An entropy-guided approximation framework for accelerating probability updates within Bayesian networks

Bayesian networks (BNs) have emerged as a fundamental mathematical tool for developing system digital twins (SDTs).Despite substantial advancements, the scalability of SDTs remains constrained by the increasing storage and computational demands associated with large BNs.To address this limitation, this paper proposes an entropy-based formulation to improve the computational efficiency of BNs while maintaining predictive accuracy.The validity of entropy in capturing node uncertainty is first demonstrated through two representative BN structures: (1) in the chain structure, entropy change decreases with distance from observations; and (2) in the common effect structure, entropy change increases as additional observations become available.Then, analytic expressions are derived from a twonode BN structure.It shows that key statistical parameters, including entropy, mean, and variance, can effectively model uncertainty propagation between connected nodes within BNs, achieving an average RMSE of 0.027 across 100 random BNs.The formulation is further generalized to the common effect structure, yielding an average RMSE of 0.082 for entropy prediction.By reducing BN storage requirements under varying network complexities, the proposed formulation offers a promising pathway for enabling scalable and efficient SDTs for complex infrastructure systems. INTRODUCTIONWith rapid advancements in artificial intelligence (AI), Internet of Things (IoT), and computational power, digital twin (DT) has emerged as a promising and transformative tool for effective management of infrastructure systems.By definition, DTs are virtual representations of physical assets or systems, wherein digital entities are dynamically and continuously synchronized with their physical counterparts through bidirectional information exchange [1].Specifically, the digital replicas are updated through integrating muti-source data from the real world to mirror the real-time condition and state of the physical assets.The updated virtual representations can provide insights into informed decision-making for the operation, management, and maintenance of physical systems.This closed-loop feedback between the physical and virtual spaces holds the potential to enhance the performance of infrastructure Ziheng Geng and Minghui Cheng 2 systems and significantly reduce their life-cycle costs.Recently, the concept of system digital twin (SDT) was proposed by Cheng et al. [2][3][4] to develop DTs from the perspective of complex systems.The SDT framework involves three phases: (a) construction of a knowledge graph (KG) to capture the statistical correlations and interdependencies across various levels of the complex system; (b) transformation of the KG into a Bayesian network (BN) by fitting conditional probability tables (CPTs) to quantify probabilistic dependencies; and (c) conversion of the BN into an SDT by specifying data and performance nodes to enable automated Bayesian inference.The SDT framework is demonstrated via a case study for monitoring the risk of bridge network in Miami-Dade County.This county-scale SDT interlinks three systems (bridge, traffic, and river) for probabilistic modeling and risk updating.However, the SDT faces significant computational challenges: the SDT comprises 6,478 nodes and 10,584 edges, requiring over 256 GB of memory to store its CPTs even with a coarse discretization.Such demands severely limit the scalability and practical applications of SDTs in large-scale infrastructure systems.To address this challenge, this paper proposes a novel entropy-based formulation as an efficient surrogate for BNs.The formulation is designed to quantify uncertainty propagation within BNs in a computationally tractable manner while preserving predictive accuracy.The rationale for using entropy as an indicator of uncertainty propagation is first demonstrated through two representative BN topologies: the chain structure and the common effect structure.Subsequently, analytic expressions are derived from a simple two-node BN to capture the relationship between the entropies of connected nodes, thereby replacing the computationally intensive probabilistic updates via CPTs.Finally, the proposed formation is extended to a complex BN topology, demonstrating strong generalization capability and robust performance in modeling uncertainty propagation within BN.