Numerical techniques for Black hole solutions in f(R) gravity 

This project aims to research and develop numerical techniques for finding black hole solutions in modified gravity theories, namely the f(R) gravity. 

I started by building a physics-informed neural net for solving the 1st-order Einstein equation in a vacuum (plot attached). I further worked on training these nets for solving the 2nd-order coupled equations and benchmarking the solutions against traditional numerical methods. A key issue in finding numerical solutions to these equations is their highly-nonlinear nature and convergence of the net on the trivial solution.  

Once we achieve vacuum solutions with high accuracy, we can easily modify the net for modified gravity models.