相关论文: Multi-dimensional filtering: Reducing the dimensio…
In recent years, the widespread use of deep neural networks (DNNs) has facilitated great improvements in performance for computer vision tasks like image classification and object recognition. In most realistic computer vision applications,…
We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard…
Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. %In particular, Bender and \"Offner developed entropy-conservative discontinuous Galerkin (DG) methods to…
Semi-implicit multilevel spectral deferred correction (SI-MLSDC) methods provide a promising approach for high-order time integration for nonlinear evolution equations including conservation laws. However, existing methods lack robustness…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
In this paper, we present and analyze a staggered discontinuous Galerkin method for Darcy flows in fractured porous media on fairly general meshes. A staggered discontinuous Galerkin method and a standard conforming finite element method…
Dynamic surface control (DSC) method uses high gain filters to avoid the "explosion of complexity" issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
We consider the filtering and smoothing problems for an infinite-dimensional diffusion process X, observed through a finite-dimensional representation at discrete points in time. At the heart of our proposed methodology lies the…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…
Diffusion-based image compression has demonstrated impressive perceptual performance. However, it suffers from two critical drawbacks: (1) excessive decoding latency due to multi-step sampling, and (2) poor fidelity resulting from…
The current high-fidelity generation and high-precision detection of DeepFake images are at an arms race. We believe that producing DeepFakes that are highly realistic and 'detection evasive' can serve the ultimate goal of improving future…
The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…
Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail…
We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in early numerical methods, whereas they are employed to an increasing extent in…
High-order entropy-stable discontinuous Galerkin (DG) methods for nonlinear conservation laws reproduce a discrete entropy inequality by combining entropy conservative finite volume fluxes with summation-by-parts (SBP) discretization…