293 citations · 1.2k across the 39 of their papers we have counts for
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Data Driven Governing Equations Approximation Using Deep Neural Networks
Tong Qin, Kailiang Wu, Dongbin Xiu
We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual netw…
Numerical Aspects for Approximating Governing Equations Using Data
Kailiang Wu, Dongbin Xiu
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g.,…
An Explicit Neural Network Construction for Piecewise Constant Function Approximation
Kailiang Wu, Dongbin Xiu
We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions. The proposed FNN has two hid…
Provably Positive High-Order Schemes for Ideal Magnetohydrodynamics: Analysis on General Meshes
Kailiang Wu, Chi-Wang Shu
This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and finite volume methods which provably preserve the positivity of density and pressure for the…
Provably Positive Discontinuous Galerkin Methods for Multidimensional Ideal Magnetohydrodynamics
Kailiang Wu, Chi-Wang Shu
The density and pressure are positive physical quantities in magnetohydrodynamics (MHD). Design of provably positivity-preserving (PP) numerical schemes for ideal compressible MHD…
Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics
Kailiang Wu
Numerical schemes provably preserving the positivity of density and pressure are highly desirable for MHD, but the rigorous positivity-preserving (PP) analysis remains challenging.…