Indexing for function approximation

Abstract

Simulation is one of the most powerful tools that scientists have at their disposal for studying and understanding real-world physical phenomena. In order to be realistic, the mathematical models which drive simulations are often very complex and run for a very large number of simulation steps. The required computational resources often make it infeasible to evaluate simulation models exactly at each step, and thus scientists trade accuracy for reduced simulation cost.In this paper, we explore function approximation for a combustion simulation. In particular, we model high-dimensional function approximation (HFA) as a storage and retrieval problem, and we show that HFA defines a novel class of applications for high dimensional index structures. The interesting property of HFA is that it imposes a mixed query/update workload on the index which leads to novel tradeoffs between the efficiency of search versus updates. We investigate in detail one specific approach to HFA based on Taylor Series expansions and we analyze tradeoffs in index structure design through a thorough experimental study.