13 citations · 22 across the 3 of their papers we have counts for
8 papers
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi +1
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kr…
A Caputo fractional derivative-based algorithm for optimization
Yeonjong Shin, Jérôme Darbon, George Em Karniadakis
We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a ge…
Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
Beichuan Deng, Yeonjong Shin, Lu Lu +2
We present convergence analysis of operator learning in [Chen and Chen 1995] and [Lu et al. 2020], where continuous operators are approximated by a sum of products of branch and tr…
Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification and Avoidance
Mark Ainsworth, Yeonjong Shin
The ability of neural networks to provide `best in class' approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural ne…
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
Yeonjong Shin, Jerome Darbon, George Em Karniadakis
Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Gu…
Effects of Depth, Width, and Initialization: A Convergence Analysis of Layer-wise Training for Deep Linear Neural Networks
Yeonjong Shin
Deep neural networks have been used in various machine learning applications and achieved tremendous empirical successes. However, training deep neural networks is a challenging ta…