TY - JOUR
T1 - Using adaptive multi-accurate function evaluations in a surrogate-assisted method for computer experiments
AU - Wang, Weichung
AU - Chen, Ray Bing
AU - Hsu, Chia Lung
N1 - Funding Information:
The authors are grateful to the anonymous referees for their valuable comments and suggestions. This work is partially supported by the National Science Council , the Taida Institute for Mathematical Sciences , the Mathematics Division of the National Center for Theoretical Sciences (Taipei Office) in Taiwan , and the Mathematics Division of the National Center for Theoretical Sciences (South) in Taiwan .
PY - 2011/3/15
Y1 - 2011/3/15
N2 - In many computer experiments, surrogates are used to assist in searching for certain target points. If the surrogates are defined by response function values evaluated by costly iterative processes, the computational burdens may impede the efficiency of regular surrogate-assisted methods. Instead of computing the fully convergent response function values, we propose to control the function evaluation iterations dynamically to save time on function evaluations without degrading the overall performance. Our new algorithms adaptively determine whether each of the function evaluation iterations should be paused, kept running, or restarted; we then use the approximate function values with various levels of accuracy to construct the surrogates. The numerical results show that the proposed algorithms achieve significant savings when solving super-level set searching problems that involve identifying positive Lyapunov exponents of a dynamical system.
AB - In many computer experiments, surrogates are used to assist in searching for certain target points. If the surrogates are defined by response function values evaluated by costly iterative processes, the computational burdens may impede the efficiency of regular surrogate-assisted methods. Instead of computing the fully convergent response function values, we propose to control the function evaluation iterations dynamically to save time on function evaluations without degrading the overall performance. Our new algorithms adaptively determine whether each of the function evaluation iterations should be paused, kept running, or restarted; we then use the approximate function values with various levels of accuracy to construct the surrogates. The numerical results show that the proposed algorithms achieve significant savings when solving super-level set searching problems that involve identifying positive Lyapunov exponents of a dynamical system.
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U2 - 10.1016/j.cam.2010.12.021
DO - 10.1016/j.cam.2010.12.021
M3 - Article
AN - SCOPUS:79952193646
VL - 235
SP - 3151
EP - 3162
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 10
ER -