Revealing hidden features in approximations via convolution kernel multi-resolution analysis

The idea of convolution filtering is ubiquitous in many areas of application: data compression, shock filtering, post-processing, machine learning, etc. When paired with multi-resolution analysis, it becomes a powerful tool for extracting hidden features from data. This is an emerging area of research that is increasingly necessary in multi-scale applications.

The proposed research will develop convolution kernel multi-resolution analysis (CKMRA) that provides useful algorithms for time-dependent simulations with a cross-over application of imaging.

These novel techniques are based on the PIs development of Smoothness-Increasing Accuracy-Conserving (SIAC) kernels using (flexible) spline functions that can adapt to the given data in real time.

This will allow for efficient computational codes that enhance the accurate capturing and filtering of multi-scale physics. The development of these mathematically efficient algorithms will include:1.

Establishing an analytical framework for accurate, flexible, physics-based kernels for multi-dimensional applications.2.

Developing locally adaptive, variable convolution kernels for both shock capturing and enhancing accuracy in time-dependent simulations.3. Developing multi-scale compression algorithms for scientific data.