Deep BSDE Solver in TensorFlow
python main.py --problem=SquareGradient
Command-line flags:
problem_name: Name of partial differential equation (PDE) to solve. There are seven PDEs implemented so far. See Problems section below.num_run: Number of experiments to repeatedly run for the same problem.log_dir: Directory to write event logs and output array.
equation.py and config.py now support the following problems:
AllenCahn: Allen-Cahn equation with a cubic nonlinearity.HJB: Hamilton-Jacobi-Bellman (HJB) equation.PricingOption: Nonlinear Black-Scholes equation for the pricing of European financial derivatives with different interest rates for borrowing and lending.PricingDefaultRisk: Nonlinear Black-Scholes equation with default risk in consideration.BurgesType: Multidimensional Burgers-type PDEs with explicit solution.QuadraticGradients: An example PDE with quadratically growing derivatives and an explicit solution.ReactionDiffusion: Time-dependent reaction-diffusion-type example PDE with oscillating explicit solutions.
New problems can be added very easily. Inherit the class equation
in equation.py and define the new problem. Note that the generator function
and terminal function should be TensorFlow operation while the sample function
can be python operation. Also remember to a give proper config in config.py.
[1] Han, J., Jentzen, A., and E, W. Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning.
arXiv:1707.02568 (2017)
[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.
arXiv:1706.04702 (2017)