Adaptive Grid Designs for Classifying Monotonic Binary Deterministic Computer Simulations

TL;DR

This paper introduces adaptive grid designs for efficiently classifying outcomes in time-consuming, deterministic, binary, monotonic computer simulations, significantly reducing the number of simulation runs needed compared to static designs.

Contribution

It derives lower bounds on evaluation counts and proposes adaptive grid designs that outperform static methods in classification accuracy with fewer simulations.

Findings

Adaptive grid designs require fewer runs than static designs.

Numerical results validate the efficiency of adaptive grid designs.

Adaptive designs achieve near-optimal evaluation counts.

Abstract

This research is motivated by the need for effective classification in ice-breaking dynamic simulations, aimed at determining the conditions under which an underwater vehicle will break through the ice. This simulation is extremely time-consuming and yields deterministic, binary, and monotonic outcomes. Detecting the critical edge between the negative-outcome and positive-outcome regions with minimal simulation runs necessitates an efficient experimental design for selecting input values. In this paper, we derive lower bounds on the number of functional evaluations needed to ensure a certain level of classification accuracy for arbitrary static and adaptive designs. We also propose a new class of adaptive designs called adaptive grid designs, which are sequences of grids with increasing resolution such that lower resolution grids are proper subsets of higher resolution grids. By prioritizing simulation runs at lower resolution points and skipping redundant runs, adaptive grid designs require the same order of magnitude of runs as the best possible adaptive design, which is an order of magnitude fewer than the best possible static design. Numerical results across test functions, the road crash simulation and the ice-breaking simulation validate the superiority of adaptive grid designs.