Balancing Molecular Information and Empirical Data in the Prediction of Physico-Chemical Properties

Abstract

Predicting the physico-chemical properties of pure substances and mixtures is a central task in thermodynamics. Established prediction methods range from fully physics-based ab-initio calculations, which are only feasible for very simple systems, over descriptor-based methods that use some information on the molecules to be modeled together with fitted model parameters (e.g., quantitative-structure-property relationship methods or classical group contribution methods), to representation-learning methods, which may, in extreme cases, completely ignore molecular descriptors and extrapolate only from existing data on the property to be modeled (e.g., matrix completion methods). In this work, we propose a general method for combining molecular descriptors with representation learning using the so-called expectation maximization algorithm from the probabilistic machine learning literature, which uses uncertainty estimates to trade off between the two approaches. The proposed hybrid model exploits chemical structure information using graph neural networks, but it automatically detects cases where structure-based predictions are unreliable, in which case it corrects them by representation-learning based predictions that can better specialize to unusual cases. The effectiveness of the proposed method is demonstrated using the prediction of activity coefficients in binary mixtures as an example. The results are compelling, as the method significantly improves predictive accuracy over the current state of the art, showcasing its potential to advance the prediction of physico-chemical properties in general.

Figures (7)

• Figure 1: Model and data flow for training the proposed model. Left: graph neural networks take chemical structure information and output the parameters of conditional prior probability distributions (\ref{['eq:priors']}) over abstract representation vectors. Right: the likelihood (\ref{['eq:likelihood']}) models how well given representation vectors explain experimentally measured activity coefficients $\gamma_{i,j}^\infty$. We use variational EM (\ref{['sec:vem-intuition', 'sec:vem-formal']}) to fit the neural network weights $\theta$ (parametric, descriptor-based part), and to find variational distributions for each solute and solvent (nonparametric, representation-based part).
• Figure 2: Influence of prior uncertainty estimates (turquoise) on the final fitted parameters (black) for methylsulfolane (least frequent solvent, left) and water (most frequent solvent, right). Concentric ellipses show 25%, 75%, and 95% quantiles, respectively. For low prior uncertainty (small turquoise ellipses, left), the final fit is forced to closely match the prior, while a large prior uncertainty (right) admits more freedom to the final fit. Discussion in \ref{['sec:vem-intuition']} and model architectures in \ref{['sec:evaluation-setup']}.
• Figure 3: Data flow for a prediction where the solvent appears in the training set (in-domain) but the solute does not (out-of-domain). We thus predict the solute representation vector $\hat{u}_i$ from the prior, and the solvent representation vector $\hat{v}_j$ from the variational distribution $q_\phi$, see \ref{['eq:prediction']}.
• Figure 4: In-domain prediction errors (upper part), out-of-domain prediction errors (middle part), and ablations (lower section). The "reduced" dataset (light hatched bars) contains only mixtures to which UNIFAC is applicable. The proposed GNN MCM (gold highlighting) has the best predictive accuracy for both in-domain and out-of-domain predictions. Results labeled "ablation 1" (lower section) show errors for in-domain prediction tasks only, but performed as if these were out of domain.
• Figure 5: Improvement (in terms of mean average error, MAE) of the proposed GNN MCM method over UNIFAC and MCM, grouped by chemical category of the solute (see \ref{['tab:compound-categories']} in the supplementary information for a definition of the categories). Our method consistently improves over both UNIFAC and MCM across almost all solute categories; we see regressions (negative improvements) only on three categories with poor statistics in this evaluation due to small sample sizes (see gray numbers).