High-Dimensional Database for Continuous Physical Phenomena with Uncertainty

he objective of this project is to advance the state of knowledge in efficiently representing, interrogating, visualizing, updating and manipulating vast amounts of geophysical data. The research combines, in a synergistic effort, database and visualization expertise from computer science, computational geometry expertise, advanced concepts from theoretical and applied mathematics with concrete geophysical data with the goal to prove the practicality of the developed database concepts for a challenging automated navigation problem. Specific objectives are: (1) to attack the problem of multidimensional physical data representation using advanced higher dimensional geometric concepts; (2) to address the problem of uncertainty in data representation and computation by invoking the concept of interval splines and the theory of interval arithmetic; (3) to study the problem of geometric and physical information storage, retrieval, reconstruction and interrogation by applying methods from differential topology and algebraic topology; (4) to develop new methods for continuous non-linear data representation and interrogation using global topological generalized boundary representation databases based on the cell-tuple structure; and (5) to evaluate the developed concepts in a preliminary fashion in a practical example involving autonomous underwater vehicle (AUV) navigation using a marine geophysical database. The database techniques developed in this project will enhance the conduct of research in environmental and ocean sciences and engineering and other disciplines studying continuous physical phenomena.