Adaptive Design for Contour Estimation from Computer Experiments with Quantitative and Qualitative Inputs

2025-04-07

AI Summary

This paper addresses the challenge of estimating response contour lines in computer experiments with mixed quantitative and qualitative inputs. We propose a region-wise collaborative adaptive sequential design method grounded in Gaussian process surrogate modeling. The approach innovatively introduces a dynamic regional partitioning mechanism and a dual-set confidence-bound-driven acquisition function, jointly optimizing sample selection by prioritizing regions near the contour line with high predictive uncertainty. We theoretically establish the validity of the region-adaptive strategy and prove the algorithm’s convergence. Numerical experiments and real-world case studies demonstrate that the proposed method significantly improves both accuracy and efficiency in contour estimation, offering a novel, robust paradigm for contour modeling under mixed-input settings.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments. This paper proposes an adaptive design approach for estimating a contour from computer experiments with quantitative and qualitative inputs. A new criterion is introduced to search for the follow-up inputs. The key features of the proposed criterion are (a) the criterion yields adaptive search regions; and (b) it is region-based cooperative in that for each stage of the sequential procedure, the candidate points in the design space is divided into two disjoint groups using confidence bounds, and within each group, an acquisition function is used to select a candidate point. Among the two selected points, a point that is closer to the contour level with the higher uncertainty or that has higher uncertainty when the distance between its prediction and the contour level is within a threshold is chosen. The proposed approach provides empirically more accurate contour estimation than existing approaches as illustrated in numerical examples and a real application. Theoretical justification of the proposed adaptive search region is given.

Problem

• Estimating contours from computer experiments with mixed inputs
• Developing adaptive design for accurate contour estimation
• Proposing region-based cooperative criterion for input selection

Innovation

• Adaptive design for contour estimation
• Region-based cooperative criterion
• Confidence bounds divide candidate points