Xinyue (Leslie) Xu

Reliable model selection is a cornerstone of developing physics-based models of engineering systems. However, existing model selection criteria has not been investigated across a variety of calibration scenarios, where selection choices can be affected by (i) parameter dimensionality, (ii) model form, (iii) prior informativeness, (iv) reparameterization, and (v) data characteristics. Moreover, it remains unclear whether these criteria can reliably distinguish model fidelity that genuinely improves explanatory power. These limitations restrict the broader applicability of model selection criteria in physics-based modeling, where balancing goodness-of-fit, complexity, and generalization is critical. To address these gaps, this study systematically evaluates information-theoretic and Bayesian model selection criteria through two case studies. The first case study employs polynomial regression models to isolate the effects of calibration factors and investigate their influence on the selection behavior of criteria. The second case study extends the analysis to a hierarchy of thermal models for double-pane windows, examining the ability of selection criteria to differentiate effective complexity from superficial increases in model fidelity. Results indicate that classical information-theoretic criteria are sensitive to parameter dimensionality, while covariance-based criteria reflect changes in model form and data characteristics, and Bayesian criteria exhibit sensitivity to all examined calibration factors. Furthermore, both covariance-based and Bayesian criteria effectively identify secondary physical mechanisms as sources of ineffective complexity, penalizing redundant fidelity. These findings underscore that model selection is not a one-size-fits-all task, and the choice of model selection criteria should be informed by the calibration scenario and the modeling objective.

Uncertainty quantification (UQ) is critical for modeling complex dynamic systems, ensuring robustness and interpretability. This study extends Physics-Guided Bayesian Neural Networks (PG-BNNs) to enhance model robustness by integrating physical laws into Bayesian frameworks. Unlike Artificial Neural Networks (ANNs), which provide deterministic predictions, and Bayesian Neural Networks (BNNs), which handle uncertainty probabilistically but struggle with generalization under sparse and noisy data, PG-BNNs incorporate the laws of physics, such as governing equations and boundary conditions, to enforce physical consistency. This physics-guided approach improves generalization across different noise levels while reducing data dependency. The effectiveness of PG-BNNs is validated through a one-degree-of-freedom vibration system with multiple noise levels, serving as a representative case study to compare the performance of Monte Carlo (MC) dropout ANNs, BNNs, and PG-BNNs across interpolation and extrapolation domains. Model accuracy is assessed using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAE), and Coefficient of Variation of Root Mean Square Error (CVRMSE), while UQ is evaluated through 95% Credible Intervals (CIs), Mean Prediction Interval Width (MPIW), the Quality of Confidence Intervals (QCI), and Coverage Width-based Criterion (CWC). Results demonstrate that PG-BNNs can achieve high accuracy and good adherence to physical laws simultaneously, compared to MC dropout ANNs and BNNs, which confirms the potential of PG-BNNs in engineering applications related to dynamic systems.

Uncertainty quantification (UQ) has received increasing attention for improving the reliability, transparency, and robustness of machine learning (ML)-based building energy modeling (BEM). As ML methods are widely integrated into BEM applications, there is a growing need for a structured and comprehensive understanding of UQ implementations in ML-based BEM. This paper addresses this gap by presenting a thorough review of literatures at the intersection of ML, BEM, and UQ, guided by a systematic literature search using a Keyword Synonym Search strategy. First, three primary sources of uncertainty are identified in ML-based BEM, which are building system operations, building simulation tools, and ML models. The contributing factors of these sources are further categorized into aleatoric and epistemic uncertainty. The review then examines ten state-of-the-art UQ techniques, respectively ensemble modeling, prior network, Bayesian neural networks, Markov Chain Monte Carlo, variational inference, dropout networks, Bayes by Backprop, Bayesian active learning, variational autoencoders, and Gaussian process. Each UQ technique is reviewed in terms of its modeling principles and applications within ML-based BEM. The discussion offers critical insights into the necessity, practical implementation, comparative performance, and research gaps of UQ in ML-based BEM. Five research challenges are discussed, such as the underrepresentation of aleatoric uncertainty in building datasets and limited adoptions of advanced UQ techniques within ML-based BEM. Finally, this review concludes with recommendations for future research to support the development of uncertainty-aware ML-based BEMs.