Related papers: Dynamical Systems as Temporal Feature Spaces

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency…

Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern in the real-world applications. For more accurate prediction, the methods had better grasp more data characteristics. Different from ordinary time series, ISTS is…

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Event cameras unlock new frontiers that were previously unthinkable with standard frame-based cameras. One notable example is low-latency motion estimation (optical flow), which is critical for many real-time applications. In such…

Machine learning techniques offer an effective approach to modeling dynamical systems solely from observed data. However, without explicit structural priors -- built-in assumptions about the underlying dynamics -- these techniques typically…

The echo state network (ESN) is a special type of recurrent neural networks for processing the time-series dataset. However, limited by the strong correlation among sequential samples of the agent, ESN-based policy control algorithms are…

Structured state space sequence (S4) models have recently achieved state-of-the-art performance on long-range sequence modeling tasks. These models also have fast inference speeds and parallelisable training, making them potentially useful…

Machine learning has become a widely popular and successful paradigm, including in data-driven science and engineering. A major application problem is data-driven forecasting of future states from a complex dynamical. Artificial neural…

The theory of state tracking in recurrent architectures has predominantly focused on expressive capacity: whether a fixed architecture can theoretically realize a set of symbolic transition rules. We argue that equally important is error…

Deep neural networks based on state space models (SSMs) are attracting significant attention in sequence modeling since their computational cost is much smaller than that of Transformers. While the capabilities of SSMs have been…

In this study, we propose a novel approach, namely the combined Convolutional Deep Autoencoder Echo State Network (CDAE ESN) model, for the analysis and forecasting of dynamics and low order statistics in coupled turbulent channel porous…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Supralinear and sublinear pre-synaptic and dendritic integration is considered to be responsible for nonlinear computation power of biological neurons, emphasizing the role of nonlinear integration as opposed to nonlinear output…

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…

Recently, studies on deep Reservoir Computing (RC) highlighted the role of layering in deep recurrent neural networks (RNNs). In this paper, the use of linear recurrent units allows us to bring more evidence on the intrinsic hierarchical…

Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and…

Aero-engine fault prediction aims to accurately predict the development trend of the future state of aero-engines, so as to diagnose faults in advance. Traditional aero-engine parameter prediction methods mainly use the nonlinear mapping…

Modeling long range dependencies in sequential data is a fundamental step towards attaining human-level performance in many modalities such as text, vision, audio and video. While attention-based models are a popular and effective choice in…

The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…