GPU-Accelerated, Interval-Based Parameter Identification Methods Illustrated Using the Two-Compartment Problem

Interval methods are helpful in the context of scientific computing for reliable treatment of problems with bounded uncertainty. Most traditional interval algorithms, however, were designed for sequential execution while internally depending on processor-specific instructions for directed rounding. Nowadays, many-core processors and dedicated hardware for massively parallel data processing have become the de facto standard for high-performance computers. Interval libraries have yet to adapt to this heterogeneous computing paradigm. In this article, we investigate the parallelization of interval methods with an emphasis on modern graphics processors. Using a parameter identification scenario in combination with newly developed or enhanced GPU-based interval software, we evaluate different methods for reducing the size of large interval search domains. For the first time, algorithmic differentiation can be used with intervals on the GPU. Different versions of interval optimization algorithms are compared wrt. their functionality, run times, and energy consumption.