相关论文: Continuing dynamic assimilation of the inner regio…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
This paper concerns the study of the generalized Bolza problem governed by differential inclusions satisfying the so-called "relaxed one-sided Lipschitzian" (ROSL) condition with respect to the state variables subject to various types of…
We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently large choices of the control parameter and resolution and…
Today's ocean numerical prediction skills depend on the availability of in-situ and remote ocean observations at the time of the predictions only. Because observations are scarce and discontinuous in time and space, numerical models are…
In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-dimensional B\'enard convection problem. Specifically we consider the two-dimensional Boussinesq system of a layer of incompressible fluid between two…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…
A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
Existing work on data-driven optimization focuses on problems in static environments, but little attention has been paid to problems in dynamic environments. This paper proposes a data-driven optimization algorithm to deal with the…
We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of "weak Dirichlet process" in this context. Such a process $\X$,…
When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
Understanding time-dependent blood flow dynamics in arteries is crucial for diagnosing and treating cardiovascular diseases. However, accurately predicting time-varying flow patterns requires integrating observational data with…
A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…
Relevant comprehension of flood hazards has emerged as a crucial necessity, especially as the severity and the occurrence of flood events intensify with climate changes. Flood simulation and forecast capability have been greatly improved…
This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable assumptions on local-energy estimates for approximate…