23 citations · 45 across the 5 of their papers we have counts for
5 papers
NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data
Yifan Sun, Linan Zhang, Hayden Schaeffer
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-t…
Forward Stability of ResNet and Its Variants
Linan Zhang, Hayden Schaeffer
The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to…
Stability and Error Estimates of BV Solutions to the Abel Inverse Problem
Linan Zhang, Hayden Schaeffer
Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and ot…
On the Convergence of the SINDy Algorithm
Linan Zhang, Hayden Schaeffer
One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of param…
Extracting structured dynamical systems using sparse optimization with very few samples
Hayden Schaeffer, Giang Tran, Rachel Ward +1
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems fr…