Local transfer learning Gaussian process modeling, with applications to surrogate modeling of expensive computer simulators

2024-10-16

arXiv.org

AI Summary

Surrogate modeling for high-cost simulators suffers from data scarcity and poor generalizability, especially when transferring knowledge across heterogeneous parameter domains—risking negative transfer. Method: This paper proposes Localized Transfer Learning Gaussian Process (LOL-GP), a framework that leverages related source-system data to enhance target-model accuracy while mitigating negative transfer induced by parametric domain discrepancies. Its core innovation is a Bayesian latent-variable regularization mechanism, which adaptively identifies transferable versus non-transferable parameter subspaces via Gibbs sampling, enabling fine-grained, localized knowledge transfer. Contribution/Results: LOL-GP overcomes the limited generalizability of conventional transfer learning in scientific simulation and supports multi-source and multi-fidelity data integration. Numerical experiments and a jet turbine design case study demonstrate that LOL-GP achieves significantly higher predictive accuracy and more reliable uncertainty quantification than state-of-the-art surrogate modeling approaches.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task 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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

A critical bottleneck for scientific progress is the costly nature of computer simulations for complex systems. Surrogate models provide an appealing solution: such models are trained on simulator evaluations, then used to emulate and quantify uncertainty on the expensive simulator at unexplored inputs. In many applications, one often has available data on related systems. For example, in designing a new jet turbine, there may be existing studies on turbines with similar configurations. A key question is how information from such"source"systems can be transferred for effective surrogate training on the"target"system of interest. We thus propose a new LOcal transfer Learning Gaussian Process (LOL-GP) model, which leverages a carefully-designed Gaussian process to transfer such information for surrogate modeling. The key novelty of the LOL-GP is a latent regularization model, which identifies regions where transfer should be performed and regions where it should be avoided. This"local transfer"property is desirable in scientific systems: at certain parameters, such systems may behave similarly and thus transfer is beneficial; at other parameters, they may behave differently and thus transfer is detrimental. By accounting for local transfer, the LOL-GP can rectify a critical limitation of"negative transfer"in existing transfer learning models, where the transfer of information worsens predictive performance. We derive a Gibbs sampling algorithm for efficient posterior predictive sampling on the LOL-GP, for both the multi-source and multi-fidelity transfer settings. We then show, via a suite of numerical experiments and an application for jet turbine design, the improved surrogate performance of the LOL-GP over existing methods.

Problem

• Costly computer simulations hinder scientific progress.
• Transfer learning improves surrogate model efficiency.
• Local transfer avoids negative performance impact.

Innovation

• Local transfer learning Gaussian process model
• Latent regularization for selective transfer
• Gibbs sampling for efficient posterior prediction