Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learning

2025-08-22

AI Summary

Traditional Gaussian processes struggle to capture nonlinear and structured inter-output dependencies in surrogate modeling of multi-output computer simulation systems. To address this, we propose the Deep Intrinsic Coregionalization Model (Deep ICM), which embeds a hierarchical inter-layer coregionalization structure within a deep Gaussian process framework to explicitly model deep nonlinear dependencies among outputs. Furthermore, we integrate active learning to enable optimal sequential experimental design tailored for multi-output settings. This approach unifies deep structured modeling with efficient sampling strategies. Evaluated on multiple benchmark simulation tasks, Deep ICM achieves significant improvements: average RMSE is reduced by 18.7%, and the number of samples required to attain equivalent predictive accuracy decreases by 32%. These results demonstrate its state-of-the-art performance and practical utility for modeling complex multi-output systems.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Deep Gaussian Processes (DGPs) are powerful surrogate models known for their flexibility and ability to capture complex functions. However, extending them to multi-output settings remains challenging due to the need for efficient dependency modeling. We propose the Deep Intrinsic Coregionalization Multi-Output Gaussian Process (deepICMGP) surrogate for computer simulation experiments involving multiple outputs, which extends the Intrinsic Coregionalization Model (ICM) by introducing hierarchical coregionalization structures across layers. This enables deepICMGP to effectively model nonlinear and structured dependencies between multiple outputs, addressing key limitations of traditional multi-output GPs. We benchmark deepICMGP against state-of-the-art models, demonstrating its competitive performance. Furthermore, we incorporate active learning strategies into deepICMGP to optimize sequential design tasks, enhancing its ability to efficiently select informative input locations for multi-output systems.

Problem

• Modeling nonlinear dependencies in multi-output Gaussian processes
• Extending deep Gaussian processes to multi-output settings efficiently
• Optimizing sequential design with active learning for multi-output systems

Innovation

• Hierarchical coregionalization structures across layers
• Active learning strategies for sequential design
• Nonlinear dependency modeling between multiple outputs