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Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…

The behaviour of molecules in space is to a large extent governed by where they freeze out or sublimate. The molecular binding energy is thus an important parameter for many astrochemical studies. This parameter is usually determined with…

The tunability of the mechanical properties of refractory multi-principal-element alloys (RMPEAs) make them attractive for numerous high-temperature applications. It is well-established that the phase stability of RMPEAs control their…

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

For machine learning of interatomic potentials a scalable sparse Gaussian process regression formalism is introduced with a data-efficient on-the-fly adaptive sampling algorithm. With this approach, the computational cost is effectively…

Predictions of nuclear models guide the design of nuclear facilities to ensure their safe and efficient operation. Because nuclear models often do not perfectly reproduce available experimental data, decisions based on their predictions may…

The computational complexity of calculating phase diagrams for multi-parameter models significantly limits the ability to select parameters that correspond to experimental data. This work presents a machine learning method for solving the…

Recently supervised machine learning has been ascending in providing new predictive approaches for chemical, biological and materials sciences applications. In this Perspective we focus on the interplay of machine learning algorithm with…

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

We develop and test new machine learning strategies for accelerating molecular crystal structure ranking and crystal property prediction using tools from geometric deep learning on molecular graphs. Leveraging developments in graph-based…

We show that by using intuitive and accessible molecular features it is possible to predict the temperature-dependent second virial coefficient of organic and inorganic compounds using Gaussian process regression. In particular, we built a…

Refractory multi-principal element alloys (RMPEAs) represent a novel class of alloys characterized by an extensive compositional design space and the potential for exceptional mechanical performance under extreme conditions. While accurate…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…