Related papers: Full Lyapunov Exponents spectrum with Deep Learnin…

Complex phenomena are generally modeled with sophisticated simulators that, depending on their accuracy, can be very demanding in terms of computational resources and simulation time. Their time-consuming nature, together with a typically…

The success of modern deep learning is attributed to two key elements: huge amounts of training data and large model sizes. Where a vast amount of data allows the model to learn more features, the large model architecture boosts the…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

A variety of pruning methods have been introduced for over-parameterized Recurrent Neural Networks to improve efficiency in terms of power consumption and storage utilization. These advances motivate a new paradigm, termed `hyperpruning',…

This paper addresses learning end-to-end models for time series data that include a temporal alignment step via dynamic time warping (DTW). Existing approaches to differentiable DTW either differentiate through a fixed warping path or apply…

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…

We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through…

We present a new supervised deep-learning approach to the problem of the extraction of smeared spectral densities from Euclidean lattice correlators. A distinctive feature of our method is a model-independent training strategy that we…

The Learning Rate (LR) has a high impact on deep learning training performance. A common practice is to train a Deep Neural Network (DNN) multiple times with different LR policies to find the optimal LR policy, which has been widely…

We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix…

Complex-valued neural networks (CVNNs) are an emerging field of research in neural networks due to their potential representational properties for audio, image, and physiological signals. It is common in signal processing to transform…

Machine Learning is an efficient method for analyzing and interpreting the increasing amount of astronomical data that is available. In this study, we show, a pedagogical approach that should benefit anyone willing to experiment with Deep…

The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…

We present a representation learning framework for financial time series forecasting. One challenge of using deep learning models for finance forecasting is the shortage of available training data when using small datasets. Direct trend…

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we…

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…

Consider a non-autonomous continuous-time linear system in which the time-dependent matrix determining the dynamics is piecewise constant and takes finitely many values $A_1, \dotsc, A_N$. This paper studies the equality cases between the…

The choice of learning rate (LR) functions and policies has evolved from a simple fixed LR to the decaying LR and the cyclic LR, aiming to improve the accuracy and reduce the training time of Deep Neural Networks (DNNs). This paper presents…

In the use of deep neural networks, it is crucial to provide appropriate input representations for the network to learn from. In this paper, we propose an approach to learn a representation that focus on rhythmic representation which is…