Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/125635


Title: 利用神經網路解微分方程
Neural Network Methods for Solving Differential Equation
Authors: 黃振維
Huang, Chen-Wei
Contributors: 符聖珍
黃振維
Huang, Chen-Wei
Keywords: 微分方程
神經網路
Date: 2019
Issue Date: 2019-09-05 16:13:07 (UTC+8)
Abstract: 本文是在敘述利用前饋人工神經網路的數值方法去近似微分方程的解,其中分別利用邊界條件或是初始條件去造出試驗函數去讓神經網路去近似,或是試驗函數不隱含初始條件或邊界條件,直接把初始條件與邊界條件當作神經網路的目標函數的優化條件,利用SGD和ADAM優化器去更新神經網路參數,再分別做比較。

其中在常微分方程分別去試驗了邊界值問題、特徵值問題、初始值問題、生態系統、及三種經典的偏微分方程,依照不同的方法去滿足不同的條件,進一步的去降低數值解的誤差。
This paper descirbes how to use the feed forward artificial neural network method to find the approximate solution of differential equations. Two types of the trial funcitons are used, and the objective function is minimized by SGD and ADAM methods respectively.

We test the boundary value problem, eigenvalue problem, initial value problem, two types of the ecological systems, and three classical types of the partial differential equations. We illustrate some examples and give some comparison results in Chapter 4.
Reference: Bibliography
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Description: 碩士
國立政治大學
應用數學系
105751003
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0105751003
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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