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It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequencies. The amplitude is not required to be small (apart…

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…

Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to reduce the size of the problem, hence reducing the…

Non-invasive surface wave methods have become a popular alternative to traditional invasive forms of site-characterization for inferring a site's subsurface shear wave velocity (Vs) structure. The advantage of surface wave methods over…

It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent…

Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…

Many methods for performing multi-objective optimisation of computationally expensive problems have been proposed recently. Typically, a probabilistic surrogate for each objective is constructed from an initial dataset. The surrogates can…

This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging…

Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy,…

Real-time sea state estimation is vital for applications like shipbuilding and maritime safety. Traditional methods rely on accurate wave-vessel transfer functions to estimate wave spectra from onboard sensors. In contrast, our approach…

Accurate Monte Carlo (MC) modelling in high-energy physics is challenging, particularly in complex scenarios where simulations fail to reproduce observed data. In practice, experimental information is often limited to one-dimensional (1D)…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as $K$-fold cross validation suffer from large biases. Motivated by the low bias of the leave-one-out cross…

We present the method of Direct van der Waals simulation (DVS) to study computationally flows with liquid-vapor phase transformations. Our approach is based on a novel discretization of the Navier-Stokes-Korteweg equations, that couple flow…

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…

In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

Reduced models for free-surface flows are required due to the high dimensionality of the underlying incompressible Navier-Stokes equations, which need to fully resolve the flow in vertical direction to compute the surface height. On the…

Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep…