Deep Feynman-Kac Methods for High-dimensional Semilinear Parabolic Equations: Revisit
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917963402051584 |
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| author | Zheng, Xiaotao Yue, Xingye Shi, Jiyang |
| author_facet | Zheng, Xiaotao Yue, Xingye Shi, Jiyang |
| contents | Deep Feynman-Kac method was first introduced to solve parabolic partial differential equations(PDE) by Beck et al. (SISC, V.43, 2021), named Deep Splitting method since they trained the Neural Networks step by step in the time direction. In this paper, we propose a new training approach with two different features. Firstly, neural networks are trained at all time steps globally, instead of step by step. Secondly, the training data are generated in a new way, in which the method is consistent with a direct Monte Carlo scheme when dealing with a linear parabolic PDE. Numerical examples show that our method has significant improvement both in efficiency and accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Feynman-Kac Methods for High-dimensional Semilinear Parabolic Equations: Revisit Zheng, Xiaotao Yue, Xingye Shi, Jiyang Computational Engineering, Finance, and Science Deep Feynman-Kac method was first introduced to solve parabolic partial differential equations(PDE) by Beck et al. (SISC, V.43, 2021), named Deep Splitting method since they trained the Neural Networks step by step in the time direction. In this paper, we propose a new training approach with two different features. Firstly, neural networks are trained at all time steps globally, instead of step by step. Secondly, the training data are generated in a new way, in which the method is consistent with a direct Monte Carlo scheme when dealing with a linear parabolic PDE. Numerical examples show that our method has significant improvement both in efficiency and accuracy. |
| title | Deep Feynman-Kac Methods for High-dimensional Semilinear Parabolic Equations: Revisit |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2503.16407 |