相关论文: Continuous data assimilation for hydrodynamics: co…

Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment…

Data assimilation combines (imperfect) knowledge of a flow's physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow statistics. Assimilation by nudging (from 1964), while…

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using coarse mesh observations, converge at an exponential rate…

We present a numerical discretisation of the coupled moment systems, previously introduced in Dahm and Helzel, which approximate the kinetic multi-scale model by Helzel and Tzavaras for sedimentation in suspensions of rod-like particles for…

This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon the prior research incorporating a data-driven finite-difference approximation of smooth solutions…

The Reynolds-averaged Navier-Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their…

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically…

In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the…

Nudging is a data assimilation technique that has proved to be capable of reconstructing several highly turbulent flows from a set of partial spatiotemporal measurements. In this study we apply the nudging protocol on the temperature field…

Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…

The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such…

The relativistic method of moments is one of the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. The equations can be systematically improved to higher order, and they have…

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 propose moment relaxations for data-driven Wasserstein distributionally robust optimization problems. Conditions are identified to ensure asymptotic consistency of such relaxations for both single-stage and two-stage problems, together…