Department of Applied Mathematics and Statistics, Colorado School of Mines
Title
Designing effective, efficient, and flexible convolution kernels
Abstract
Convolution kernels are powerful tools that have proven useful in multiple areas, such as data compression, shock filtering,
post-processing, and machine learning. The popularity of this approach has given rise to the need for effective and efficient design
of convolution kernels, suitable for a variety of applications. In this talk, we focus on the design of
convolution kernels for efficiency, effectiveness and flexibility. Well-designed convolution kernels, such as the one that gives rise
to Smoothness-Increasing Accuracy-Conserving (SIAC) post-processing filters, can be used to extract hidden information in certain
numerical simulations, creating even more accurate representations of the data. They can be adapted for boundaries, unstructured
grids, and non-smooth solutions. Furthermore, such well-designed convolution kernels have the potential to accurately
capture multi-scale physics, and are flexible enough to combine simulation information with experimental data. This
presentation will focus on identifying the essential properties in convolution kernel design, what information it
is exploiting and the possibilities in applications.
