rushhan / bsde_torch

A pytorch implementation of Backward Stochastic Differential Equation

[bsde_torch]

A pytorch implementation of Backward Stochastic Differential Equation

To execute:

python main.py

Currently Supports and Tested (CPU only):

• HJBLQ: Hamilton-Jacobi-Bellman (HJB) equation.

More to follow!!

Dependencies

torch 1.10.0 munch 2.5.0 torchvision 1.6.3

Reference

[1] Han, J., Jentzen, A., and E, W. Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning, Proceedings of the National Academy of Sciences, 115(34), 8505-8510 (2018). [journal] [arXiv]
[2] E, W., Han, J., and Jentzen, A. Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, Communications in Mathematics and Statistics, 5, 349–380 (2017). [journal] [arXiv]

Note and Thanks:

This Repo is heavily based on the work done by [frankhan91]. THe original work is in Tensorflow and can be found [here]. The current model reuses the same network for all the subswquent time step insteaad of creating new for each time step. This greatly reduced the parameters to train (about 1/20 the of the tf counterpart).