Related papers: A quasi-optimal coarse problem and an augmented Kr…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or PDEs) under uncertainty. As an example, we focus on the so-called Conditional…
In this paper, we consider weakly regular Sturm-Liouville eigenproblems with unbounded potential at both endpoints of the domain. We propose a Galerkin spectral matrix method for its solution and we study the error in the eigenvalue…
Wearable devices enable continuous health monitoring from multimodal signals, but real-world deployment is hindered by limited labeled data and pervasive sensor incompleteness. While large-scale self-supervised pretraining reduces label…
The Ultra Weak Variational Formulation (UWVF) is a special Trefftz discontinuous Galerkin method, here applied to the time-harmonic Maxwell's equations. The method uses superpositions of plane waves to represent solutions element-wise on a…
Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap,…
Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of…
The general theory of non-bremsstrahlung radiation by non-equilibrium medium is proposed on the base of the new (PRL, 2004; JETP, 2004) quantum theory of Vavilov-Cherenkov radiation (VCR), where Abraham's form for the true photon momentum…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
This paper provides an alternative methodology for analysis of three-wave interactions under the exact dispersion relation associated with gravity waves in fluid of intermediate depth. A Korteweg-de Vries type of equation with exact…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in…
Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…
There are numerous contexts where one wishes to describe the state of a randomly evolving system. Effective solutions combine models that quantify the underlying uncertainty with available observational data to form relatively optimal…
Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample…
Using Levi-Civita's theory of ideal fluids, we derive the complex Korteweg-de Vries (KdV) equation, describing the complex velocity of a shallow fluid up to first order. We use perturbation theory, and the long wave, slowly varying velocity…
A paramount goal in the field of nuclear physics is to unify ab-initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound state calculations in light systems…
There are numerous contexts where one wishes to describe the state of a randomly evolving system. Effective solutions combine models that quantify the underlying uncertainty with available observational data to form scientifically…