Related papers: Boundary conditions control for a Shallow-Water mo…
Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
Data assimilation combines prior (or background) information with observations to estimate the initial state of a dynamical system over a given time-window. A common application is in numerical weather prediction where a previous forecast…
This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul…
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…
Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…
The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…
We consider the Blume-Capel spin model on a finite cylinder with reservoirs at the boundary. A model with spin variable $\sigma$ taking values in {-1, 0, 1}, with the superposition of two dynamics: in the bulk, the spins evolve according to…
``Online" data assimilation (DA) is used to generate a new seasonal-resolution reanalysis dataset over the last millennium by combining forecasts from an ocean--atmosphere--sea-ice coupled linear inverse model with climate proxy records.…
Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
A formulation is developed to assimilate ocean-wave data into the Numerical Flow Analysis (NFA) code. NFA is a Cartesian-based implicit Large-Eddy Simulation (LES) code with Volume of Fluid (VOF) interface capturing. The sequential…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
In this work are presented and discussed some results related to the validation process of a software module based on PETSc which implements a Data Assimilation algorithm.
This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such an analysis can be used for pruning redundant measurements, and for designing future sensor…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…