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Your search keyword '"Yang, Yunlei"' showing total 3 results
Start Over Author "Yang, Yunlei" Topic differential equations
3 results on '"Yang, Yunlei"'

1. Numerical solution of several kinds of differential equations using block neural network method with improved extreme learning machine algorithm.

Author

Yang, Yunlei, Hou, Muzhou, Luo, Jianshu, and Tian, Zhongchu

Subjects
*DIFFERENTIAL equations, *MACHINE learning, *WEIGHT training
Abstract

In this paper, block neural network (BNN) method is proposed to solve several kinds of differential equations. BNN is used to construct approximating functions and its derivatives, the improved extreme learning machine (IELM) algorithm are designed to train network weights. To evaluate the performance of the proposed method, numerical examples are performed by the presented method. Comparison of the numerical results with exact solutions validate the feasibility of the proposed method in accuracy. Results compared with other recent research works also validate the superiority of the proposed approach. Numerical results show that the proposed BNN with IELM algorithm perform well in accuracy and requires less hidden neurons. [ABSTRACT FROM AUTHOR]

Published
2020
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2. Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm.

Author

Sun, Hongli, Hou, Muzhou, Yang, Yunlei, Zhang, Tianle, Weng, Futian, and Han, Feng

Subjects
PARTIAL differential equations, MACHINE learning, SUPPORT vector machines, ARTIFICIAL neural networks, BERNSTEIN polynomials, DIFFERENTIAL equations
Abstract

In this paper, we introduce a new method based on Bernstein Neural Network model (BeNN) and extreme learning machine algorithm to solve the differential equation. In the proposed method, we develop a single-layer functional link BeNN, the hidden layer is eliminated by expanding the input pattern by Bernstein polynomials. The network parameters are obtained by solving a system of linear equations using the extreme learning machine algorithm. Finally, the numerical experiment is carried out by MATLAB, results obtained are compared with the existing method, which proves the feasibility and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Published
2019
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3. Numerical solving of generalized Black-Scholes differential equation using deep learning based on blocked residual connection.

Author

Hou, Muzhou, Fu, Huawei, Hu, Zheng, Wang, Jia, Chen, Yinghao, and Yang, Yunlei

Subjects
*DEEP learning, *DIFFERENTIAL equations, *NUMERICAL solutions to equations, *MACHINE learning, *FINITE element method, *DERIVATIVE securities
Abstract

Option pricing in the financial derivatives market is worth studying. When the volatility and the rate of return are not fixed in Blacks-Scholes (BS) equation, the analytical form of the solution is difficult to be obtained. In this paper, we propose deep learning based on blocked residual connection method (DLBR) for the numerical solving of BS equations. The validity period and inventory price are the inputs of the network, while the option price is the solution. Neurons on the multiple hidden layers are processed in blocks and each block is connected to the residuals. The boundary conditions are constructed as a part of the numerical solution and the loss function is minimized to obtain the optimal network parameters. The DLBR method has strong applicability and overcomes the shortcomings of extreme learning machines. Three experiment calculated the numerical solution of the BS equation about European options and promoted the option pricing model. Compared with the existing algorithms such as finite element method and physics-informed neural networks (PINN) method, the obtained numerical solution has higher precision and smaller error, which shows the feasibility and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Published
2022
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