Development of Topological Data Analysis Techniques for Noisy and Sparse 2D Time-Dependent Datasets

This project leverages Topological Data Analysis (TDA) and Wasserstein Distance (WD) to identify turbulence transitions on the Large Plasma Device (LAPD), utilizing high-speed visible camera data. TDA is an analysis technique that extracts topological features from digital data, while the WD metric enables the interpretation of TDA on noisy datasets by allowing the measurement of coarse topological properties (Panaretos et al., 2018). Because plasmas are examples of nonlinear systems that undergo changes due to instability or transition to a new equilibrium, the methods support predictions in plasma turbulent behaviors, which correlate to solar and atmospheric investigations. TDA is implemented with WD on LAPD to identify transitional occurrences in magnetically confined plasma. With noise added to turbulence simulations, the initial results demonstrated the ability to identify the dominant turbulent flow from zonal regimes without knowledge of the energy in various turbulence scales (Kiewel et al., 2024). Furthermore, probe turbulence measurements from LAPD experiments are analyzed to identify transition changes leveraging this technique. In the case of noisy datasets, limitations on the spatial resolution of measurements will be assessed with respect to the noise levels. These techniques look to be extended to datasets in solar dynamics and atmospheric flows to yield more precise measurements in scientific experiments. Work supported by US DOE under DE-SC0007880 and NSF PHY under 2144099.