Related papers: Chaos Meets Attention: Transformers for Large-Scal…
We proved that for the countably infinite number of one-parameterized one dimensional dynamical systems, they preserve the Lebesgue measure and they are ergodic for the measure (infinite ergodicity). Considered systems connect the parameter…
The use of attention-based deep learning models in stochastic filtering, e.g. transformers and deep Kalman filters, has recently come into focus; however, the potential for these models to solve stochastic filtering problems remains largely…
We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential…
The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism…
Phase transitions mark qualitative reorganizations of collective behavior, yet identifying their boundaries remains challenging whenever analytic solutions are absent and conventional simulations fail. Here we introduce learnability as a…
We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The…
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…
Accurate trajectory prediction of nearby vehicles is crucial for the safe motion planning of automated vehicles in dynamic driving scenarios such as highway merging. Existing methods cannot initiate prediction for a vehicle unless observed…
The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various…
The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…
We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size…
A model for a lattice of coupled cat maps has been recently introduced. This new and specific choice of the coupling makes the description especially easy and nontrivial quantities as Lyapunov exponents determined exactly. We studied the…
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…
Predicting extreme events in high-dimensional chaotic dynamical systems remains a fundamental challenge, as such events are rare, intermittent, and arise from transient dynamical mechanisms that are difficult to infer from limited…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…