Related papers: Exploring the robust extrapolation of high-dimensi…

The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet…

The capacity to generalize beyond the range of training data is a pivotal challenge, often synonymous with a model's utility and robustness. This study investigates the comparative abilities of traditional machine learning (ML) models and…

Neural network (NN) interatomic potentials provide fast prediction of potential energy surfaces, closely matching the accuracy of the electronic structure methods used to produce the training data. However, NN predictions are only reliable…

Over the past decade inter-atomic potentials based on machine-learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure…

We present a physically motivated strategy for the construction of training sets for transferable machine learning interatomic potentials. It is based on a systematic exploration of all possible space groups in random crystal structures,…

Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output…

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods…

Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate: (i) the…

Recent advances in machine-learning interatomic potentials have enabled the efficient modeling of complex atomistic systems with an accuracy that is comparable to that of conventional quantum mechanics based methods. At the same time, the…

We study the generalization of over-parameterized deep networks (for image classification) in relation to the convex hull of their training sets. Despite their great success, generalization of deep networks is considered a mystery. These…

Learning deep representations to solve complex machine learning tasks has become the prominent trend in the past few years. Indeed, Deep Neural Networks are now the golden standard in domains as various as computer vision, natural language…

In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…

We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set,…

The extrapolation of self-consistent nuclear mean-field models to the region of superheavy elements is discussed with emphasis on the extrapolating power of the models. The predictions of modern mean-field models are confronted with recent…

Given the importance of nuclear mass predictions, numerous models have been developed to extrapolate the measured data into unknown regions. While neural networks -- the core of modern artificial intelligence -- have been recently suggested…

Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…

In the past two decades, machine learning potentials (MLP) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics and materials science. Different…

This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…

Machine learning potentials have revolutionised the field of atomistic simulations in recent years and are becoming a mainstay in the toolbox of computational scientists. This paper aims to provide an overview and introduction into machine…