相关论文: Data-driven learning for the Mori-Zwanzig formalis…

System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor…

Coarse-grained (CG) models are simplified representations of soft matter systems that are commonly employed to overcome size and time limitations in computational studies. Many approaches have been developed to construct and parametrise…

In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized empirical loss minimization in the infinite-dimensional space of…

This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity…

Model reduction techniques have emerged as a powerful paradigm across different fronts of scientific computing. Despite their success, the provided tools and methodologies remain limited if high-dimensional dynamical systems subject to…

Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…

The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

A data-driven, model-free approach to modeling the temporal evolution of physical systems mitigates the need for explicit knowledge of the governing equations. Even when physical priors such as partial differential equations are available,…

The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…

Forecasting physical systems over long horizons from irregularly sampled observations demands models that are stable, computationally efficient, and free of fixed-timestep assumptions. We address this with a continuous-time Koopman…

One of the central challenge for extracting governing principles of dynamical system via Dynamic Mode Decomposition (DMD) is about the limit data availability or formally called as Limited Data Acquisition in the present paper. In the…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

A careful derivation of the generalized Langevin equation using "Zwanzig flavor" projection operator formalism is presented. We provide arguments why this formalism has better properties compared to alternative projection-operator…

Fuzzy modeling has many advantages over the non-fuzzy methods, such as robustness against uncertainties and less sensitivity to the varying dynamics of nonlinear systems. Data-driven fuzzy modeling needs to extract fuzzy rules from the…

Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…

The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled…

Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…

Data-driven safety verification of robotic systems often relies on zonotopic reachability analysis due to its scalability and computational efficiency. However, for nonlinear systems, these methods can become overly conservative, especially…

This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…