Holey Sampling: Topological Analysis of Sampling Patterns for Assessing Error in High-Dimentional Quadrature project
Congratulation to Karctic Subr who has secured funding for his project.
Numerical integration is commonly encountered across the computational sciences. Often the integrands involved are ill-behaved functions that span high-dimensional domains. In such cases, sampling-based integrators are ubiquitous. The errors of sampling-based integrators is critically dependent on the sampling strategies used.
This project is concerned with assessment of samples, towards predicting errors resulting from their use in high-dimensional numerical integration.
Researchers propose to develop mathematical connections between the statistics of holes, or gaps, in high-dimensional sampling patterns and the approximation error of the sampling-based integrators that use those patterns.