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Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…
Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequential designs based…
We develop a generative model for the nuclear matter equation of state at zero net baryon density using the Gaussian Process Regression method. We impose first-principles theoretical constraints from lattice QCD and hadron resonance gas at…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
Based on high-order harmonic generation (HHG) spectra obtained from solving the time-dependent Schrodinger equation for atoms, we established quantitatively that the HHG yield can be expressed as the product of a returning electron wave…
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…
A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…
The algorithm to calculate the generating function for the number of ``skeleton'' diagrams for the irreducible self-energy and vertex parts is derived for the problems with Gaussian random fields. We find an exact recurrence relation…
We show that the Floquet approach with a Sturmian basis means an efficient description of high-order harmonic generation with monochromatic excitation. This method, although involves numerical calculations, is close to analytic approaches…
The complement functions in the free complement (FC) method are constructed by decontracting the Gaussian expansions of the Slater functions formed by the initial wavefunction and the $g$ functions. The helium ground state is used to…
We build a multi-output generative model for quasar spectra and the properties of their black hole engines, based on a Gaussian process latent-variable model. This model treats every quasar as a vector of latent properties such that the…
Understanding the structure of our universe and the distribution of matter is an area of active research. As cosmological surveys grow in complexity, the development of emulators to efficiently and effectively predict matter power spectra…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
An accurate analytic model describing high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results…
Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences,…
High harmonic generation is a convenient way to obtain extreme ultraviolet light from table-top laser systems and the experimental tools to exploit this simple and powerful light source for time-resolved spectroscopy are being developed by…
Attosecond light sources based on high-order harmonic generation (HHG) constitute to date the only table-top solution for producing coherent broadband radiation covering the spectral range from the extreme ultraviolet to the soft X-rays.…
High-harmonic generation (HHG) in solids has emerged in recent years as a rapidly expanding and interdisciplinary field, attracting attention from both the condensed-matter and the atomic, molecular, and optics communities. It has exciting…