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Twinning Complex Networked Systems: Data-Driven Calibration of the mABCD Synthetic Graph Generator

Piotr Bródka, Michał Czuba, Bogumił Kamiński, Łukasz Kraiński, Katarzyna Musial, Paweł Prałat, Mateusz Stolarski

TL;DR

This work tackles the inverse-generator problem for multilayer networks by calibrating the mABCD synthetic graph generator to real data to produce digital twins. It proposes a modular parameter-retrieval framework that estimates groups of mABCD parameters from an observed network by minimizing a set of divergence scores, with Bayesian optimization handling latent components. The experiments reveal strong interdependencies among configuration parameters, indicating that joint-prediction approaches may outperform independent estimation. The study demonstrates feasibility for data-driven digital twins in complex networked systems and provides a public Python implementation to support future research.

Abstract

The increasing availability of relational data has contributed to a growing reliance on network-based representations of complex systems. Over time, these models have evolved to capture more nuanced properties, such as the heterogeneity of relationships, leading to the concept of multilayer networks. However, the analysis and evaluation of methods for these structures is often hindered by the limited availability of large-scale empirical data. As a result, graph generators are commonly used as a workaround, albeit at the cost of introducing systematic biases. In this paper, we address the inverse-generator problem by inferring the configuration parameters of a multilayer network generator, mABCD, from a real-world system. Our goal is to identify parameter settings that enable the generator to produce synthetic networks that act as digital twins of the original structure. We propose a method for estimating matching configurations and for quantifying the associated error. Our results demonstrate that this task is non-trivial, as strong interdependencies between configuration parameters weaken independent estimation and instead favour a joint-prediction approach.

Twinning Complex Networked Systems: Data-Driven Calibration of the mABCD Synthetic Graph Generator

TL;DR

This work tackles the inverse-generator problem for multilayer networks by calibrating the mABCD synthetic graph generator to real data to produce digital twins. It proposes a modular parameter-retrieval framework that estimates groups of mABCD parameters from an observed network by minimizing a set of divergence scores, with Bayesian optimization handling latent components. The experiments reveal strong interdependencies among configuration parameters, indicating that joint-prediction approaches may outperform independent estimation. The study demonstrates feasibility for data-driven digital twins in complex networked systems and provides a public Python implementation to support future research.

Abstract

The increasing availability of relational data has contributed to a growing reliance on network-based representations of complex systems. Over time, these models have evolved to capture more nuanced properties, such as the heterogeneity of relationships, leading to the concept of multilayer networks. However, the analysis and evaluation of methods for these structures is often hindered by the limited availability of large-scale empirical data. As a result, graph generators are commonly used as a workaround, albeit at the cost of introducing systematic biases. In this paper, we address the inverse-generator problem by inferring the configuration parameters of a multilayer network generator, mABCD, from a real-world system. Our goal is to identify parameter settings that enable the generator to produce synthetic networks that act as digital twins of the original structure. We propose a method for estimating matching configurations and for quantifying the associated error. Our results demonstrate that this task is non-trivial, as strong interdependencies between configuration parameters weaken independent estimation and instead favour a joint-prediction approach.
Paper Structure (21 sections, 6 equations, 5 figures, 1 table)

This paper contains 21 sections, 6 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Multilayer networks
  4. Complex Networked System Analysis with Twinning Approach
  5. The Synthetic Network Generators --- mABCD
  6. Proposed mABCD Configuration Retrieval Method
  7. Dimension of reference layer ($d$).
  8. Inter-layer edge correlation ($\mathbf{R}$).
  9. Correlation coefficient between degrees and labels ($\tau_i$).
  10. Correlation strength between communities and the reference layer ($r_i$).
  11. Degree distributions ($\gamma_i, \delta_i, \Delta_i$).
  12. Distributions of community sizes ($\beta_i, s_i, S_i$).
  13. Level of noise ($\xi_i$).
  14. Cumulative Divergence Score.
  15. Experiments
  16. ...and 6 more sections

Figures (5)

  • Figure 1: Spread control pipeline utilising the configuration retrieval approach to create adjusted twins of the evaluated system. The process begins by determining the parameters of mABCD that match the analysed system. Its digital twin is then generated and evaluated under the appropriate dynamics. Note that the pipeline's efficacy depends on addressing inherent errors.
  • Figure 2: A typical optimisation trajectory projected on $\mathfrak{R}^2$ space of $r$ obtained during the experimental part. Note the trade-off between exploration and exploitation that the employed method preserves, by which it avoids getting stuck in local minima.
  • Figure 3: Divergence scores (log scale) for configuration retrieval with fixed $d = 2^k$ dimension, $k\in \{0, 1, 2, 3\}$; estimation with tuned $r$ and loss $\mathcal{D}_{r} ( \hat{G}, G )$.
  • Figure 4: Divergence scores for four configuration estimation methods; fixed $d=2$.
  • Figure 5: $\mathcal{D}_{\tau} ( \hat{G}, G )$, $\mathcal{D}_{r} ( \hat{G}, G )$, and $(\mathcal{D}_{r} ( \hat{G}, G )+\mathcal{D}_{\tau} ( \hat{G}, G )) /2$ scores as functions of the optimisation step in finding the best matching $r$ or $\tau$.

Theorems & Definitions (1)

  • definition 1: Multilayer network