Related papers: Chaos Meets Attention: Transformers for Large-Scal…

We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state…

We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of…

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…

Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme…

This paper presents a Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. It combines predictor-based feedback and Hessian inverse estimation via stochastic…

Traffic forecasting is an indispensable part of Intelligent transportation systems (ITS), and long-term network-wide accurate traffic speed forecasting is one of the most challenging tasks. Recently, deep learning methods have become…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information…

In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…

Low-latency communication has recently attracted considerable attention owing to its potential of enabling delay-sensitive services in next-generation industrial cyber-physical systems. To achieve target average or maximum delay given…

Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal…

We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…

We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…

Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3…

Temporal set prediction involves forecasting the elements that will appear in the next set, given a sequence of prior sets, each containing a variable number of elements. Existing methods often rely on intricate architectures with…

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

The analysis of long sequence data remains challenging in many real-world applications. We propose a novel architecture, ChunkFormer, that improves the existing Transformer framework to handle the challenges while dealing with long time…