Network Dynamics as an Inverse Problem

Casadiego, Jose; Timme, Marc

doi:10.1007/978-3-319-16619-3_4

Cited by 5 publications

(9 citation statements)

References 100 publications

(257 reference statements)

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“…Other properties such as edge weights, connectivity pattern or degree sequence are indistinguishable and cannot be reconstructed ( proposition 2b in electronic supplementary material 5). This is a consequence of the assumed prior knowledge of the coupling functions, because only the adjacency pattern is invariant to the transformations in G indistinguishability will appear if the temporal data are not informative enough in the sense that different interaction matrices produce the same node trajectories (figure 2b); see, for example, [37,38] and references therein. Equation (1.4) shows that indistinguishability due to uninformative data appears when v 1 À v 2 [ ker M i and ker M i contains a subspace different from 0.…”

Section: Introductionmentioning

confidence: 99%

“…This is a consequence of the assumed prior knowledge of the coupling functions, because only the adjacency pattern is invariant to the transformations in G Ã i , but other properties of A are not. Second, even if the coupling functions are exactly known, indistinguishability will appear if the temporal data are not informative enough in the sense that different interaction matrices produce the same node trajectories (figure 2b); see, for example, [37,38] and references therein. Equation (1.4) shows that indistinguishability due to uninformative data appears when v 1 À v 2 [ ker M i and ker M i contains a subspace different from 0.…”

Section: Introductionmentioning

confidence: 99%

“…they are structurally unidentifiable [37,39,40]) and hence they are indistinguishable for all temporal data. Indeed, despite the fact that the identifiability of the identity property has been studied in different disciplines including statistics and system identification [19,20,25,37,38], a similar analysis for all the other properties we can reconstruct using NR was lacking. The impact of uncertain coupling functions on the properties that can be reconstructed was unknown too.…”

Section: Introductionmentioning

confidence: 99%

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Fundamental limitations of network reconstruction from temporal data

Angulo

Moreno

Lippner

et al. 2017

J. R. Soc. Interface.

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Inferring properties of the interaction matrix that characterizes how nodes in a networked system directly interact with each other is a well-known network reconstruction problem. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations governing which properties of the interaction matrix (e.g. adjacency pattern, sign pattern or degree sequence) can be inferred from given temporal data of individual nodes remain unknown. Here, we rigorously derive the necessary conditions to reconstruct any property of the interaction matrix. Counterintuitively, we find that reconstructing any property of the interaction matrix is generically as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. Revealing these fundamental limitations sheds light on the design of better network reconstruction algorithms that offer practical improvements over existing methods.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fundamental limitations of network reconstruction from temporal data

Angulo

Moreno

Lippner

et al. 2017

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…Designing a network often means to engineer network static structures for particular function. And thanks to the intricate relation existing between the function and structure in networks, very disparate networks may yield identical dynamics [24]. This phenomenon has been reported in networks of spiking neurons [25][26][27] and gene regulatory networks [28,29].…”

Section: Introductionmentioning

confidence: 86%

“…As an example, we rewire networks of Kuramoto [86] and Kuramoto-like [87] oscillators with random network topologies into different networks that display the same collective dynamics. Parts of the results of this chapter were published in [24].…”

Section: Chapter Parametrization Of Network Dynamicsmentioning

confidence: 99%

Network Dynamics as an Inverse Problem

Luis¹

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Unravelling the backbone of climate networks from the analysis of collective dynamics and time reversal

Naghipour

Aalami

Nourani

2022

Intl Journal of Climatology

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Many complex systems are characterized by interconnected units often difficult, or even impossible, to map through direct observations, while the dynamics of units is mostly easier to measure. The reconstruction of an unknown structure from the observed dynamics is a typical inverse problem in network-based approaches to overcome such obstacles. However, this procedure is affected by the interplay between the structure and dynamics, as well as by the choice of the statistical method. In this study, collective behaviour of the Earth's climate system was investigated by focusing on three distinct climatological variables in monthly time step using a causality measure to separately construct climate networks through a robust statistical analysis. Multiplex network (MUX) was used to integrate the information obtained from collective dynamics and time reversal for better filtering spurious connectivity. In fact, the proposed approach mitigates undesired effects of pairwise statistical inference by adjusting for unphysical relationships in two layers of the constructed networks. The results indicate that the mere existence of statistical errors allowed by the hypothesis testing lead, inevitably, to reconstruct spurious connections in the null models even when the collective dynamics consists of white-noise datasets from uncoupled units. The impact of spurious connections with the MUX dynamics is not remarkable to reconstruct the underlying plausible interactions; therefore, the concepts of MUX might be employed with the statistical analysis to unravel the backbone of climate networks. In this way that the inferred connections could distinguish highly connected regions for better understanding interconnected dynamical patterns, yielding deep insights into underlying physical interactions between the oceans and atmosphere. More specifically, edge directionality features provide a complementary tool for analysing topology of the networks with respect to the climatological variables, identifying relevant patterns in the climate system.

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Network Dynamics as an Inverse Problem

Cited by 5 publications

References 100 publications

Fundamental limitations of network reconstruction from temporal data

Fundamental limitations of network reconstruction from temporal data

Network Dynamics as an Inverse Problem

Unravelling the backbone of climate networks from the analysis of collective dynamics and time reversal

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