Related papers: Statistical inference for Axiom A attractors
Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…
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…
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…
Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main…
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…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…
Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a…
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Predicting the dynamics of chaotic systems is one of the most challenging tasks for neural networks, and machine learning in general. Here we aim to predict the spatiotemporal chaotic dynamics of a high-dimensional non-linear system. In our…