paper/2407.18011/) (2024)
- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [Hybridizing Physical and Data-driven Prediction Methods for Physicochemical Properties](https://mlsanity.com/paper/2202.08804/) (2022)

## Built on by (most cited first, 4 of 4)

- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Batch Distillation Data for Developing Machine Learning Anomaly Detection Methods](https://mlsanity.com/paper/2510.18075/) (2025)
- [Prediction of Diffusion Coefficients in Mixtures with Tensor Completion](https://mlsanity.com/paper/2602.23142/) (2026)
- [Predicting Activities in Aqueous Electrolyte Solutions with Hybrid Machine Learning](https://mlsanity.com/paper/2607.19114/) (2026)

## Abstract (arXiv)

Predicting the thermodynamic properties of mixtures is crucial for process design and optimization in chemical engineering. Machine learning (ML) methods are gaining increasing attention in this field, but experimental data for training are often scarce, which hampers their application. In this work, we introduce a novel generic approach for improving data-driven models: inspired by the ancient rule "similia similibus solvuntur", we lump components that behave similarly into chemical classes and model them jointly in the first step of a hierarchical approach. While the information on class affiliations can stem in principle from any source, we demonstrate how classes can reproducibly be defined based on mixture data alone by agglomerative clustering. The information from this clustering step is then used as an informed prior for fitting the individual data. We demonstrate the benefits of this approach by applying it in connection with a matrix completion method (MCM) for predicting isothermal activity coefficients at infinite dilution in binary mixtures. Using clustering leads to significantly improved predictions compared to an MCM without clustering. Furthermore, the chemical classes learned from the clustering give exciting insights into what matters on the molecular level for modeling given mixture properties.