Related papers: DeepKoopFormer: A Koopman Enhanced Transformer Bas…
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.…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
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…
Recently, there has been a surge of Transformer-based solutions for the long-term time series forecasting (LTSF) task. Despite the growing performance over the past few years, we question the validity of this line of research in this work.…
Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its…
Accurate and reliable energy forecasting is essential for power grid operators who strive to minimize extreme forecasting errors that pose significant operational challenges and incur high intra-day trading costs. Incorporating planning…
Rapid progress in machine learning and deep learning has enabled a wide range of applications in the electricity load forecasting of power systems, for instance, univariate and multivariate short-term load forecasting. Though the strong…
Long-term time series forecasting (LTSF) represents a critical frontier in time series analysis, characterized by extensive input sequences, as opposed to the shorter spans typical of traditional approaches. While longer sequences…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
One critical component in lossy deep image compression is the entropy model, which predicts the probability distribution of the quantized latent representation in the encoding and decoding modules. Previous works build entropy models upon…
The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of…
We present a novel data-driven approach for learning linear representations of a class of stable nonlinear systems using Koopman eigenfunctions. By learning the conjugacy map between a nonlinear system and its Jacobian linearization through…
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…
In recent years, numerous Transformer-based models have been applied to long-term time-series forecasting (LTSF) tasks. However, recent studies with linear models have questioned their effectiveness, demonstrating that simple linear layers…
The Koopman representation is an infinite dimensional linear representation of linear or nonlinear dynamical systems. It represents the dynamics of output maps (aka observables), which are functions on the state space whose evaluation is…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…
Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find…
Time series forecasting is prevalent in extensive real-world applications, such as financial analysis and energy planning. Previous studies primarily focus on time series modality, endeavoring to capture the intricate variations and…
The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…