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As terrestrial resources become increasingly depleted, the demand for deep-sea resource exploration has intensified. However, the extreme conditions in the deep-sea environment pose significant challenges for underwater operations,…
The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of…
Non-hydrostatic atmospheric models often use semi-implicit temporal discretisations in order to negate the time step limitation of explicitly resolving the fast acoustic and gravity waves. Solving the resulting system to machine precision…
In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…
For high contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to…
An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30km resolution shallow water ocean…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
Analysing the impact of bottom friction on shallow water waves over bottom terrains is important in areas including environmental and coastal engineering as well as the oceanic and atmospheric sciences. However, current theoretical…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
Today, low-altitude fixed-wing Unmanned Aerial Vehicles (UAVs) are largely limited to primitively follow user-defined waypoints. To allow fully-autonomous remote missions in complex environments, real-time environment-aware navigation is…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
A data-driven algorithm is proposed that employs sparse data from velocity and/or scalar sensors to forecast the future evolution of three dimensional turbulent flows. The algorithm combines time-delayed embedding together with Koopman…
In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…
We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can…
In the context of filtering chaotic dynamical systems it is well-known that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both…
U.S. Tsunami Warning Centers use real-time bottom pressure (BP) data transmitted from a network of buoys deployed in the Pacific and Atlantic Oceans to tune source coefficients of tsunami forecast models. For accurate coefficients and…
Accurate marine wind forecasts are essential for safe navigation, ship routing, and energy operations, yet they remain challenging because observations over the ocean are sparse, heterogeneous, and temporally variable. We reformulate wind…
Interesting analogies between shallow water dynamics and astrophysical phenomena have offered valuable insight from both the theoretical and experimental point of view. To help organize these efforts, here we analyze systematically the…