293 citations · 677 across the 21 of their papers we have counts for
8 papers · 1 filter
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks
Victor Churchill, Dongbin Xiu
Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems. A remarkable feature of FML is t…
Learning Stochastic Dynamical System via Flow Map Operator
Yuan Chen, Dongbin Xiu
We present a numerical framework for learning unknown stochastic dynamical systems using measurement data. Termed stochastic flow map learning (sFML), the new framework is an exten…
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence
Victor Churchill, Dongbin Xiu
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 term prediction of the dynamic…
Deep Learning of Chaotic Systems from Partially-Observed Data
Victor Churchill, Dongbin Xiu
Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method ut…
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…
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data
Jun Hou, Tong Qin, Kailiang Wu +1
A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a…
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…