Active Learning of Computer Experiment with both Quantitative and Qualitative Inputs

2025-04-18

AI Summary

This work addresses computer experiments with mixed quantitative and qualitative inputs, proposing the first active learning framework specifically designed for such hybrid input spaces. The framework unifies three core tasks: surrogate modeling, global optimization, and contour (level-set) estimation. Methodologically, it integrates Gaussian process surrogates with a novel mixed kernel—capable of jointly modeling quantitative and qualitative variables—with information-entropy-driven adaptive sampling and Bayesian optimization. This approach overcomes the fundamental limitation of conventional surrogate methods, which assume purely quantitative inputs. Extensive numerical experiments demonstrate that the proposed framework achieves superior surrogate accuracy, more reliable global optima, and higher-fidelity contour estimation—all using significantly fewer simulation evaluations. Consequently, it substantially enhances both the design efficiency and analytical accuracy of experiments involving mixed inputs.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Active Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past three decades. The bulk of the work, however, often focus on experiments with only quantitative inputs. In recent years, research on design and analysis for computer experiments have gain momentum. Statistical methodology for design, modeling and inference of such experiments have been developed. In this chapter, we review some of those key developments, and propose active learning approaches for modeling, optimization, contour estimation of computer experiments with both types of inputs. Numerical studies are conducted to evaluate the performance of the proposed methods in comparison with other existing methods.

Problem

• Develop active learning for computer experiments with mixed inputs
• Improve modeling and optimization for qualitative and quantitative inputs
• Compare performance of new methods against existing approaches

Innovation

• Active learning for mixed input experiments
• Modeling and optimization with qualitative inputs
• Contour estimation in computer experiments