Efficient Volume Computation

The current state-of-the-art algorithms for the volume computation of high dimensional convex bodies, such as the one currently used within the VolEsti package, use uniform sampling techniques. This proposal represents a GeomScale project that aims to develop an algorithm for volume computation of high dimensional convex bodies that would be more efficient than those by using the new advancements in non-uniform sampling techniques. Leveraged to provide scalability and efficiency for this computationally intensive process, methods such as the Hamiltonian Monte Carlo (HMC) stand out for their excellent fit for such a task, where the algorithm has to deal with truncated multivariate distributions, as highlighted by Pakman and Paninski. Seamless integration within the VolEsti package is ensured using C++, which aligns with the best practices for developing high-performance mathematical software discussed by Fisikopoulos et al. Throughout this project's entire research and development process, a blog will be maintained, monitoring all the insights, challenges, optimizations, and developments that will happen. This blog will represent the final deliverable, showcasing all the work done towards the project’s goals during the GSoC program.