This project is part of my master thesis at Imperial College of London. We propose a deep learning approach to solve high-dimensional partial differential equations. The solver is tested on the Black-Scholes Barenblatt equation in 100 dimensions.
The repository needs to be cloned and running the BlackScholesBarenblatt100D.py will solve the Black-Scholes equation.
$ git clone https://github.com/batuhanguler/Deep-BSDE-Solver.git
$ cd Deep-BSDE-Solver
$ python BlackScholesBarenblatt100D.py
Different architectures are available changing the mode and activation variables in the BlackScholesBarenblatt100D.py file.
| Model | mode | activation |
|---|---|---|
| Fully-connected with sine activation | "FC" | "Sine" |
| Fully-connected with ReLU activation | "FC" | "ReLU" |
| Resnet with sine activation | "Resnet" | "Sine" |
| Resnet with ReLU activation | "Resnet" | "ReLU" |
| NAIS-Net with sine activation | "NAIS-Net" | "Sine" |
| NAIS-Net with ReLU activation | "NAIS-Net" | "ReLU" |
Fully-connected
A Pytorch version of Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations, a work from Maziar Raissi, is proposed. A simple fully-connected neural network with 5 layers of 256 parameters is implemented.
Resnet Residual networks were proposed in 2015 and helped to backpropagate efficiently the gradient using identity mappings (shortcut connections).
NAIS-Net NAIS-Net were proposed to overcome the problem of forward stability in Residual Networks.
