| Author: | Deng, Jie |
| Title: | The BSDE solvers for high-dimensional PDEs and BSDEs |
| Advisors: | Lin, Yanping (AMA) Qiao, Zhonghua (AMA) |
| Degree: | M.Phil. |
| Year: | 2020 |
| Subject: | Stochastic differential equations -- Numerical solutions Differential equations, Parabolic -- Numerical solutions Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Applied Mathematics |
| Pages: | xxvi, 111 pages : color illustrations |
| Language: | English |
| Abstract: | Conventional numerical methods for high-dimensional parabolic partial differential equations (PDEs) suffer from the notorious "curse of dimensionality". Inspired by the FCNN-based deep BSDE solver in E et al. (2017) and Han et al. (2018), this thesis presents a CNN3H-based deep BSDE solver and a CNN2H-based BSDE solver by converting the fully connected neural networks (FCNNs) to the convolutional neural networks with 3 hidden layers (CNN3Hs) or with 2 hidden layers (CNN2Hs), and a linear BSDE solver by replacing the FCNNs with linear combinations. We also employ the connection between PDEs and backward stochastic differential equations (BSDEs), i.e. the Feynman-Kac formula. Owing to fewer parameters, the proposed BSDE solvers demonstrate higher efficiency than the FCNN-based deep BSDE solver without sacrificing accuracy when solving some 100-dimensional and 1000-dimensional PDEs. |
| Rights: | All rights reserved |
| Access: | open access |
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