相关论文: Simple and efficient continuous data assimilation …

Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…

Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance…

We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is…

Data Assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state. This…

The over-parameterized models attract much attention in the era of data science and deep learning. It is empirically observed that although these models, e.g. deep neural networks, over-fit the training data, they can still achieve small…

Knowledge distillation is one of the primary methods of transferring knowledge from large to small models. However, it requires massive task-specific data, which may not be plausible in many real-world applications. Data augmentation…

Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…

Data assimilation (DA) methods combine model predictions with observational data to improve state estimation in dynamical systems, inspiring their increasingly prominent role in geophysical and climate applications. Classical DA methods…

We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier-Stokes equations of fluid dynamics, are characterized…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

The idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat…

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…

The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…

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…

We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a…

In order to solve Prandtl-type equations we propose a collocation-quadrature method based on VP filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder - Zygmund spaces of locally…