538 citations · 706 across the 12 of their papers we have counts for
12 papers
IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning
Ling Guo, Hao Wu, Wenwen Zhou +2
We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression…
Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations
Ling Guo, Hao Wu, Xiaochen Yu +1
We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential eq…
Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models
Ling Guo, Hao Wu, Tao Zhou
We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a norma…
Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach
Ling Guo, Akil Narayan, Yongle Liu +1
One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about…
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
Dongkun Zhang, Ling Guo, George Em Karniadakis
One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking adva…
Efficient multistep methods for tempered fractional calculus: Algorithms and Simulations
Ling Guo, Fanhai Zeng, Ian Turner +2
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative opera…
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Dongkun Zhang, Lu Lu, Ling Guo +1
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids,…
Stochastic collocation methods via minimization of Transformed penalty
Ling Guo, Jing Li, Yongle Liu
We study the properties of sparse reconstruction of transformed (TL1) minimization and present improved theoretical results about the recoverability and the accuracy of th…
Data-driven polynomial chaos expansions: a weighted least-square approximation
Ling Guo, Yongle Liu, Tao Zhou
In this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of…
A gradient enhanced -minimization for sparse approximation of polynomial chaos expansions
Ling Guo, Akil Narayan, Tao Zhou
We investigate a gradient-enhanced -minimization for constructing sparse polynomial chaos expansions. In addition to function evaluations, measurements of the function grad…
Weighted approximate Fekete points: Sampling for least-squares polynomial approximation
Ling Guo, Akil Narayan, Liang Yan +1
We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations o…
Stochastic collocation methods via minimization using randomized quadratures
Ling Guo, Akil Narayan, Tao Zhou +1
In this work, we discuss the problem of approximating a multivariate function via minimization method, using a random chosen sub-grid of the corresponding tensor grid of G…