Related papers: Linear and nonlinear filtering for a two-layer qua…

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing…

Many multiscale wave systems exhibit macroscale emergent behaviour, for example, the fluid dynamics of floods and tsunamis. Resolving a large range of spatial scales typically requires a prohibitively high computational cost. The small…

A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…

Understanding subsurface ocean dynamics is essential for quantifying oceanic heat and mass transport, but direct observations at depth remain sparse due to logistical and technological constraints. In contrast, satellite missions provide…

We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation…

The derivation of a quasi-geostrophic (QG) system from the rotating shallow water equations on a midlatitude beta-plane coupled with moisture is presented. Condensation is prescribed to occur whenever the moisture at a point exceeds a…

By considering the features of the airport runway image filtering, an improved bilateral filtering method was proposed which can remove noise with edge preserving. Firstly the steerable filtering decomposition is used to calculate the…

The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parameterized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a…

In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, however, usually require wave equations stated in their standard…

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an…

Data from direct numerical simulations of turbulent flows are commonly used to train neural network-based models as subgrid closures for large-eddy simulations; however, models with low a priori accuracy have been observed to fortuitously…

The subgrid-scale modelling of a low Mach number strongly anisothermal turbulent flow is investigated using direct numerical simulations. The study is based on the filtering of the low Mach number equations, suited to low Mach number flows…

In this paper, a novel pre- and post-processing algorithm is presented that can double the convergence rate of finite element approximations for linear wave problems. In particular, it is shown that a $q$-step pre- and post-processing…

A model reduction technique based on an optimization principle is employed to coarse-grain inviscid, incompressible fluid dynamics in two dimensions. In this reduction the spectrally-truncated vorticity equation defines the microdynamics,…

We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two…

In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…

Effective reef monitoring requires the quantification of coral growth via accurate volumetric and surface area estimates, which is a challenging task due to the complex morphology of corals. We propose a novel, lightweight, and scalable…

Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as…

Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear…

This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…