Physics-informed band structure-integrated continuous-time inhomogeneous Markov chains for stochastic occupancy modeling

Abstract

Understanding and predicting occupancy patterns are crucial for enhancing the efficiency of building energy systems and supporting occupant-centric building design. Traditional discrete-time inhomogeneous Markov chain (DTIMC) models have been widely used for stochastic occupancy modeling; however, the assumption that state transition probabilities can change arbitrarily results in high model complexity and a potential of over-fitting. This study introduces a novel band structure-integrated continuous-time inhomogeneous Markov chain (CTIMC) modeling method based on the physical process of occupancy movement. The proposed method impose physical constrains on state transitions to confined neighboring states within infinitesimal time intervals, significantly reducing the quadratic model complexity to linear and improving interpretability and generalization ability. An extended band structure is further developed to account for the condition with rapid and drastic occupancy variation. The models are validated using a nine-month, high-resolution occupancy data exhibiting drastic occupancy variation pattern, which are divided into training and testing set. Results on the testing set show that the proposed band-structure-integrated CTIMC method outperforms the traditional DTIMC method in terms of daily log-likelihood. Notably, under high-complexity conditions, when the number of scaling coefficients exceeds 7, the DTIMC model exhibits severe overfitting, yielding log-likelihood values between –568 and –426. In contrast, the CTIMC model maintains robust under the same conditions, achieving substantially higher log-likelihoods in the range of –124 to –107. These findings highlight the potential of physical informed CTIMC models for robust stochastic occupancy modeling.