相关论文: Data-driven Spatio-temporal Prediction of High-dim…

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…

Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…

The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system identification and…

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal…

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features…

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…

We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state…

A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting…

A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This approach approximates the Koopman operator using a set of…

This research presents a novel, analytical, Koopman Operator based formulation for position and attitude dynamics which can be used to derive control strategies for underactuated systems. Compared to data driven Koopman based techniques,…

This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…

We present a data-driven method for spectral analysis of the Koopman operator based on direct construction of the pseudo-resolvent from time-series data. Finite-dimensional approximation of the Koopman operator, such as those obtained from…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…

We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically…

The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…

We present a novel machine learning approach to reduce the dimensionality of state variables in stratified turbulent flows governed by the Navier-Stokes equations in the Boussinesq approximation. The aim of the new method is to perform an…

Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…

This chapter provides an introduction to data-driven techniques for the development and calibration of closure models for the Reynolds-Averaged Navier--Stokes (RANS) equations. RANS models are the workhorse for engineering applications of…