Luca M. Ghiringhelli

Leonardo Medrano Sandonas, David Balcells, Anton Bochkarev et al.

Artificial intelligence is transforming molecular and materials science, but its growing computational and data demands raise critical sustainability challenges. In this Perspective, we examine resource considerations across the AI-driven discovery pipeline--from quantum-mechanical (QM) data generation and model training to automated, self-driving research workflows--building on discussions from the ``SusML workshop: Towards sustainable exploration of chemical spaces with machine learning'' held in Dresden, Germany. In this context, the availability of large quantum datasets has enabled rigorous benchmarking and rapid methodological progress, while also incurring substantial energy and infrastructure costs. We highlight emerging strategies to enhance efficiency, including general-purpose machine learning (ML) models, multi-fidelity approaches, model distillation, and active learning. Moreover, incorporating physics-based constraints within hierarchical workflows, where fast ML surrogates are applied broadly and high-accuracy QM methods are used selectively, can further optimize resource use without compromising reliability. Equally important is bridging the gap between idealized computational predictions and real-world conditions by accounting for synthesizability and multi-objective design criteria, which is essential for practical impact. Finally, we argue that sustainable progress will rely on open data and models, reusable workflows, and domain-specific AI systems that maximize scientific value per unit of computation, enabling efficient and responsible discovery of technological materials and therapeutics.

Luigi Sbailò, Luca Ghiringhelli

The configuration of latent representations plays a critical role in determining the performance of deep neural network classifiers. In particular, the emergence of well-separated class embeddings in the latent space has been shown to improve both generalization and robustness. In this paper, we propose a method to induce the collapse of latent representations belonging to the same class into a single point, which enhances class separability in the latent space while enforcing Lipschitz continuity in the network. We demonstrate that this phenomenon, which we call \textit{latent point collapse}, is achieved by adding a strong $L_2$ penalty on the penultimate-layer representations and is the result of a push-pull tension developed with the cross-entropy loss function. In addition, we show the practical utility of applying this compressing loss term to the latent representations of a low-dimensional linear penultimate layer. The proposed approach is straightforward to implement and yields substantial improvements in discriminative feature embeddings, along with remarkable gains in robustness to input perturbations.

Daniel T. Speckhard, Tim Bechtel, Luca M. Ghiringhelli et al.

Big data has ushered in a new wave of predictive power using machine learning models. In this work, we assess what {\it big} means in the context of typical materials-science machine-learning problems. This concerns not only data volume, but also data quality and veracity as much as infrastructure issues. With selected examples, we ask (i) how models generalize to similar datasets, (ii) how high-quality datasets can be gathered from heterogenous sources, (iii) how the feature set and complexity of a model can affect expressivity, and (iv) what infrastructure requirements are needed to create larger datasets and train models on them. In sum, we find that big data present unique challenges along very different aspects that should serve to motivate further work.

Luigi Sbailò, Luca M. Ghiringhelli

Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an algorithm that exploits the latent-space representation of data points fed into the network, to assess the accuracy of their prediction. Using the latent-space representation generated by the fraction of training set that the network classifies correctly, we build a statistical model that is able to capture the likelihood of a given prediction. We show on a synthetic dataset that commonly used methods are mostly overconfident. Overconfidence occurs also for predictions made on data points that are outside the distribution that generated the training data. In contrast, our method can detect such out-of-distribution data points as inaccurately predicted, thus aiding in the automatic detection of outliers.

Benjamin Regler, Matthias Scheffler, Luca M. Ghiringhelli

The identification of relevant features, i.e., the driving variables that determine a process or the properties of a system, is an essential part of the analysis of data sets with a large number of variables. A mathematical rigorous approach to quantifying the relevance of these features is mutual information. Mutual information determines the relevance of features in terms of their joint mutual dependence to the property of interest. However, mutual information requires as input probability distributions, which cannot be reliably estimated from continuous distributions such as physical quantities like lengths or energies. Here, we introduce total cumulative mutual information (TCMI), a measure of the relevance of mutual dependences that extends mutual information to random variables of continuous distribution based on cumulative probability distributions. TCMI is a non-parametric, robust, and deterministic measure that facilitates comparisons and rankings between feature sets with different cardinality. The ranking induced by TCMI allows for feature selection, i.e., the identification of variable sets that are nonlinear statistically related to a property of interest, taking into account the number of data samples as well as the cardinality of the set of variables. We evaluate the performance of our measure with simulated data, compare its performance with similar multivariate-dependence measures, and demonstrate the effectiveness of our feature-selection method on a set of standard data sets and a typical scenario in materials science.