Related papers: Attractor Memory for Long-Term Time Series Forecas…

Deep learning has achieved strong performance in Time Series Forecasting (TSF). However, we identify a critical representation paradox, termed Latent Chaos: models with accurate predictions often learn latent representations that are…

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…

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…

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…

For Multivariate Time Series Forecasting (MTSF), recent deep learning applications show that univariate models frequently outperform multivariate ones. To address the difficiency in multivariate models, we introduce a method to Construct…

As a crucial component in intelligent transportation systems, traffic flow prediction has recently attracted widespread research interest in the field of artificial intelligence (AI) with the increasing availability of massive traffic…

Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…

Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…

We forecast two different chaotic dynamics of the quasiperiodically forced logistic map using the well-known deep learning framework Long Short-Term Memory. We generate two data sets and use one in the training process and the other in the…

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…

Time Series Foundation Models (TSFMs) have borrowed the long context paradigm from natural language processing under the premise that feeding more history into the model improves forecast quality. But in stochastic domains, distant history…

Forecasting Multivariate Time Series (MTS) involves significant challenges in various application domains. One immediate challenge is modeling temporal patterns with the finite length of the input. These temporal patterns usually involve…

Chaotic time series forecasting has been far less understood despite its tremendous potential in theory and real-world applications. Traditional statistical/ML methods are inefficient to capture chaos in nonlinear dynamical systems,…

Deep learning is playing an increasingly important role in time series analysis. We focused on time series forecasting using attention free mechanism, a more efficient framework, and proposed a new architecture for time series prediction…

A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…

Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which…

Transformer-based models have recently become dominant in Long-term Time Series Forecasting (LTSF), yet the variations in their architecture, such as encoder-only, encoder-decoder, and decoder-only designs, raise a crucial question: What…

Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…

Multivariate time series forecasting is widely used in various fields. Reasonable prediction results can assist people in planning and decision-making, generate benefits and avoid risks. Normally, there are two characteristics of time…