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Predictive models of thermodynamic properties of mixtures are paramount in chemical engineering and chemistry. Classical thermodynamic models are successful in generalizing over (continuous) conditions like temperature and concentration. On the other hand, matrix completion methods (MCMs) from machine learning successfully generalize over (discrete) binary systems; these MCMs can make predictions without any data for a given binary system by implicitly learning commonalities across systems. In the present work, we combine the strengths from both worlds in a hybrid approach. The underlying idea is to predict the pair-interaction energies , as they are used in basically all physical models of liquid mixtures, by an MCM. As an example, we embed an MCM into UNIQUAC, a widely-used physical model for the Gibbs excess energy. We train the resulting hybrid model in a Bayesian machine-learning framework on experimental data for activity coefficients in binary systems of 1146 components from the Dortmund Data Bank. We thereby obtain, for the first time, a complete set of UNIQUAC parameters for all binary systems of these components, which allows us to predict, in principle, activity coefficients at arbitrary temperature and composition for any combination of these components, not only for binary but also for multicomponent systems. The hybrid model even outperforms the best available physical model for predicting activity coefficients, the modified UNIFAC (Dortmund) model. 

Anomaly detection aims at identifying data points that show systematic deviations from the major- ity of data in an unlabeled dataset. A common assumption is that clean training data (free of anomalies) is available, which is often violated in practice. We propose a strategy for training an anomaly detector in the presence of unlabeled anomalies that is compatible with a broad class of models. The idea is to jointly infer binary la- bels to each datum (normal vs. anomalous) while updating the model parameters. Inspired by out- lier exposure (Hendrycks et al., 2018) that con- siders synthetically created, labeled anomalies, we thereby use a combination of two losses that share parameters: one for the normal and one for the anomalous data. We then iteratively proceed with block coordinate updates on the parameters and the most likely (latent) labels. Our exper- iments with several backbone models on three image datasets, 30 tabular data sets, and a video anomaly detection benchmark showed consistent and significant improvements over the baselines.