Related papers: DeepKoopFormer: A Koopman Enhanced Transformer Bas…
The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism…
Time series data is a key element of big data analytics, commonly found in domains such as finance, healthcare, climate forecasting, and transportation. In large scale real world settings, such data is often high dimensional and…
Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Multivariate time series forecasting focuses on predicting future values based on historical context. State-of-the-art sequence-to-sequence models rely on neural attention between timesteps, which allows for temporal learning but fails to…
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…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
We present DLKoopman -- a software package for Koopman theory that uses deep learning to learn an encoding of a nonlinear dynamical system into a linear space, while simultaneously learning the linear dynamics. While several previous…
Multi-dimensional time series data, such as matrix and tensor-variate time series, are increasingly prevalent in fields such as economics, finance, and climate science. Traditional Transformer models, though adept with sequential data, do…
Long-term time-series forecasting (LTTF) has become a pressing demand in many applications, such as wind power supply planning. Transformer models have been adopted to deliver high prediction capacity because of the high computational…
Wind power forecasting (WPF), as a significant research topic within renewable energy, plays a crucial role in enhancing the security, stability, and economic operation of power grids. However, due to the high stochasticity of…
The emergence of deep learning has yielded noteworthy advancements in time series forecasting (TSF). Transformer architectures, in particular, have witnessed broad utilization and adoption in TSF tasks. Transformers have proven to be the…
We present a conformal prediction method for time series using the Transformer architecture to capture long-memory and long-range dependencies. Specifically, we use the Transformer decoder as a conditional quantile estimator to predict the…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
Transformer-based models, despite their promise for long-term time series forecasting (LTSF), suffer from an inherent low-pass filtering effect that limits their effectiveness. This issue arises due to undifferentiated propagation of…
This paper introduces WeatherFormer, a transformer encoder-based model designed to learn robust weather features from minimal observations. It addresses the challenge of modeling complex weather dynamics from small datasets, a bottleneck…
The Koopman autoencoder, a data-driven technique, has gained traction for modeling nonlinear dynamics using deep learning methods in recent years. Given the linear characteristics inherent to the Koopman operator, controlling its…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
Time series forecasting at scale presents significant challenges for modern prediction systems, particularly when dealing with large sets of synchronized series, such as in a global payment network. In such systems, three key challenges…
Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability…