Related papers: TensorFlow Chaotic Prediction and Blow Up
We construct a data-driven dynamical system model for a macroscopic variable the Reynolds number of a high-dimensionally chaotic fluid flow by training its scalar time-series data. We use a machine-learning approach, the reservoir computing…
We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the…
Machine-learning models, which are known to accurately predict patterns from large datasets, are crucial in decision making. Consequently, counterfactual explanations-methods explaining predictions by introducing input perturbations-have…
A neural-networks predictor library has been developed to deploy machine learning (ML) models into computational fluid dynamics (CFD) codes. The pointer-to-implementation strategy is adopted to isolate the implementation details in order to…
Learning-to-Rank deals with maximizing the utility of a list of examples presented to the user, with items of higher relevance being prioritized. It has several practical applications such as large-scale search, recommender systems,…
Unsteady flow fields over a circular cylinder are trained and predicted using four different deep learning networks: convolutional neural networks with and without consideration of conservation laws, generative adversarial networks with and…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
Tipping behavior can occur when an equilibrium of a dynamical system loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
Chaotic flow is studied in a series of numerical magnetohydrodynamical simulations that use the shearing box formalism. This mimics important features of local accretion disk dynamics. The magnetorotational instability gives rise to flow…
Different 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…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference…
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…
An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the…
When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…
Optical computing has gained significant attention as a potential solution to the growing computational demands of machine learning, particularly for tasks requiring large-scale data processing and high energy efficiency. Optical systems…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…