Design and analysis of computer experiment via dimensional analysis

Design and analysis techniques for computer experiments have been largely developed. However, empirical emulators generated based on experimental data usually fail to incorporate physical principles and dimensional constraints the computer model follows. In this article, we propose a new design and analysis framework based on dimensional analysis (DA), a widely used reduction technique in physics and engineering. We show that implementing DA in computer experiments is efficient, scalable, interpretable, robust and costless. We demonstrate the benefits and improvement in details by theoretical derivations and numerical examples of the borehole model and the damped harmonic oscillation.