Due to strong learning ability, convolutional neural networks (CNNs) have been developed
in image denoising. However, convolutional operations may change original distributions of …

This work proposes a stochastic domain decomposition method for solving steady-state
partial differential equations (PDEs) with random inputs. Specifically, based on the efficiency …

The image denoising algorithm based on partial differential equation can selectively solve
the problem of noise and image smoothing, which has become the focus of current image …

Elasticity is a fundamental model in mechanics and material sciences. In the article, we
present an ensemble variable-separated multiscale method for elasticity problems in …

As efficient separation of variables plays a central role in model reduction for nonlinear and
nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation …

Deep convolution neural networks (CNNs) have become popular for image denoising due to
their robust learning capabilities. However, many methods tend to increase the receptive …

This work presents a new bi‐fidelity model reduction approach to the inverse problem under
the framework of Bayesian inference. A low‐rank approximation is introduced to the solution …

This work presents a stochastic multiscale model reduction approach to solve PDEs with
random coefficients. An ensemble-based low-rank approximation method is proposed to …

Parametric dynamical systems are widely used to model physical systems, but their
numerical simulation can be computationally demanding due to nonlinearity, long-time …

This work presents a two-stage variable-separation Kalman filter (T-VSKF) to the combined
parameters and state estimation in Bayesian data assimilation. The variable-separation …