NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

A multi-stage deep learning based algorithm for multiscale model reduction

(2021) Eric Chung et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Computational multiscale methods for quasi-gas dynamic equations

(2021) Boris Chetverushkin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

(2021) Sifan Wang et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations

(2020) Zecheng Zhang et al.   Mathematics

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

(2020) Liu Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Constraint Energy Minimizing Generalized Multiscale Finite Element Method

(2018) Eric T. Chung et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients

(2018) Eric T. Chung et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

(2016) Eric Chung et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Generalized multiscale finite element methods (GMsFEM)

(2013) Yalchin Efendiev et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multiphysics and Multiscale Methods for Modeling Fluid Flow Through Naturally Fractured Carbonate Karst Reservoirs

(2009) Peter Popov et al.   SPE RESERVOIR EVALUATION & ENGINEERING

An Efficient Two-Stage Sampling Method for Uncertainty Quantification in History Matching Geological Models

(2008) Xianlin Ma et al.   SPE JOURNAL

Asymptotic and numerical homogenization

(2008) B. Engquist et al.   ACTA NUMERICA