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Transformer architectures have been widely adopted for time series forecasting, yet whether the representational mechanisms that make them powerful in NLP actually engage on time series data remains unexplored. The persistent…
Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of…
In multivariate time series forecasting (MTSF), accurately modeling the intricate dependencies among multiple variables remains a significant challenge due to the inherent limitations of traditional approaches. Most existing models adopt…
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…
In this paper, we present SSDNet, a novel deep learning approach for time series forecasting. SSDNet combines the Transformer architecture with state space models to provide probabilistic and interpretable forecasts, including trend and…
While recent advancements in foundation models have significantly impacted machine learning, rigorous tests on the performance of time series foundation models (TSFMs) remain largely underexplored. This paper presents an empirical study…
Recent advances in machine learning, specifically transformer architecture, have led to significant advancements in commercial domains. These powerful models have demonstrated superior capability to learn complex relationships and often…
A Transformer-based Koopman autoencoder is proposed for linearizing Fisher's reaction-diffusion equation. The primary focus of this study is on using deep learning techniques to find complex spatiotemporal patterns in the reaction-diffusion…
The Transformer model has shown strong performance in multivariate time series forecasting by leveraging channel-wise self-attention. However, this approach lacks temporal constraints when computing temporal features and does not utilize…
Transformer-based methods have shown great potential in long-term time series forecasting. However, most of these methods adopt the standard point-wise self-attention mechanism, which not only becomes intractable for long-term forecasting…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
Long-term time series forecasting (LTSF) has been widely applied in finance, traffic prediction, and other domains. Recently, patch-based transformers have emerged as a promising approach, segmenting data into sub-level patches that serve…
Deep models have demonstrated remarkable performance in time series forecasting. However, due to the partially-observed nature of real-world applications, solely focusing on the target of interest, so-called endogenous variables, is usually…
Time series forecasting is widely used in the fields of equipment life cycle forecasting, weather forecasting, traffic flow forecasting, and other fields. Recently, some scholars have tried to apply Transformer to time series forecasting…
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…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an…
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…
Understanding the robustness of deep learning models for multivariate long-term time series forecasting (M-LTSF) remains challenging, as evaluations typically rely on real-world datasets with unknown noise properties. We propose a…
In recent times, Large Language Models (LLMs) have captured a global spotlight and revolutionized the field of Natural Language Processing. One of the factors attributed to the effectiveness of LLMs is the model architecture used for…