Related papers: Toward Physics-guided Time Series Embedding
Time series forecasting plays a crucial role in many real-world applications, and numerous complex forecasting models have been proposed in recent years. Despite their architectural innovations, most state-of-the-art models report only…
We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…
We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
We address a three-tier numerical framework based on manifold learning for the forecasting of high-dimensional time series. At the first step, we embed the time series into a reduced low-dimensional space using a nonlinear manifold learning…
Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. Due to their multidimensional nature, time series often need to be embedded into a fixed-dimensional feature space to…
This work studies the problem of time series analysis with generalist (or foundation) models, which are models trained across many data domains. Drawing inspiration from the widespread success of large language models, we consider the…
In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…
Time series modeling has attracted extensive research efforts; however, achieving both reliable efficiency and interpretability from a unified model still remains a challenging problem. Among the literature, shapelets offer interpretable…
Likelihood-free inference is quickly emerging as a powerful tool to perform fast/effective parameter estimation. We demonstrate a technique of optimizing likelihood-free inference to make it even faster by marginalizing symmetries in a…
Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many…
Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…
A robust model for time series forecasting is highly important in many domains, including but not limited to financial forecast, air temperature and electricity consumption. To improve forecasting performance, traditional approaches usually…
Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…
Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…
A hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks (ANN), is proposed to model time series generated by complex dynamic systems. We introduce well known features used in the study of dynamic…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such…