Kirill Zubov / Aug 24 2019
Remix of Julia by Nextjournal

JSoC Final Report

Julia Season of Contribution 2019 has come to an end. I worked on implementation the library for solve high-dimensional PDEs using neural networks. You can find the project in the repository for this link - NeuralNetDiffEq.jl. This post is about a summary result of my work in JSoC.


Earlier I wrote posts about the work done. For details about the work you can visit the previous blog posts and also I breaf describe what was done:

In addition to what has been described above, there has also been wrote many tests for each methods (you can find them in the repo). Each test represent a numerical solve for semi-liner high-dimensional differential equation that to compare with right answer.

There was written tests for next differential equations:

  • Heat equation
  • Black Scholes Barenblatt equation
  • Allen-Cahn equation
  • Hamilton Jacobi Bellman equation
  • Nonlinear Black-Scholes equation with Default Risk

In addition, besides everything that is describe above we started writing an article using the results of work in the project at JSoC

Future issues

Anyway, there is a lot more stuff to be done, from solving small bugs to implementing major features.

For example:

  • Optimal stopping problems through neural networks
  • Kolmogorov equations through neural nets
  • Deep learning for random PDEs
  • Deep learning methods for stochastic elliptic PDEs
  • Deep learning methods for free-boundary PDEs
  • GPU and TPU support
  • Option that allow get solution of differential equation on every time step

Final word

It's been exciting be part of all that. I had fun and very productive summer at JSoC. Moreover, I would be exactly glad to continue working on NeuralNetDiffEq project.

It was a pleasure working under my mentor Chris Rackauckas, who has helped me tremendously throughout this journey.

Thanks to the Julia community for this marvelous opportunity to participate in the project.