MCMC with Adaptive Principal-Component Transformation: Rotation-Invariant Universal Samplers for Bayesian Structural System Identification

2026-04-25

AI Summary

This work addresses the inefficiency of traditional MCMC methods in Bayesian structural system identification and the limitations of existing data-driven approaches, which rely on task similarity and are constrained by neural architecture design. The authors propose the APM-SGHMC algorithm, which, within a unified framework, achieves efficient sampling with translation, scale, and rotation invariance for the first time. This is accomplished by dynamically constructing a rotation-invariant coordinate system via adaptive principal component analysis and integrating stochastic gradient Hamiltonian Monte Carlo with meta-learning strategies. The method enables zero-shot generalization across tasks, maintaining consistently superior performance on diverse system models without retraining. Its effectiveness and universality are validated through two structural identification case studies.

Technology Category

• Machine Learning: Structured Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To address the issue of excessively low sampling efficiency in generic MCMC methods when applied to specific problems, researchers developed several MCMC algorithms that integrate trainable neural networks to replace and enhance their critical components. Later, meta-learning MCMC methods emerged to reduce training time. However, they require considerable similarity between test and training tasks, while their sampling efficiency is constrained by trade-off-simplified network designs. This paper proposes the Adaptive Principal-Component (PC) Meta-learning Stochastic Gradient Hamiltonian Monte Carlo (APM-SGHMC) algorithm. It adaptively rotates coordinate axes in the parameter space to align with the PC directions of the current posterior samples, ensuring rotation-invariance of sampling performance with respect to the posterior distribution. By incorporating translation-invariance, scale-invariance, and rotation-invariance in a unified framework, APM-SGHMC enables universal samplers to acquire generalizable knowledge across diverse Bayesian system identification tasks using minimalistic tasks while eliminating the constraints imposed by network design trade-offs on sampling efficiency. Practical feasibility issues are also addressed. Two Bayesian system identification case studies demonstrate its effectiveness and universality: our method overcomes the case-by-case limitations of traditional data-driven approaches, achieving zero-shot generalization across structurally distinct models without retraining and maintaining consistent superior performance across all scenarios.

Problem

• Bayesian structural system identification
• Markov chain Monte Carlo
• sampling efficiency
• rotation-invariance
• zero-shot generalization

Innovation

• rotation-invariance
• adaptive principal-component transformation
• meta-learning MCMC
• universal sampler
• Bayesian structural system identification