135 citations · 219 across the 18 of their papers we have counts for
18 papers
Adaptive deep density approximation for stochastic dynamical systems
Junjie He, Qifeng Liao, Xiaoliang Wan
In this paper we consider adaptive deep neural network approximation for stochastic dynamical systems. Based on the Liouville equation associated with the stochastic dynamical syst…
An adaptive ANOVA stochastic Galerkin method for partial differential equations with high-dimensional random inputs
Guanjie Wang, Smita Sahu, Qifeng Liao
It is known that standard stochastic Galerkin methods encounter challenges when solving partial differential equations with high-dimensional random inputs, which are typically caus…
Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems
Yani Feng, Kejun Tang, Xiaoliang Wan +1
We present a dimension-reduced KRnet map approach (DR-KRnet) for high-dimensional Bayesian inverse problems, which is based on an explicit construction of a map that pushes forward…
VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problems
Yingzhi Xia, Qifeng Liao, Jinglai Li
Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspect…
A domain-decomposed VAE method for Bayesian inverse problems
Zhihang Xu, Yingzhi Xia, Qifeng Liao
Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by exp…
Streaming data recovery via Bayesian tensor train decomposition
Yunyu Huang, Yani Feng, Qifeng Liao
In this paper, we study a Bayesian tensor train (TT) decomposition method to recover streaming data by approximating the latent structure in high-order streaming data. Drawing on t…
Domain-decomposed Bayesian inversion based on local Karhunen-Loève expansions
Zhihang Xu, Qifeng Liao, Jinglai Li
In many Bayesian inverse problems the goal is to recover a spatially varying random field. Such problems are often computationally challenging especially when the forward model is…
Reduced basis stochastic Galerkin methods for partial differential equations with random inputs
Guanjie Wang, Qifeng Liao
We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the st…
Deep neural network based adaptive learning for switched systems
Junjie He, Zhihang Xu, Qifeng Liao
In this paper, we present a deep neural network based adaptive learning (DNN-AL) approach for switched systems. Currently, deep neural network based methods are actively developed…
A deep domain decomposition method based on Fourier features
Sen Li, Yingzhi Xia, Yu Liu +1
In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods ar…
Adaptive deep density approximation for Fokker-Planck equations
Kejun Tang, Xiaoliang Wan, Qifeng Liao
In this paper we present an adaptive deep density approximation strategy based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P) equations. F-P equations are usua…
Tensor Train Random Projection
Yani Feng, Kejun Tang, Lianxing He +2
This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically…
ANOVA Gaussian process modeling for high-dimensional stochastic computational models
Chen Chen, Qifeng Liao
In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random…
D3M: A deep domain decomposition method for partial differential equations
Ke Li, Kejun Tang, Tianfan Wu +1
A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be form…
A hierarchical neural hybrid method for failure probability estimation
Ke Li, Kejun Tang, Jinglai Li +2
Failure probability evaluation for complex physical and engineering systems governed by partial differential equations (PDEs) are computationally intensive, especially when high-di…
Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs
Kejun Tang, Qifeng Liao
This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random paramete…
An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems
Qifeng Liao, Jinglai Li
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or re…
Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization
Shengfeng Zhu, Xianliang Hu
Numerical computation of shape gradients from Eulerian derivatives is essential to wildly used gradient type methods in shape optimization. Boundary type Eulerian derivatives are p…