**JSoC Final Report**

**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.

## Achievements

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.