Symmetry transformations induce invariances and are a crucial building block of modern machine learning algorithms. Some transformations can be described analytically, e.g. geometric invariances. However, in many complex domains, such as the chemical space, invariances can be observed yet the corresponding symmetry transformation cannot be formulated analytically. Thus, the goal of our work is to learn the symmetry transformation that induced this invariance. To address this task, we propose learning two latent subspaces, where the first subspace captures the property and the second subspace the remaining invariant information. Our approach is based on the deep information bottleneck principle in combination with a mutual information regulariser. Unlike previous methods however, we focus on estimating mutual information in continuous rather than binary settings. This poses many challenges as mutual information cannot be meaningfully minimised in continuous domains. Therefore, we base the calculation of mutual information on correlation matrices in combination with a bijective variable transformation. Extensive experiments demonstrate that our model outperforms state-of-the-art methods on artificial and molecular datasets.

Material scientists are increasingly adopting the use of machine learning (ML) for making potentially important decisions, such as, discovery, development, optimization, synthesis and characterization of materials. However, despite ML's impressive performance in commercial applications, several unique challenges exist when applying ML in materials science applications. In such a context, the contributions of this work are twofold. First, we identify common pitfalls of existing ML techniques when learning from underrepresented/imbalanced material data. Specifically, we show that with imbalanced data, standard methods for assessing quality of ML models break down and lead to misleading conclusions. Furthermore, we found that the model's own confidence score cannot be trusted and model introspection methods (using simpler models) do not help as they result in loss of predictive performance (reliability-explainability trade-off). Second, to overcome these challenges, we propose a general-purpose explainable and reliable machine-learning framework. Specifically, we propose a novel pipeline that employs an ensemble of simpler models to reliably predict material properties. We also propose a transfer learning technique and show that the performance loss due to models' simplicity can be overcome by exploiting correlations among different material properties. A new evaluation metric and a trust score to better quantify the confidence in the predictions are also proposed. To improve the interpretability, we add a rationale generator component to our framework which provides both model-level and decision-level explanations. Finally, we demonstrate the versatility of our technique on two applications: 1) predicting properties of crystalline compounds, and 2) identifying novel potentially stable solar cell materials.