Related papers: Physical extrapolation of quantum observables by g…

The intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this…

Physics-Informed Machine Learning (PIML) has gained momentum in the last 5 years with scientists and researchers aiming to utilize the benefits afforded by advances in machine learning, particularly in deep learning. With large scientific…

We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to judge when computational errors are irrelevant and estimate the…

We assess the accuracy of Bayesian polynomial extrapolations from small parameter values, x, to large values of x. We consider a set of polynomials of fixed order, intended as a proxy for a fixed-order effective field theory (EFT)…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

The fact that we can build models from data, and therefore refine our models with more data from experiments, is usually given for granted in scientific inquiry. However, how much information can we extract, and how precise can we expect…

Gaussian processes (GPs) are a mature and widely-used component of the ML toolbox. One of their desirable qualities is automatic hyperparameter selection, which allows for training without user intervention. However, in many realistic…

Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological…

We propose a non-parametric extrapolation method based on constrained Gaussian processes for configuration interaction methods. Our method has many advantages: (i) applicability to small data sets such as results of {\it ab initio} methods,…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

Extrapolation is defined as making predictions beyond the range of the data used to estimate a statistical model. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the…

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML algorithm…

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Physics-informed machine learning (PIML), referring to the combination of prior knowledge of physics, which is the high level abstraction of natural phenomenons and human behaviours in the long history, with data-driven machine learning…

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation…

Predicting nuclear masses is a longstanding challenge. One path forward is machine learning (ML) which trains on experimental data, but can suffer large errors when extrapolating toward neutron-rich species. In nature, such masses shape…

Morse projections are well-known in chemistry and allow one, within a Morse potential approximation, to redefine the potential in a simple quadratic form. The latter, being a non-linear transform, is also very helpful for machine learning…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…