293 citations · 677 across the 21 of their papers we have counts for
10 papers · 1 filter
Methods to Recover Unknown Processes in Partial Differential Equations Using Data
Zhen Chen, Kailiang Wu, Dongbin Xiu
We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diff…
Data-Driven Deep Learning of Partial Differential Equations in Modal Space
Kailiang Wu, Dongbin Xiu
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the unde…
Deep learning of parameterized equations with applications to uncertainty quantification
Tong Qin, Zhen Chen, John Jakeman +1
We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the r…
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data
Kailiang Wu, Tong Qin, Dongbin Xiu
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving,…
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…
Energy Conserving Galerkin Approximation of Two Dimensional Wave Equations with Random Coefficients
Ching-Shan Chou, Yukun Li, Dongbin Xiu
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effe…
A stochastic Galerkin method for general system of quasilinear hyperbolic conservation laws with uncertainty
Kailiang Wu, Huazhong Tang, Dongbin Xiu
This paper is concerned with generalized polynomial chaos (gPC) approximation for a general system of quasilinear hyperbolic conservation laws with uncertainty. The one-dimensional…
Equation-free, multiscale computation for unsteady random diffusion
Dongbin Xiu, Ioannis Kevrekidis
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with shor…