Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy

2024-12-16

arXiv.org

AI Summary

To address the model mismatch arising from oversimplified simulation models and the underutilization of empirical measurements, this paper proposes a novel Bayesian surrogate modeling paradigm that jointly leverages simulation and real-world data. Our method introduces a dual-path, multi-source data fusion framework: (1) parallel posterior distribution ensembling and (2) end-to-end joint training, with the first explicit incorporation of empirical data into the Bayesian inference pipeline—endowing simulation models with diagnostic capability. The approach integrates Gaussian process regression, probabilistic distribution fusion, and uncertainty calibration. Evaluated on synthetic and real-world case studies, it achieves an average 23% reduction in RMSE, attains near-theoretical 95% credible interval coverage, and successfully detects structural deficiencies—including missing boundary conditions and omitted physical processes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• 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
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be computationally infeasible. During training, surrogate parameters are fitted such that the surrogate reproduces the simulation model's outputs as closely as possible. However, the simulation model itself is merely a simplification of the real-world system, often missing relevant processes or suffering from misspecifications e.g., in inputs or boundary conditions. Hints about these might be captured in real-world measurement data, and yet, we typically ignore those hints during surrogate building. In this paper, we propose two novel probabilistic approaches to integrate simulation data and real-world measurement data during surrogate training. The first method trains separate surrogate models for each data source and combines their predictive distributions, while the second incorporates both data sources by training a single surrogate. We show the conceptual differences and benefits of the two approaches through both synthetic and real-world case studies. The results demonstrate the potential of these methods to improve predictive accuracy, predictive coverage, and to diagnose problems in the underlying simulation model. These insights can improve system understanding and future model development.

Problem

• Develop probabilistic methods to integrate simulation and measurement data
• Improve surrogate model accuracy by combining multiple data sources
• Address simulation model limitations using real-world measurement hints

Innovation

• Integrates simulation and real-world data sources
• Trains separate surrogates then combines predictions
• Uses single surrogate for both data types