131 citations · 164 across the 8 of their papers we have counts for
8 papers
Failure-informed adaptive sampling for PINNs
Zhiwei Gao, Liang Yan, Tao Zhou
Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. It is noticed, however, the performance of PINNs can va…
Optimal design for kernel interpolation: applications to uncertainty quantification
Akil Narayan, Liang Yan, Tao Zhou
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation us…
An acceleration strategy for randomize-then-optimize sampling via deep neural networks
Liang Yan, Tao Zhou
Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO may be computationally intensive for complexity pr…
Stein variational gradient descent with local approximations
Liang Yan, Tao Zhou
Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develo…
An adaptive surrogate modeling based on deep neural networks for large-scale Bayesian inverse problems
Liang Yan, Tao Zhou
In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. Howeve…
A non-intrusive reduced basis EKI for time-fractional diffusion inverse problems
Fenglian Yang, Liang Yan
In this study, we consider an ensemble Kalman inversion (EKI) for the numerical solution of time-fractional diffusion inverse problems (TFDIPs). Computational challenges in the EKI…
An adaptive multi-fidelity PC-based ensemble Kalman inversion for inverse problems
Liang Yan, Tao Zhou
The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become mode…
Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems
Liang Yan, Tao Zhou
The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the u…