44 citations · 154 across the 14 of their papers we have counts for
14 papers
A non-intrusive bi-fidelity reduced basis method for time-independent problems
Jun Sur Richard Park, Xueyu Zhu
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However…
Forward and inverse problems for Eikonal equation based on DeepONet
Yifan Mei, Yijie Zhang, Xueyu Zhu +1
Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios…
Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion
Andrew Pensoneault, Xueyu Zhu
Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on par…
Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread
Giulia Bertaglia, Chuan Lu, Lorenzo Pareschi +1
When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibrati…
Bayesian Physics-Informed Neural Networks for the Subsurface Tomography based on the Eikonal Equation
Rongxi Gou, Yijie Zhang, Xueyu Zhu +1
The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty du…
Multi-fidelity methods for uncertainty propagation in kinetic equations
Giacomo Dimarco, Liu Liu, Lorenzo Pareschi +1
The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computation…
Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
Giulia Bertaglia, Liu Liu, Lorenzo Pareschi +1
Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertain…
A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs
Liu Liu, Lorenzo Pareschi, Xueyu Zhu
In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the pr…
Nonnegativity-Enforced Gaussian Process Regression
Andrew Pensoneault, Xiu Yang, Xueyu Zhu
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical prop…
A Bi-fidelity Surrogate Modeling Approach for Uncertainty Propagation in Three-Dimensional Hemodynamic Simulations
Han Gao, Xueyu Zhu, Jian-Xun Wang
Image-based computational fluid dynamics (CFD) modeling enables derivation of hemodynamic information, which has become a paradigm in cardiovascular research and healthcare. Noneth…
A bi-fidelity method for the multiscale Boltzmann equation with random parameters
Liu Liu, Xueyu Zhu
In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C.…
Bifidelity data-assisted neural networks in nonintrusive reduced-order modeling
Chuan Lu, Xueyu Zhu
In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper ortho…
An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models
Ming Cheng, Yi Qin, Akil Narayan +3
We develop a numerical framework to implement the cumulative density function (CDF) method for obtaining the probability distribution of the system state described by a kinematic w…
When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method
Xiu Yang, Xueyu Zhu, Jing Li
In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-mo…