Profile Bayesian Optimization for Expensive Computer Experiments

2025-12-29

AI Summary

This study addresses expensive, deterministic black-box simulation with a single control parameter and multiple disturbance parameters, aiming to efficiently compute the “profile optimum”—i.e., the optimal response as a function of the control parameter over its full domain. We propose a two-stage Bayesian optimization (BO) framework: first, we formally embed the profile optimization objective into BO; second, we introduce a dual-layer Gaussian process surrogate—comprising shallow and deep components—to jointly enable global exploration in the control space and high-fidelity local approximation of the profile. The method integrates uncertainty quantification with adaptive sequential experimental design. Evaluated on multiple benchmarks and a rotating detonation engine diffuser simulation, it significantly outperforms conventional BO and classical profile optimization methods. It accurately captures the optimal relationship between total pressure loss and diffuser length, delivering an interpretable, computationally efficient optimization tool for high-performance thermal system design.

Technology Category

Search and Optimization: Sampling/Simulation-based SearchReasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: Learning & Optimization for ROB

Application Category

User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systemsSystems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterizationSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a novel Bayesian optimization (BO) procedure aimed at identifying the ``profile optima'' of a deterministic black-box computer simulation that has a single control parameter and multiple nuisance parameters. The profile optima capture the optimal response values as a function of the control parameter. Our objective is to identify them across the entire plausible range of the control parameter. Classic BO, which targets a single optimum over all parameters, does not explore the entire control parameter range. Instead, we develop a novel two-stage acquisition scheme to balance exploration across the control parameter and exploitation of the profile optima, leveraging deep and shallow Gaussian process surrogates to facilitate uncertainty quantification. We are motivated by a computer simulation of a diffuser in a rotating detonation combustion engine, which returns the energy lost through diffusion as a function of various design parameters. We aim to identify the lowest possible energy loss as a function of the diffuser's length; understanding this relationship will enable well-informed design choices. Our ``profile Bayesian optimization'' procedure outperforms traditional BO and profile optimization methods on a variety of benchmarks and proves effective in our motivating application.

Problem

• Identifies profile optima across a control parameter range
• Balances exploration and exploitation with a two-stage acquisition scheme
• Optimizes expensive black-box simulations with multiple nuisance parameters

Innovation

• Two-stage acquisition balances exploration and exploitation
• Deep and shallow Gaussian process surrogates quantify uncertainty
• Identifies profile optima across control parameter range