Deep PPDE solver

Authors: Jiang Yu Nguwi and Nicolas Privault.

If this code is used for research purposes, please cite as
J.Y. Nguwi and N. Privault. A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations. arXiv preprint arXiv:2209.15010 (2022).

The paper is available here.

Quick Start

Deep PPDE solver aims to solve path-dependent PDE. Since the project involves comparison with other works, which use different versions of tensorflow, it is recommended to use Colab to handle package dependencies. Click the following link for quick start.

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Explanation

All python files are organized as follows:

1. main.py is our PPDE solver.
2. regression.py is the PPDE solver based on [RT17].
3. deep_galerkin.py is the PPDE solver based on [SZ20].
4. ppde_asian.py and ppde_barrier.py are the PPDE solvers based on [SVSS20].
5. deep_bsde.py is the PDE solver based on [HJE18].
6. deep_split.py is the PDE solver based on [BBC+2019].
7. stats.py summarizes the statistics of the simulations above. It outputs lit_compare.csv, which can be compared with Table 1-3 in the paper.

References

[RT17] Z. Ren and X. Tan. On the convergence of monotone schemes for path-dependent PDEs. Stochastic Process. Appl., 127(6):1738--1762, 2017.

[SZ20] Y.F. Saporito and Z. Zhang. PDGM: A neural network approach to solve path-dependent partial differential equations. Preprint arXiv:2003.02035, 2020.

[SVSS20] M. Sabate-Vidales, D. Siska, and L. Szpruch. Solving path dependent PDEs with LSTM networks and path signatures. Preprint arXiv:2011.10630, 2020.

[HJE18] J. Han, A. Jentzen, and W. E. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34):8505--8510, 2018.

[BBC+2019] C. Beck, S. Becker, P. Cheridito, A. Jentzen, and A. Neufeld. Deep splitting method for parabolic PDEs. Preprint arXiv:1907.03452, 2019.