Fast Emulation and Modular Calibration for Simulators with Functional Response

2024-05-25

AI Summary

To address the scalability challenge in constructing surrogate models for functional-response computer models—such as those producing spatiotemporal or time-series outputs—this paper proposes a highly scalable hybrid framework. The method integrates global input-space adaptive length-scale scaling with local approximate Gaussian processes (Gramacy–Apley type), preserving the modeling fidelity of established functional-response approaches (e.g., Higdon and Kennedy–O’Hagan) while overcoming the cubic computational bottleneck of standard Gaussian processes. Designed for modular calibration, it is particularly suited to multi-physics fluid dynamics simulators like FLAG. Evaluated on a dataset of 20,000 FLAG simulations, the framework achieves order-of-magnitude speedup in prediction time without sacrificing accuracy. The implementation is publicly available as the R package FlaGP.

Technology Category

• Machine Learning: Scalability of ML Systems
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Scalable surrogate models enable efficient emulation of computer models (or simulators), particularly when dealing with large ensembles of runs. While Gaussian Process (GP) models are commonly employed for emulation, they face limitations in scaling to truly large datasets. Furthermore, when dealing with dense functional output, such as spatial or time-series data, additional complexities arise, requiring careful handling to ensure fast emulation. This work presents a highly scalable emulator for functional data, building upon the works of Kennedy and O'Hagan (2001) and Higdon et al. (2008), while incorporating the local approximate Gaussian Process framework proposed by Gramacy and Apley (2015). The emulator utilizes global GP lengthscale parameter estimates to scale the input space, leading to a substantial improvement in prediction speed. We demonstrate that our fast approximation-based emulator can serve as a viable alternative to the methods outlined in Higdon et al. (2008) for functional response, while drastically reducing computational costs. The proposed emulator is applied to quickly calibrate the multiphysics continuum hydrodynamics simulator FLAG with a large ensemble of 20000 runs. The methods presented are implemented in the R package FlaGP.

Problem

• Scalable surrogate models for efficient computer simulator emulation
• Handling dense functional output like spatial or time-series data
• Fast calibration of multiphysics simulators with large ensembles

Innovation

• Local Gaussian process regression for functional data
• Global GP lengthscale parameters to scale input space
• Fast approximation-based emulator reduces computational costs