Related papers: Reconstructing nonlinear networks subject to fast-…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with…
We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…
Loewner rational interpolation provides a versatile tool to learn low-dimensional dynamical-system models from frequency-response measurements. This work investigates the robustness of the Loewner approach to noise. The key finding is that…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…
It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…
This article investigates the use of a model-based neural-network for the traffic reconstruction problem using noisy measurements coming from probe vehicles. The traffic state is assumed to be the density only, modeled by a partial…
An artificial neural network architecture, parameterization networks, is proposed for simulating extrapolated dynamics beyond observed data in dynamical systems. Parameterization networks are used to ensure the long term integrity of…
Deep convolutional networks often append additive constant ("bias") terms to their convolution operations, enabling a richer repertoire of functional mappings. Biases are also used to facilitate training, by subtracting mean response over…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…