Tensor network dynamical message passing for epidemic models
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911427511451648 |
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| author | Ye, Cheng Shen, Zi-Song Zhang, Pan |
| author_facet | Ye, Cheng Shen, Zi-Song Zhang, Pan |
| contents | While epidemiological modeling is pivotal for informing public health strategies, a fundamental trade-off limits its predictive fidelity: exact stochastic simulations are often computationally intractable for large-scale systems, whereas efficient analytical approximations typically fail to account for essential short-range correlations and network loops. Here, we resolve this trade-off by introducing Tensor Network Dynamical Message Passing (TNDMP), a framework grounded in a rigorous property we term \textit{Susceptible-Induced Factorization}. This theoretical insight reveals that a susceptible node acts as a dynamical decoupler, factorizing the global evolution operator into localized components. Leveraging this, TNDMP provides a dual-mode algorithmic suite: an exact algorithm that computes local observables with minimal redundancy on tractable topologies and a scalable and tunable approximation for complex real-world networks. We demonstrate that widely adopted heuristics, such as Dynamical Message Passing (DMP) and Pair Approximation (PA), are mathematically recoverable as low-order limits of our framework. Numerical validation in synthetic and real-world networks confirms that TNDMP significantly outperforms existing methods to predict epidemic thresholds and steady states, offering a rigorous bridge between the efficiency of message passing and the accuracy of tensor network formalisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor network dynamical message passing for epidemic models Ye, Cheng Shen, Zi-Song Zhang, Pan Statistical Mechanics Physics and Society While epidemiological modeling is pivotal for informing public health strategies, a fundamental trade-off limits its predictive fidelity: exact stochastic simulations are often computationally intractable for large-scale systems, whereas efficient analytical approximations typically fail to account for essential short-range correlations and network loops. Here, we resolve this trade-off by introducing Tensor Network Dynamical Message Passing (TNDMP), a framework grounded in a rigorous property we term \textit{Susceptible-Induced Factorization}. This theoretical insight reveals that a susceptible node acts as a dynamical decoupler, factorizing the global evolution operator into localized components. Leveraging this, TNDMP provides a dual-mode algorithmic suite: an exact algorithm that computes local observables with minimal redundancy on tractable topologies and a scalable and tunable approximation for complex real-world networks. We demonstrate that widely adopted heuristics, such as Dynamical Message Passing (DMP) and Pair Approximation (PA), are mathematically recoverable as low-order limits of our framework. Numerical validation in synthetic and real-world networks confirms that TNDMP significantly outperforms existing methods to predict epidemic thresholds and steady states, offering a rigorous bridge between the efficiency of message passing and the accuracy of tensor network formalisms. |
| title | Tensor network dynamical message passing for epidemic models |
| topic | Statistical Mechanics Physics and Society |
| url | https://arxiv.org/abs/2602.06497 |