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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...
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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 ...
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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 ...
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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...
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04/06/2021
A Caputo fractional derivative-based algorithm for optimization
We propose a novel Caputo fractional derivative-based optimization algor...
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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...
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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-...
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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 ...
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04/03/2020
On the Convergence and generalization of Physics Informed Neural Networks
Physics informed neural networks (PINNs) are deep learning based techniq...
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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...
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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...
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03/15/2019