相关论文: KODA: A Data-Driven Recursive Model for Time Serie…

Time series forecasting plays a vital role across scientific, industrial, and environmental domains, especially when dealing with high-dimensional and nonlinear systems. While Transformer-based models have recently achieved state-of-the-art…

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…

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…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

In always-on HAR deployments, model accuracy erodes silently as domain shift accumulates over time. Addressing this challenge requires moving beyond one-off updates toward instance-driven adaptation from streaming data. However, continuous…

This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…

This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a non-abelian operator algebra, which provides a representation of…

In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…

We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…

A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly…

The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra 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…

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…

The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…