相关论文: Analysis of continuous data assimilation with larg…

We present an algorithm for solving stochastic heat equations, whose key ingredient is a non-uniform time discretization of the driving Brownian motion $W$. For this algorithm we derive an error bound in terms of its number of evaluations…

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…

We prove convergence of a finite difference approximation of the compressible Navier--Stokes system towards the strong solution in $R^d,$ $d=2,3,$ for the adiabatic coefficient $\gamma>1$. Employing the relative energy functional, we find a…

We describe a new approach allowing for systematic causal attribution of weather and climate-related events, in near-real time. The method is purposely designed to facilitate its implementation at meteorological centers by relying on data…

This paper is concerned with high moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with general additive noise. The implicit Euler-Maruyama scheme and standard…

In the era of Big Data, scalable and accurate clustering algorithms for high-dimensional data are essential. We present new Bayesian Distance Clustering (BDC) models and inference algorithms with improved scalability while maintaining the…

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…

We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…

We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into regions of higher likelihood. We argue that the optimal…

This paper proposes a data-driven version of the Benders decomposition algorithm applied to the stochastic unit commitment (SUC) problem. The proposed methodology aims at finding a trade-off between the size of the Benders master problem…

We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in…

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…

We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using the incompressible Euler equations and a suitably chosen…

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that…

In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…

We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate the well-posedness and convergence of the truncated Carleman…