EXPLOITING SYMMETRY IN HIGH ORDER TENSOR-BASED SERIES EXPANSION ALGORITHMS

Many applications in science and engineering require the calculations of partial derivative models. Computational differentiation has been developed as a software technology for addressing this need. General numerical models are available for generating first-fourth order sensitivity models. The challenge addressed in this work is concerned with efficiently generating and storing the tensor based calculations. Sensitivity calculations are of interest for both initial conditions and parameters. A major challenge encountered in high dimensioned real world applications, is that both the computations and data storage requirements scale nonlinearly. This work addresses the problem of exploiting the tensor symmetry arising in the generation, storage, and computation using symmetrized models for hessian and higher order sensitivity tensors. Extensive modifications are required for operator-overloaded derivative tools for exploiting the symmetrized tensor models. Typical applications include problems in applied mathematics, probability theory, optimization, control theory, and computer science. Several applications are presented to demonstrate the significant impact on both memory allocations and symmetric-based computational algorithms.