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System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…
Critical transitions are the abrupt shifts between qualitatively different states of a system, and they are crucial to understanding tipping points in complex dynamical systems across ecology, climate science, and biology. Detecting these…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how…
The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…
Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…