서지주요정보
다층 신경회로망을 이용한 간접적인 미분방정식 해법에 관한 연구 = Development of the indirect algorithm for solving differential equations using multi-layer neural networks
서명 / 저자 다층 신경회로망을 이용한 간접적인 미분방정식 해법에 관한 연구 = Development of the indirect algorithm for solving differential equations using multi-layer neural networks / 엄진용.
발행사항 [대전 : 한국과학기술원, 2003].
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8014142

소장위치/청구기호

학술문화관(문화관) 보존서고

MEE 03057

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In most cases, differential equations in the real world don't have their solutions as closed forms. So numerical methods are prefered to obtain an approximated solution. However, the most popular numerical method to solve differential equations, FEM (finite element method) has some drawbacks with their solutions. It provides its solution as a set of discrete values at the specific points in the domain. Therefore, the solution is not differentiable and it is not straitforward to obtain the values of the solution at the other points in the domain. Moreover, it requires lots of memory in order to present the solution at the specific points in the domain. Neural networks are good alternative tools for overcoming these drawbacks of FEM, because they are universal approximators, have continuous and differentiable outputs and require small memory space. Up to now, the MLP-based and the RBF-based techniques are proposed respectively as differential equation solvers using neural networks. The MLP-based technieque among them obtains the solution directly, that is from the MLP itself by approximating the solution with the MLP. In this thesis, The MLP-based technique that approximates not the solution but the derivative of the solution with the MLP is proposed. This technique obtains the solution indirectly, that is from the integrated function of the MLP with respect to the input. It can be a issue how to deal with the integration constants in the training phase of the MLP. This thesis proposed an algorithm for determining the integration constants using the pseudo-inverse. The proposed structure with the algorithm has been tested on several ODEs and PDEs with and without the noise. The results show that the proposed indirect method is more robust against the overfitting problems than the conventional direct one especially on the ODEs without the noise. And it requires less memory spaces than the RBF-based techniques. The results from the simulation with the noise show that the MLP-based techniques yields better solutions than the RBF-based techniques bacause of their small number of parameters and the abilities of choosing their stopping criteria to avoid learning the noise.

서지기타정보

서지기타정보
청구기호 {MEE 03057
형태사항 viii, 59 p. : 삽도 ; 26 cm
언어 한국어
일반주기 저자명의 영문표기 : Jin-Yong Uhm
지도교수의 한글표기 : 박철훈
지도교수의 영문표기 : Cheol-Hoon Park
학위논문 학위논문(석사) - 한국과학기술원 : 전기및전자공학전공,
서지주기 참고문헌 : p. 58-59
주제 신경회로망
미분방정식
상미분방정식
편미분방정식
neural networks
differential equations
MLP
ODE
PDE
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