Actively Learning Joint Contours of Multiple Computer Experiments

2025-12-15

AI Summary

This work addresses the isosurface localization problem for jointly modeling multiple independent computer experiments, aiming to efficiently identify common input configurations where multiple responses (e.g., three-axis rotational torques of an aircraft) simultaneously attain prescribed target values (e.g., zero). To this end, we propose the joint Contour Localization (jCL) framework—the first method explicitly designed for multi-response isosurface intersection identification. jCL dynamically balances exploration of individual response surfaces with exploitation of their intersecting contour lines, thereby extending beyond conventional single-response active learning paradigms. The approach integrates shallow and deep Gaussian process surrogate models and constructs an adaptive sampling strategy grounded in posterior predictive distributions, supporting diverse probabilistic surrogate architectures. Evaluated on a multi-torque zero-point localization task for aircraft dynamics, jCL substantially reduces the number of function evaluations while improving both accuracy and efficiency in locating the joint isosurface.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Contour location$unicode{x2014}$the process of sequentially training a surrogate model to identify the design inputs that result in a pre-specified response value from a single computer experiment$unicode{x2014}$is a well-studied active learning problem. Here, we tackle a related but distinct problem: identifying the input configuration that returns pre-specified values of multiple independent computer experiments simultaneously. Motivated by computer experiments of the rotational torques acting upon a vehicle in flight, we aim to identify stable flight conditions which result in zero torque forces. We propose a "joint contour location" (jCL) scheme that strikes a strategic balance between exploring the multiple response surfaces while exploiting learning of the intersecting contours. We employ both shallow and deep Gaussian process surrogates, but our jCL procedure is applicable to any surrogate that can provide posterior predictive distributions. Our jCL designs significantly outperform existing (single response) CL strategies, enabling us to efficiently locate the joint contour of our motivating computer experiments.

Problem

• Identifying joint contours of multiple computer experiments simultaneously
• Locating stable flight conditions with zero torque forces
• Developing a joint contour location scheme for efficient surrogate modeling

Innovation

• Joint contour location for multiple computer experiments
• Balancing exploration of multiple response surfaces
• Using Gaussian process surrogates for posterior predictions