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Machine learning (ML) models often struggle to maintain performance under distribution shifts, leading to inaccurate predictions on unseen future data. In this work, we investigate whether and under what conditions models can achieve such a…

In this paper we consider the machine learning (ML) task of predicting tipping point transitions and long-term post-tipping-point behavior associated with the time evolution of an unknown (or partially unknown), non-stationary, potentially…

Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the known molecules seen in training. We find that a key limitation is…

While the basic laws of Newtonian mechanics are well understood, explaining a physical scenario still requires manually modeling the problem with suitable equations and associated parameters. In order to adopt such models for artificial…

Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…

The ultimate purpose of most computational models is to make predictions, commonly in support of some decision-making process (e.g., for design or operation of some system). The quantities that need to be predicted (the quantities of…

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…

We study the functional task of deep learning image classification models and show that image classification requires extrapolation capabilities. This suggests that new theories have to be developed for the understanding of deep learning as…

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…

While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…

Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the…

Machine learning methods and uncertainty quantification have been gaining interest throughout the last several years in low-energy nuclear physics. In particular, Gaussian processes and Bayesian Neural Networks have increasingly been…

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…

Accurate determination of fuel properties of complex mixtures over a wide range of pressure and temperature conditions is essential to utilizing alternative fuels. The present work aims to construct cheap-to-compute machine learning (ML)…

This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of…

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…

This article investigates the origin of numerical issues in maximum likelihood parameter estimation for Gaussian process (GP) interpolation and investigates simple but effective strategies for improving commonly used open-source software…

Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be…

Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…

Machine learning (ML) techniques are increasingly applied to decision-making and control problems in Cyber-Physical Systems among which many are safety-critical, e.g., chemical plants, robotics, autonomous vehicles. Despite the significant…