no code implementations • 20 Jul 2023 • 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.
no code implementations • 25 Aug 2022 • Victor Churchill, Anne Gelb
As proposed, the method was not well-suited for large problems, however, as the sampling was inefficient.
no code implementations • 3 Jun 2022 • 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 dynamics of the unknown system.
no code implementations • 12 May 2022 • Victor Churchill, Dongbin Xiu
A distinct feature of chaotic systems is that even the smallest perturbations will lead to large (albeit bounded) deviations in the solution trajectories.
no code implementations • 7 Mar 2022 • Victor Churchill, Steve Manns, Zhen Chen, Dongbin Xiu
In the proposed ensemble averaging method, multiple models are independently trained and model predictions are averaged at each time step.
no code implementations • 7 Jun 2021 • Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu
Consequently, a trained DNN defines a predictive model for the underlying unknown PDE over structureless grids.
no code implementations • 17 Jul 2020 • Victor Churchill, Anne Gelb
This expands the class of problems available to Bayesian learning to include, e. g., inverse problems dealing with the recovery of piecewise smooth functions or signals from data.