Local transfer learning Gaussian process modeling, with applications to surrogate modeling of expensive computer simulators (2410.12690v2)

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.

• The paper introduces LOL-GP, a surrogate modeling framework that mitigates negative transfer via latent regularization.
• It applies Gaussian processes with a novel ReLU-based technique to selectively transfer knowledge in multi-source and multi-fidelity setups.
• Empirical results show significant improvements in RMSE and CRPS, demonstrating robustness in complex engineering simulations.

Local Transfer Learning Gaussian Process Modeling

The paper presents a novel approach to surrogate modeling for expensive computer simulations. The proposed LOcal transfer Learning Gaussian Process (LOL-GP) model addresses key challenges in utilizing transfer learning for surrogate modeling, specifically focusing on the issue of negative transfer. This problem occurs when transferring knowledge from related source systems results in diminished predictive performance for the target system. The LOL-GP model introduces a latent regularization approach to identify when and where transfer should occur, mitigating negative transfer by accommodating for local transfer properties.

Model and Methodology

The LOL-GP framework is introduced for both multi-source and multi-fidelity transfer learning contexts. In both scenarios, the model employs Gaussian Processes (GPs) with a novel regularization technique using ReLU activation. This approach selectively applies transfer based on a latent function, ensuring transfer occurs only in beneficial regions, thus reducing negative transfer and enhancing predictive accuracy.

For the multi-source setup, the LOL-GP models the target system as a weighted sum of source systems, with weights adaptable to input parameters via GP models. This local transfer characteristic allows the model to maintain flexibility without overfitting, addressing the bias-variance trade-off inherent in many transfer models. In the multi-fidelity context, similar principles apply, allowing the model to transfer knowledge from lower to higher fidelity simulators without introducing inaccuracies that are common in non-localized transfer models.

The computational efficiency of the LOL-GP is achieved through a Gibbs sampling algorithm for posterior sampling, facilitating rapid model training and prediction even with the complexity introduced by the latent functions. Moreover, the paper discusses strategies like nested experimental designs to further optimize computational demands, particularly beneficial in the multi-fidelity scenario.

Results and Analysis

The LOL-GP's effectiveness is validated through a series of numerical experiments, including one-dimensional and multi-dimensional cases. It consistently outperforms traditional models such as the Kennedy-O'Hagan (KO) model and its Bayesian extensions by reducing RMSE and CRPS metrics significantly. These results underscore its capability in effectively leveraging transferable knowledge while mitigating negative transfer.

A practical application in jet turbine design further demonstrates LOL-GP’s utility. The model adeptly handles the complexity of predicting stress profiles under varying conditions and materials by judiciously transferring insights from related systems. This capability is crucial for reducing computational costs in designing reliable engine components, showcasing the model's application in real-world engineering problems.

Implications and Future Directions

This research offers a robust framework for probabilistic surrogate modeling in scientific and engineering domains where data from related systems are available. The introduction of a model capable of discerning beneficial transfer opportunities presents substantial improvements in predictive capabilities while controlling for computational overhead.

Looking forward, the development of experimental design methods tailored to transfer learning scenarios could further capitalize on the model’s strengths. Further exploration in areas with complex outputs, like high-dimensional vector predictions or dynamic system models, could extend the applicability of the LOL-GP model. These advancements would bolster surrogate modeling in fields like high-energy physics or climate science, where simulation costs are prohibitive.

In conclusion, the LOL-GP presents an advanced methodology for surrogate modeling under constraints typical in computationally expensive simulations. By adeptly navigating the intricacies of transfer learning, it contributes to more reliable and efficient predictive modeling frameworks in scientific research and engineering applications.