Related papers: Optimal Boundary Discretization by Variational Dat…
A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to…
The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
A 4D-Var data assimilation technique is applied to a ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of the boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the…
This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving the Cauchy-Dirichlet problem. The related boundary conditions are obtained by…
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
Motivated by recent applications requiring differential privacy over adaptive streams, we investigate the question of optimal instantiations of the matrix mechanism in this setting. We prove fundamental theoretical results on the…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
Several advances have been made in Data Assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, based on a…
This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous meta-optimization problem for parameters; the…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…