Related papers: DeepKoopFormer: A Koopman Enhanced Transformer Bas…
Time series forecasting plays a critical role in domains such as energy, finance, and healthcare, where accurate predictions inform decision-making under uncertainty. Although Transformer-based models have demonstrated success in sequential…
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…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…
Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications. Despite the generality and importance of the problem, general mathematical techniques that allow for stable long-term forecasts…
We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…
The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…
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…
Although Transformer-based methods have significantly improved state-of-the-art results for long-term series forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series…
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…
With the development of Internet of Things (IoT) systems, precise long-term forecasting method is requisite for decision makers to evaluate current statuses and formulate future policies. Currently, Transformer and MLP are two paradigms for…
Time series forecasting is a crucial challenge with significant applications in areas such as weather prediction, stock market analysis, and scientific simulations. This paper introduces an embedded decomposed transformer, 'EDformer', for…
Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…
Transformers are widely used in natural language processing due to their ability to model longer-term dependencies in text. Although these models achieve state-of-the-art performance for many language related tasks, their applicability…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…