Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor | Department of Applied Mathematics | en_US |
| dc.contributor.advisor | Lin, Yanping (AMA) | en_US |
| dc.contributor.advisor | Qiao, Zhonghua (AMA) | en_US |
| dc.creator | Deng, Jie | - |
| dc.identifier.uri | https://theses.lib.polyu.edu.hk/handle/200/10626 | - |
| dc.language | English | en_US |
| dc.publisher | Hong Kong Polytechnic University | en_US |
| dc.rights | All rights reserved | en_US |
| dc.title | The BSDE solvers for high-dimensional PDEs and BSDEs | en_US |
| dcterms.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. | en_US |
| dcterms.extent | xxvi, 111 pages : color illustrations | en_US |
| dcterms.isPartOf | PolyU Electronic Theses | en_US |
| dcterms.issued | 2020 | en_US |
| dcterms.educationalLevel | M.Phil. | en_US |
| dcterms.educationalLevel | All Master | en_US |
| dcterms.LCSH | Stochastic differential equations -- Numerical solutions | en_US |
| dcterms.LCSH | Differential equations, Parabolic -- Numerical solutions | en_US |
| dcterms.LCSH | Hong Kong Polytechnic University -- Dissertations | en_US |
| dcterms.accessRights | open access | en_US |
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