With modern computational resources rapidly advancing towards exascale, large-scale simulations useful for understanding natural and man-made phenomena are becoming increasingly accessible. As a result, the size and complexity of data representing such phenomena is also increasing, making the role of data analysis to propel science even more integral. This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields—an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented.
One of the most fundamental challenges in the analysis of a vector field is that its features are defined only for a certain reference frame. However, there does not exist a single "correct" reference frame for analysis; therefore, in the absence of an unsuitable frame, features of interest may remain undetected-thus, creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of “correctness” of features for certain goals. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (time-independent) vector fields, which can be performed using simpler and scalable techniques allowing better data management by accessing the data on a per-time-step basis.
Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws—thus, creating serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and present a new discrete theory that use combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors.
Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations.