相关论文: Data-driven complete basis set limit estimates fro…

Accurate electronic structure calculations are essential in modern materials science, but strongly correlated systems pose a significant challenge due to their computational cost. Traditional methods, such as complete active space…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…

Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a…

To effectively simulate the combustion of hydrocarbon-fueled supersonic engines, such as rocket-based combined cycle (RBCC) engines, a detailed mechanism for chemistry is usually required but computationally prohibitive. In order to…

In this paper, we consider the problem of designing a training set using the most informative molecules from a specified library to build data-driven molecular property models. Specifically, we use (i) sparse generalized group additivity…

Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…

Kernel quantile regression (KQR) extends classical quantile regression to nonlinear settings using kernel methods, offering a powerful tool for modeling conditional distributions. However, its application to large-scale datasets remains…

Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrices…

Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision…

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…

Finding optimal measurement operators is crucial for the performance of quantum reservoir computers (QRCs), since they employ a fixed quantum feature map. We formulate the training of both stateless (quantum extreme learning machines,…

Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more…

Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness Recurrent Neural Networks (RNNs). However, while their predictions are quite accurate, their learning process is complex…

As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the…

We present an efficient approach for generating highly accurate molecular potential energy surfaces (PESs) using self-correcting, kernel ridge regression (KRR) based machine learning (ML). We introduce structure-based sampling to…

Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…

The proliferation of data has sparked significant interest in leveraging findings from one study to estimate treatment effects in a different target population without direct outcome observations. However, the transfer learning process is…

The finite basis set errors for all-electron random-phase approximation (RPA) correlation energy calculations are analyzed for isolated atomic systems. We show that, within the resolution-of-identity (RI) RPA framework, the major source of…