Related papers: Prediction in Projection: A new paradigm in delay-…
Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…
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…
Delay-coordinate reconstruction is a proven modeling strategy for building effective forecasts of nonlinear time series. The first step in this process is the estimation of good values for two parameters, the time delay and the embedding…
Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay…
Delay coordinates are a widely used technique to pass from observations of a dynamical system to a representation of the dynamical system as an embedding in Euclidean space. Current proofs show that delay coordinates of a given dynamical…
Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens'…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
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…
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…
Deep learning models have grown increasingly popular in time series applications. However, the large quantity of newly proposed architectures, together with often contradictory empirical results, makes it difficult to assess which…
Due to simplicity and strong stability guarantees, predictor feedback methods have stood as a popular approach for time delay systems since the 1950s. For time-varying delays, however, implementation requires computing a prediction horizon…
Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…
With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…
In the nonlinear prediction of scalar time series, the common practice is to reconstruct the state space using time-delay embedding and apply a local model on neighborhoods of the reconstructed space. The method of false nearest neighbors…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…
To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that…
A new nudging method for data assimilation, delay-coordinate nudging, is presented. Delay-coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each…
Nowadays, time series forecasting is predominantly approached through the end-to-end training of deep learning architectures using error-based objectives. While this is effective at minimizing average loss, it encourages the encoder to…
Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode…