Coordinated discovery of mechanistic dynamics in complex networks
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PUBLIC SUMMARY
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CGS discovers symbolic laws for network dynamics from sparse noisy data.
Neural ODE proxies denoise trajectories and separate node and edge effects.
Coordinated search reduces compensatory overfitting between dynamic components.
CGS shows strong synthetic recovery and provides an influenza case study.
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ABSTRACT
Symbolic regression offers a route to mechanistic understanding of complex network dynamics, but existing methods often infer node and edge equations independently, allowing errors in one component to be compensated by the other. We present Coordinated Genetic Search (CGS), a framework for discovering governing equations from sparse and noisy network observations. CGS first trains a graph neural ordinary differential equation proxy with network inductive bias to disentangle node and edge effects and reconstruct denoised trajectories. It then co-evolves symbolic populations for node and edge dynamics, adaptively prioritizing the component that deviates most from its neural reference. This coordination is designed to reduce compensatory overfitting and improve identifiability. Across synthetic epidemic, ecological, neural, and oscillator systems on multiple graph topologies, CGS provides strong evidence of improved symbolic recovery and trajectory prediction relative to the tested baselines. On a real influenza A spreading network, where no ground-truth governing equation is available, CGS provides a proof-of-concept case study with physically plausible expressions and a modest reduction in normalized prediction error. -
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REFERENCES
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Qiu H., Liu S., Wu Y., et al. (2026). Coordinated discovery of mechanistic dynamics in complex networks. AI Plus 1:100006. https://doi.org/10.59717/ipj.aiplus.2026.100006
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Qiu H., Liu S., Wu Y., et al. (2026). Coordinated discovery of mechanistic dynamics in complex networks. AI Plus 1:100006. https://doi.org/10.59717/ipj.aiplus.2026.100006
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Figure 1.
Overview of Coordinated Genetic Search (CGS). A neural proxy model provides references (
$ \hat{F}, \hat{G} $ $ \hat{X} $ $ F^*, G^* $ -
Figure 2.
(a) Algorithm for Coordinated Genetic Search for symbolic regression. (b) Comparison with different methods for symbolic regression. (GN: graph network, NAS: neural architecture search, GS: genetic search)
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Figure 3.
(a) Performance comparison on synthetic datasets. MSE values are scaled by
$ 10^{-2} $ $ 10^{-2} $ -
Figure 4.
(a) Visualizing the predicted number of newly reported cases in two regions after transforming simulated normalized trajectories back to the raw case-count scale. (b) The symbolic expressions regressed by CGS, TP-SINDy, and SymDL on the influenza A dataset following the setup of 12. The expressions are defined on population-normalized case states, and edge summations use the normalized weighted aviation adjacency
$ \hat{A}_{ij} $ -
Figure 5.
Evaluation of robustness and the effect of denoised/interpolated trajectories. Shaded areas correspond to 95% confidence interval. (a) and (b) show the recovery probability and MSE when adding noise to observations. (c) and (d) show the recovery probability and MSE when increasing the time interval between observations. (e) Results for removing interpolated and denoised trajectories on SIS and LV dynamics in the BA graph. (f) Ablation variants compared with the full method on KUR dynamics in the BA graph.