2024-07-12 –, Method (1.5)
High-dimensional partial differential equations (PDEs) arise in various scientific domains, including physics, engineering, finance, and biology. However, simulating these PDEs is challenging due to the “curse of dimensionality.” As dimensions increase, the computational cost of solving these equations grows exponentially. HighDimPDE.jl is a Julia package that addresses this curse of dimensionality, offering deep learning-based solutions for the simulation of high-dimensional PDEs.
Building upon the SciML ecosystem in Julia, HighDimPDE.jl implements algorithms to solve problems related to high dimensional PDEs, such as non-local non-linear PDEs, Kolmogorov PDEs and their parametric families. Additionally, it provides solutions for optimal stopping strategies for pricing high-dimensional stock options (Obstacle PDEs).
In this talk, we will,
- Demonstrate the NNStopping algorithm for solving optimal expected pay-off and optimal stopping strategy for high-dimensional stock options.
- Demonstrate the NNKolmogorov algorithm for solving Kolmogorov PDEs
- Demonstrate the NNParamKolmogorov algorithm, which solves a parametric family of high-dimensional Kolmogorov PDEs, and provides a solution over all parameters and initial values of independent variables.
- Building on the previous point, we will perform parameter estimation on the model obtained from NNParamKolmogorov.
I am a software developer at JuliaHub, where I work on JuliaSim. I received my bachelor's degree in Electronics And Communication Engineering from IIT Roorkee.