Development of Geometrically-Flexible Physics-Based Convolution Kernels

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Data compression is essential in many areas of technology such as satellite imaging, speech recognition, database design, and much more. However, most of this understanding is based on data with good properties.  Increasingly, there is a necessity for techniques that can be applied to complex or incomplete data, so-called flexible data. This project contributes to the development of more advanced compression techniques that can be applied to flexible data.  The main purpose of the project is the development of physics-based computational techniques that enhance data compression algorithms by making them more accurate and efficient.  The ideas developed in this project are applicable to more traditional computational fluid dynamics applications such as hypersonics and atmospheric modeling as well as areas such as machine learning.  In addition to the scientific impact, this project broadens the participation of women in the computational sciences.  It includes support for student mentorship, traineeship, and retention.   The computational skills that the students will obtain are broadly applicable and allows them access to a variety of career options, including in areas of great national need. The PI expects that the tools developed in this proposal will also be included in future outreach talks to the general public.The overall goal of this research is to develop innovative, mathematically rigorous, geometrically flexible, physics-based, multi-dimensional convolution kernels that are useful in areas of data compression, shock filtering, post-processing, and machine learning. The GEOCONKER (GEOmetrically-flexible physics-based CONvolution KERnels) project will not only concentrate on establishing a robust analytical framework, but also on the efficient implementation of these kernels. This will allow for enhancing accurate capturing of multi-scale physics that includes information from sensor data. These techniques will be able to be applied to different types of data and in different manners.   These convolution kernels will aid in establishing provable high-order resolution filters by establishing the interaction between the mathematics, physics, numerics, and geometry in applications.  These novel techniques will use (flexible) spline functions that can adapt to the geometry of the given data on the fly. This will allow for efficient computational codes that will enhance the accurate capturing and filtering of multi-scale physics.  This will include kernels that are useful in shock capturing, accuracy enhancement, and filtering of noisy data. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.