24,706 research outputs found
Inferring Network Topology from Complex Dynamics
Inferring network topology from dynamical observations is a fundamental
problem pervading research on complex systems. Here, we present a simple,
direct method to infer the structural connection topology of a network, given
an observation of one collective dynamical trajectory. The general theoretical
framework is applicable to arbitrary network dynamical systems described by
ordinary differential equations. No interference (external driving) is required
and the type of dynamics is not restricted in any way. In particular, the
observed dynamics may be arbitrarily complex; stationary, invariant or
transient; synchronous or asynchronous and chaotic or periodic. Presupposing a
knowledge of the functional form of the dynamical units and of the coupling
functions between them, we present an analytical solution to the inverse
problem of finding the network topology. Robust reconstruction is achieved in
any sufficiently long generic observation of the system. We extend our method
to simultaneously reconstruct both the entire network topology and all
parameters appearing linear in the system's equations of motion. Reconstruction
of network topology and system parameters is viable even in the presence of
substantial external noise.Comment: 11 pages, 4 figure
Global Dynamical Structure Reconstruction from Reconstructed Dynamical Structure Subnetworks: Applications to Biochemical Reaction Networks
In this paper we consider the problem of network reconstruction, with applications to biochemical reaction networks. In particular, we consider the problem of global network reconstruction when there are a limited number of sensors that can be used to simultaneously measure state information. We introduce dynamical structure functions as a way to formulate the network reconstruction problem and motivate their usage with an example physical system from synthetic biology. In particular, we argue that in synthetic biology research, network verification is paramount to robust circuit operation and thus, network reconstruction is an invaluable tool. Nonetheless, we argue that existing approaches for reconstruction are hampered by limited numbers of biological sensors with high temporal resolution. In this way, we motivate the global network reconstruction problem using partial network information and prove that by performing a series of reconstruction experiments, where each experiment reconstructs a subnetwork dynamical structure function, the global dynamical structure function can be recovered in most cases. We illustrate these reconstruction techniques on a recently developed four gene biocircuit, an event detector, and show that it is capable of differentiating the temporal order of input events
Reconstructing dynamical networks via feature ranking
Empirical data on real complex systems are becoming increasingly available.
Parallel to this is the need for new methods of reconstructing (inferring) the
topology of networks from time-resolved observations of their node-dynamics.
The methods based on physical insights often rely on strong assumptions about
the properties and dynamics of the scrutinized network. Here, we use the
insights from machine learning to design a new method of network reconstruction
that essentially makes no such assumptions. Specifically, we interpret the
available trajectories (data) as features, and use two independent feature
ranking approaches -- Random forest and RReliefF -- to rank the importance of
each node for predicting the value of each other node, which yields the
reconstructed adjacency matrix. We show that our method is fairly robust to
coupling strength, system size, trajectory length and noise. We also find that
the reconstruction quality strongly depends on the dynamical regime
Robust Network Reconstruction in Polynomial Time
This paper presents an efficient algorithm for robust network reconstruction
of Linear Time-Invariant (LTI) systems in the presence of noise, estimation
errors and unmodelled nonlinearities. The method here builds on previous work
on robust reconstruction to provide a practical implementation with polynomial
computational complexity. Following the same experimental protocol, the
algorithm obtains a set of structurally-related candidate solutions spanning
every level of sparsity. We prove the existence of a magnitude bound on the
noise, which if satisfied, guarantees that one of these structures is the
correct solution. A problem-specific model-selection procedure then selects a
single solution from this set and provides a measure of confidence in that
solution. Extensive simulations quantify the expected performance for different
levels of noise and show that significantly more noise can be tolerated in
comparison to the original method.Comment: 8 pages, to appear in 51st IEEE Conference on Decision and Contro
Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach
International audienceWe extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the unmeasured state, and (ii) the physical equations of a prototypical chaotic dynamical system. Non-noisy and noisy datasets are considered. First, it is shown that the PI-ESN can accurately reconstruct the unmeasured state. Second, the reconstruction is shown to be robust with respect to noisy data, which means that the PI-ESN acts as a denoiser. This paper opens up new possibilities for leveraging the synergy between physical knowledge and machine learning to enhance the reconstruction and prediction of unmeasured states in chaotic dynamical systems
Exact detection of direct links in networks of interacting dynamical units
Authors NR, EB-M, CG, and MSB acknowledge the Scottish Universities Physics Alliance (SUPA). EB-M and MSB also acknowledge the Engineering and Physical Science Research Council (EPSRC) project Ref. EP/I032 606/1. ACM and CM acknowledge the LINC project (FP7-PEOPLE-2011-ITN, grant no. 289447). ACM also aknowledges PEDECIBA and CSIC(Uruguay). CM also acknowledges grant FIS2012–37655-C02–01 from the Spanish MCI, grant 2009 SGR 1168, and the ICREA Academia programme from the Generalitat de Catalunya.Peer reviewedPublisher PD
- …