293 citations · 677 across the 21 of their papers we have counts for
Showing 2019Show all
3 papers · 1 filter
math.NA2019★ 169 cited
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…
math.NA2019★ 2 cited
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…
math.NA2019★ 25 cited
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,…