50 citations · 75 across the 9 of their papers we have counts for
11 papers
The Level Set Ensemble Kalman Filter: Sequential Data Assimilation for Flows With Shocks
Michael K. Sleeman, Lorenzo Beronilla, Hangchuan Hu +4
The ensemble Kalman filter is commonly used to perform sequential data assimilation in science and engineering because of its robust performance and scalability when the state spac…
Neural ensemble Kalman filter: Data assimilation for compressible flows with shocks
Xu-Hui Zhou, Lorenzo Beronilla, Michael K. Sleeman +4
Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain sh…
BI-EqNO: Generalized Approximate Bayesian Inference with an Equivariant Neural Operator Framework
Xu-Hui Zhou, Zhuo-Ran Liu, Heng Xiao
Bayesian inference offers a robust framework for updating prior beliefs based on new data using Bayes' theorem, but exact inference is often computationally infeasible, necessitati…
Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations
Xu-Hui Zhou, Jiequn Han, Muhammad I. Zafar +4
Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, empl…
Inference of relative permeability curves in reservoir rocks with ensemble Kalman method
Xu-Hui Zhou, Haochen Wang, James McClure +2
Multiphase flows through reservoir rocks are a universal and complex phenomenon. Relative permeability is one of the primary determinants in reservoir performance calculations. Acc…
A PDE-free, neural network-based eddy viscosity model coupled with RANS equations
Ruiying Xu, Xu-Hui Zhou, Jiequn Han +2
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such…
An equivariant neural operator for developing nonlocal tensorial constitutive models
Jiequn Han, Xu-Hui Zhou, Heng Xiao
Developing robust constitutive models is a fundamental and longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to…
Frame invariance and scalability of neural operators for partial differential equations
Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou +1
Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high co…
Neural Network Based Pore Flow Field Prediction in Porous Media Using Super Resolution
Xu-Hui Zhou, James E. McClure, Cheng Chen +1
Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry…
Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids
Xu-Hui Zhou, Jiequn Han, Heng Xiao
Constitutive models are widely used for modeling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensiv…
Learning nonlocal constitutive models with neural networks
Xu-Hui Zhou, Jiequn Han, Heng Xiao
Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials ar…