Jennifer Ryan: Techniques for Data enhancement

Abstract: Extracting extra information from data can allow for more insight into the interaction between disparate scales. It can also aid in minimising error and decreasing noise in data. While the ability to move data from fine resolutions to coarser resolutions is straight forward utilizing a multi-resolution analysis framework, moving data from a coarse resolution to a finer resolution while reducing errors is more challenging. This relies on combining filtering techniques into the multi-resolution analysis framework [Ryan, CAMC 2022; Picklo & Ryan, SISC 2022]. This approach has the further advantage of requiring fewer computations to gain insight into calculations such as for Bohm speed [Picklo et al. JCP 2024]. In this talk, we present methods for data enhancement through multi-resolution analysis and the Smoothness-Increasing Accuracy-Conserving (SIAC) filtering framework. SIAC is known toinherently take advantage of the underlying physics and allow for the full resolution of the approximation and its derivatives in both the physical domain and Fourier signal space. We discuss recent advances and reliance of the approach on the underlying numerical method that generated the data.