Convergence analysis of probabilistic schemes for nonlinear partial differential equations
This project studies the Deep Second-order Backward Stochastic Equations (2BSDE) solver for fully nonlinear partial differential equations (PDE). Several improvements to the Deep BSDE solver proposed in the recent years are discussed. Results produced by [8] are served as the benchmark for this proj...
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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2025
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| Online Access: | https://hdl.handle.net/10356/184479 |
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| Summary: | This project studies the Deep Second-order Backward Stochastic Equations (2BSDE) solver for fully nonlinear partial differential equations (PDE). Several improvements to the Deep BSDE solver proposed in the recent years are discussed. Results produced by [8] are served as the benchmark for this project.
Two new ideas are proposed to improve the Deep 2BSDE solver - via modifying the objective function and incorporating an optimistic initialization of the neural networks. Numerical experiments are performed with PDEs in 1- and 5-dimensional settings to demonstrate the performance improvement of the proposed ideas. Finally, future work that can be done to extend the scope of this project is discussed. |
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