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DEEP SPLITTING METHOD FOR PARABOLIC PDEs
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DOI：10.1137/19M1297919.png)
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摘要
En 中文
In this paper, we introduce a numerical method for nonlinear parabolic partial differential equations (PDEs) that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high dimensional PDEs. We test the method on different examples from physics, stochastic control, and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times.
Keyword:
splitting-up method
neural networks
deep learning
nonlinear partial differential equations
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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