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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
Huang, Chen-Wei
Keywords: 微分方程
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。

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.
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Description: 碩士
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Data Type: thesis
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