DeepAI AI Chat
Log In Sign Up

Self-adaptive deep neural network: Numerical approximation to functions and PDEs

09/07/2021
by   Zhiqiang Cai, et al.
Purdue University
0

Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive algorithm: the adaptive network enhancement (ANE) method, written as loops of the form train, estimate and enhance. Starting with a small two-layer neural network (NN), the step train is to solve the optimization problem at the current NN; the step estimate is to compute a posteriori estimator/indicators using the solution at the current NN; the step enhance is to add new neurons to the current NN. Novel network enhancement strategies based on the computed estimator/indicators are developed in this paper to determine how many new neurons and when a new layer should be added to the current NN. The ANE method provides a natural process for obtaining a good initialization in training the current NN; in addition, we introduce an advanced procedure on how to initialize newly added neurons for a better approximation. We demonstrate that the ANE method can automatically design a nearly minimal NN for learning functions exhibiting sharp transitional layers as well as discontinuous solutions of hyperbolic partial differential equations.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/14/2021

Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs

In this paper, we study adaptive neuron enhancement (ANE) method for sol...
07/19/2021

Adaptive Two-Layer ReLU Neural Network: I. Best Least-squares Approximation

In this paper, we introduce adaptive neuron enhancement (ANE) method for...
10/26/2020

The estimation of training accuracy for two-layer neural networks on random datasets without training

Although the neural network (NN) technique plays an important role in ma...
04/28/2022

A Neural Network-enhanced Reproducing Kernel Particle Method for Modeling Strain Localization

Modeling the localized intensive deformation in a damaged solid requires...
07/02/2020

Persistent Neurons

Most algorithms used in neural networks(NN)-based leaning tasks are stro...
07/06/2017

Simultaneous Optimization of Neural Network Weights and Active Nodes using Metaheuristics

Optimization of neural network (NN) significantly influenced by the tran...