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The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the "robust identification error" framework in…

We address the problem of classifying trajectory data generated by some nonlinear dynamics, where each class corresponds to a distinct dynamical system. We propose Dynafit, a kernel-based method for learning a distance metric between…

We consider the problem of modeling, estimating, and controlling the latent state of a spatiotemporally evolving continuous function using very few sensor measurements and actuator locations. Our solution to the problem consists of two…

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power…

Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a…

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be…

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time domain input-output data. We first learn an approximate linear model of the nonlinear system using…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for…

Estimating the unknown causal dependencies among graph-connected time series plays an important role in many applications, such as sensor network analysis, signal processing over cyber-physical systems, and finance engineering. Inference of…

In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a…

Researchers are often interested in examining between-individual differences in within-individual processes. If the process under investigation is tracked for a long time, its trajectory may show a certain degree of nonlinearity, so that…

We propose a general framework for parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…

Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model.…