26 citations · 99 across the 26 of their papers we have counts for
26 papers
Topological spectral gap, multiscale Weyl's law, and homogenization in high-contrast PDEs
Eric T. Chung, Lijian Jiang, Yajun Wang
This paper introduces a unified abstract variational and topological framework to characterize the spectral gap and eigenvalue distribution in high-contrast multiscale partial diff…
Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems
Dengfei Zeng, Lijian Jiang, Shuyu Sun +1
A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport…
Decoupling scales via localized subspace iteration and temporal splitting for multiscale parabolic equations
Eric T. Chung, Lijian Jiang, Mengnan Li +1
Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computat…
Localized subspace iteration methods for elliptic multiscale problems
Xiaofei Guan, Lijian Jiang, Yajun Wang +1
This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key c…
Conditional variational autoencoder with Gaussian process regression recognition for parametric models
Xuehan Zhang, Lijian Jiang
In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can rea…
Regularized coupling multiscale method for thermomechanical coupled problems
Xiaofei Guan, Lijian Jiang, Yajun Wang
The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn…
Perron-Frobenius operator filter for stochastic dynamical systems
Ningxin Liu, Lijian Jiang
The filtering problems are derived from a sequential minimization of a quadratic function representing a compromise between model and data. In this paper, we use the Perron-Frobeni…
Data-driven probability density forecast for stochastic dynamical systems
Meng Zhao, Lijian Jiang
In this paper, a data-driven nonparametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochasti…
Online multiscale model reduction for nonlinear stochastic PDEs with multiplicative noise
Lijian Jiang, Mengnan Li, Meng Zhao
In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coeffic…
Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media
Mengnan Li, Lijian Jiang
In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media using Koopman operators. Different from the case of autonomou…
Ensemble-based implicit sampling for Bayesian inverse problems with non-Gaussian priors
Yuming Ba, Lijian Jiang
In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampli…
An improved implicit sampling for Bayesian inverse problems of multi-term time fractional multiscale diffusion models
Xiaoyan Song, Lijian Jiang, Guanghui Zheng
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov c…
Bayesian identification of discontinuous fields with an ensemble-based variable separation multiscale method
Na Ou, Guang Lin, Lijian Jiang
This work presents a multiscale model reduction approach to discontinuous fields identification problems in the framework of Bayesian inference. An ensemble-based variable separati…
A Constraint energy minimizing generalized multiscale finite element method for parabolic equations
Mengnan Li, Eric Chung, Lijian Jiang
In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising fro…
A two-stage ensemble Kalman filter based on multiscale model reduction for inverse problems in time fractional diffusion-wave equations
Yuming Ba, Lijian Jiang, Na Ou
Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. To…
Local-global model reduction method for stochastic optimal control problems constrained by partial differential equations
Lingling Ma, Qiuqi Li, Lijian Jiang
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal con…
Recovering the reaction coefficient for two dimensional time fractional diffusion equations
Xiaoyan Song, Guanghui Zheng, Lijian Jiang
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann dat…
Bayesian inference using intermediate distribution based on coarse multiscale model for time fractional diffusion equation
Lijian Jiang, Na Ou
In the paper, we present a strategy for accelerating posterior inference for unknown inputs in time fractional diffusion models. In many inference problems, the posterior may be co…
A novel variable-separation method based on sparse representation for stochastic partial differential equations
Qiuqi Li, Lijian Jiang
In this paper, we propose a novel variable-separation (NVS) method for generic multivariate functions. The idea of NVS is extended to to obtain the solution in tensor product struc…
A dimension reduction method with applications for coefficient inversion of diffusion equations
Fuchen Chen, Lijian Jiang, Guanghui Zheng
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthog…
Model's sparse representation based on reduced mixed GMsFE basis methods
Lijian Jiang, Qiuqi Li
In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. M…
Multiscale model reduction method for Bayesian inverse problems of subsurface flow
Lijian Jiang, Na Ou
This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeate…
A hybrid HDMR for mixed multiscale finite element method with application for flows in random porous media
Lijian Jiang, J. David Moulton, Jia Wei
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is ofte…
A resourceful splitting technique with applications to deterministic and stochastic multiscale finite element methods
Lijian Jiang, Michael Presho
In this paper we use a splitting technique to develop new multiscale basis functions for the multiscale finite element method (MsFEM). The multiscale basis functions are iterativel…