Nonparametric Stochastic Subspaces via the Bootstrap for Characterizing Model Error

TL;DR

This paper introduces a bootstrap-based stochastic subspace method for better characterizing model error in computational mechanics, improving reliability without strong assumptions and with minimal hyperparameters.

Contribution

It presents a novel, assumption-free bootstrap approach for stochastic subspace modeling that enhances model error characterization in reduced-order models.

Findings

Outperforms existing methods in numerical examples

Enforces boundary conditions by construction

Requires only one hyperparameter

Abstract

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction error and strongly influence engineering decisions. Because distinguishing and representing each source separately is often infeasible, their combined effect is typically analyzed using a unified model-error framework. Model error directly affects model credibility and predictive reliability; yet its characterization remains challenging. To address this need, we introduce a bootstrap-based stochastic subspace model for characterizing model error in the stochastic reduced-order modeling framework. Given a snapshot matrix of state vectors, the method leverages the empirical data distribution to induce a sampling distribution over principal subspaces for reduced order modeling. The resulting stochastic model enables improved characterization of model error in computational mechanics compared with existing approaches. The method offers several advantages: (1) it is assumption-free and leverages the empirical data distribution; (2) it enforces linear constraints (such as boundary conditions) by construction; (3) it requires only one hyperparameter, significantly simplifying the training process; and (4) its algorithm is straightforward to implement. We evaluate the method's performance against existing approaches using numerical examples in computational mechanics and structural dynamics.