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Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…

Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…

Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…

Molecular dynamics (MD) simulations are a central tool in science and engineering enabling the study of dynamical behavior and the link between microscopic structure and macroscopic function. Their high computational cost, however, has…

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…

In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…

Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…

Spatiotemporal graph neural networks (STGNNs) have shown promising results in many domains, from forecasting to epidemiology. However, understanding the dynamics learned by these models and explaining their behaviour is significantly more…

This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an…

We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging.…

A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…

Continuous monitoring of the spatio-temporal dynamic behavior of critical infrastructure networks, such as the power systems, is a challenging but important task. In particular, accurate and timely prediction of the (electro-mechanical)…

Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…

Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable…

In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…

Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode…

Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets,…

Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack…

We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more…