True Nonlinear Dynamics from Incomplete Networks
Authors: Chunheng Jiang, Jianxi Gao, Malik Magdon-Ismail131-138
AAAI 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We study nonlinear dynamics on complex networks. Each vertex i has a state xi which evolves according to a networked dynamics to a steady-state x i . We develop fundamental tools to learn the true steady-state of a small part of the network, without knowing the full network. A naive approach and the current state-of-the-art is to follow the dynamics of the observed partial network to local equilibrium. This dramatically fails to extract the true steady state. We use a mean-field approach to map the dynamics of the unseen part of the network to a single node, which allows us to recover accurate estimates of steady-state on as few as 5 observed vertices in domains ranging from ecology to social networks to gene regulation. Incomplete networks are the norm in practice, and we offer new ways to think about nonlinear dynamics when only sparse information is available. ... We demonstrate the power of our approach in Figure 1, for an ecological network... The results in Figure 1 are as expected. ... We tested our approach on the three popular dynamical systems in Table 1 and two corresponding networks for each dynamical system (see Table 2). ... The results in Figure 4 show that our approach (red) is remarkable at revealing the true steady-state, even from tiny subgraphs. |
| Researcher Affiliation | Academia | Chunheng Jiang, Jianxi Gao, Malik Magdon-Ismail Rensselaer Polytechnic Institute 110 8th Street, Troy, NY 12180 {jiangc4, gaoj8}@rpi.edu, magdon@cs.rpi.edu |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found. |
| Open Source Code | No | No explicit statement about releasing code or a link to a code repository was found. |
| Open Datasets | Yes | We tested our approach on the three popular dynamical systems in Table 1 and two corresponding networks for each dynamical system (see Table 2). Table 2: List of networks in our evaluation. Examples: Ecological ENet1(270,8074) (Arroyo, Armesto, and Primack 1985; Gao, Barzel, and Barab asi 2016) ENet2(97,972) (Clements and Long 1923; Gao, Barzel, and Barab asi 2016). Epidemic Dublin(410,2765) (Rossi and Ahmed 2015) Email(1133,5451) (Guimera et al. 2003; Kunegis 2013). |
| Dataset Splits | No | The paper does not describe explicit train/validation/test dataset splits. It focuses on predicting steady states on sampled subgraphs and comparing them to true steady states, rather than a traditional model training/validation setup. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory specifications) used for running experiments were mentioned. |
| Software Dependencies | No | No specific software names with version numbers were provided. |
| Experiment Setup | Yes | Each dynamical system contains several parameters which are set as in (Gao, Barzel, and Barab asi 2016) for ecology and gene regulation, and as in (Barzel and Barab asi 2013) for epidemics. |