Geometric Mixture Models for Electrolyte Conductivity Prediction

TL;DR

This work tackles electrolyte conductivity prediction in multi-component mixtures by addressing two key gaps: standardized benchmarks and geometry-aware modeling. It curates CALiSol and DiffMix and introduces GeoMix, a Set-$\mathrm{SE}(3)$-equivariant framework that leverages PCA-based local frames and a Geometric Interaction Network for cross-molecular message passing. GeoMix consistently outperforms a broad set of baselines (MLP, MolSets, EGNN, TFN), highlighting the importance of explicit cross-molecular geometric interactions and equivariant processing. The proposed benchmarks and geometry-aware methodology offer a practical, generalizable framework for mixture-system modeling in energy materials and beyond, with potential extensions to richer descriptors and broader chemistries.

Abstract

Accurate prediction of ionic conductivity in electrolyte systems is crucial for advancing numerous scientific and technological applications. While significant progress has been made, current research faces two fundamental challenges: (1) the lack of high-quality standardized benchmarks, and (2) inadequate modeling of geometric structure and intermolecular interactions in mixture systems. To address these limitations, we first reorganize and enhance the CALiSol and DiffMix electrolyte datasets by incorporating geometric graph representations of molecules. We then propose GeoMix, a novel geometry-aware framework that preserves Set-SE(3) equivariance-an essential but challenging property for mixture systems. At the heart of GeoMix lies the Geometric Interaction Network (GIN), an equivariant module specifically designed for intermolecular geometric message passing. Comprehensive experiments demonstrate that GeoMix consistently outperforms diverse baselines (including MLPs, GNNs, and geometric GNNs) across both datasets, validating the importance of cross-molecular geometric interactions and equivariant message passing for accurate property prediction. This work not only establishes new benchmarks for electrolyte research but also provides a general geometric learning framework that advances modeling of mixture systems in energy materials, pharmaceutical development, and beyond.

Figures (3)

• Figure 1: Overview of our GeoMix. By taking a set of molecules $\{{\mathcal{G}}_m\}_{m=1}^M$ with proportion ${\bm{w}}=[w_{m}]_M$ as input, it first constructs local frames $\vec{{\bm{F}}}_m$ via PCA, then applies an equivariant encoder to update ${\bm{H}}_m, \vec{{\bm{X}}}_m$. Intermolecular message passing is performed via GIN, which learns transformations $\overleftrightarrow{{\bm{I}}}_{\!\!\! ij}^{(m,n)}$ and $\vec{{\bm{t}}}_{ij}^{\ (m,n)}$, which enable equivariant message passing across molecules. The scalar features ${\bm{H}}_m$ are finally aggregated along with the environment descriptor ${\bm{c}}$ for prediction.
• Figure 2: Overview of the CALiSol and DiffMix datasets. (a) Summary of dataset statistics. (b) Composition diversity in terms of the number of solvents used per sample. CALiSol exhibits a more diverse mixture design space, while DiffMix contains a greater number of samples with 2 or 3 solvents. (c) Log-scaled histograms of conductivity values indicate that CALiSol exhibits a broader range and a more pronounced long-tail distribution than DiffMix dataset. (d) The t-SNE visualization van2008visualizing reveals distinct structural characteristics in each dataset. CALiSol, derived from experimental measurements, exhibits greater diversity with many scattered outliers, reflecting heterogeneous sampling. In contrast, DiffMix shows a more uniform and clustered distribution, consistent with its simulation-based origin.
• Figure 3: Regression plots for electrolyte conductivity prediction. (a–c) show results on the CALiSol dataset, using TFN-linear, GeoMix-EGNN, and GeoMix-TFN, respectively. (d–f) show corresponding results on the DiffMix dataset with the same model order.

Theorems & Definitions (13)

• Theorem 3.1: Expressivity of Intermolecular Transformation Matrix
• Lemma A.1
• proof
• Lemma A.2
• proof
• Theorem A.2: Expressivity of Intermolecular Transformation Matrix
• proof
• Theorem A.3: Enhancement of Equivariance/Invariance
• proof
• Theorem A.4: Equivariance of Local Frame