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Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…
Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters.…
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
In model-based reinforcement learning, most algorithms rely on simulating trajectories from one-step models of the dynamics learned on data. A critical challenge of this approach is the compounding of one-step prediction errors as the…
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…
The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…
Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is even greater when the physics underlying such systems is…
We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms Logistic…
Time series prediction with neural networks has been the focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and…
The characterization of dynamical processes in living systems provides important clues for their mechanistic interpretation and link to biological functions. Thanks to recent advances in microscopy techniques, it is now possible to…
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…
Many practical systems can be described by dynamic networks, for which modern technique can measure their output signals, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden…
The Linear Parameter-Varying (LPV) framework provides a modeling and control design toolchain to address nonlinear (NL) system behavior via linear surrogate models. Despite major research effort on LPV data-driven modeling, a key…
We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the…