Yeonjong Shin | DeepAI

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∙ 09/02/2023

On the training and generalization of deep operator networks

We present a novel training method for deep operator networks (DeepONets...

0 SangHyun Lee, et al. ∙

∙ 03/29/2022

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of ...

0 Jessica T. Lauzon, et al. ∙

∙ 08/31/2021

GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems

We propose the GENERIC formalism informed neural networks (GFINNs) that ...

6 Zhen Zhang, et al. ∙

∙ 05/20/2021

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

We propose a new type of neural networks, Kronecker neural networks (KNN...

38 Ameya D. Jagtap, et al. ∙

∙ 04/06/2021

A Caputo fractional derivative-based algorithm for optimization

We propose a novel Caputo fractional derivative-based optimization algor...

11 Yeonjong Shin, et al. ∙

∙ 02/21/2021

Convergence rate of DeepONets for learning operators arising from advection-diffusion equations

We present convergence rates of operator learning in [Chen and Chen 1995...

0 Beichuan Deng, et al. ∙

∙ 10/15/2020

Error estimates of residual minimization using neural networks for linear PDEs

We propose an abstract framework for analyzing the convergence of least-...

0 Yeonjong Shin, et al. ∙

∙ 07/14/2020

Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification and Avoidance

The ability of neural networks to provide `best in class' approximation ...

0 Mark Ainsworth, et al. ∙

∙ 04/03/2020

On the Convergence and generalization of Physics Informed Neural Networks

Physics informed neural networks (PINNs) are deep learning based techniq...

0 Yeonjong Shin, et al. ∙

∙ 10/14/2019

Effects of Depth, Width, and Initialization: A Convergence Analysis of Layer-wise Training for Deep Linear Neural Networks

Deep neural networks have been used in various machine learning applicat...

0 Yeonjong Shin, et al. ∙

∙ 07/23/2019

Trainability and Data-dependent Initialization of Over-parameterized ReLU Neural Networks

A neural network is said to be over-specified if its representational po...

3 Yeonjong Shin, et al. ∙

∙ 03/15/2019

Dying ReLU and Initialization: Theory and Numerical Examples

The dying ReLU refers to the problem when ReLU neurons become inactive a...

0 Lu Lu, et al. ∙

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