57 citations · 82 across the 7 of their papers we have counts for
7 papers
Designing Neural Networks for Hyperbolic Conservation Laws
Zhen Chen, Anne Gelb, Yoonsang Lee
We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerica…
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning
Victor Churchill, Steve Manns, Zhen Chen +1
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evoluti…
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
Zhen Chen, Victor Churchill, Kailiang Wu +1
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recen…
Data-driven learning of non-autonomous systems
Tong Qin, Zhen Chen, John Jakeman +1
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous na…
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…
On generalized residue network for deep learning of unknown dynamical systems
Zhen Chen, Dongbin Xiu
We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified the residu…