Related papers: Statistical inference for Axiom A attractors

Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a…

Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of large language models, foundation models pre-trained on vast…

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…

The reliability assessment of a machine learning model's prediction is an important quantity for the deployment in safety critical applications. Not only can it be used to detect novel sceneries, either as out-of-distribution or anomaly…

A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…

Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…

A crime is a punishable offence that is harmful for an individual and his society. It is obvious to comprehend the patterns of criminal activity to prevent them. Research can help society to prevent and solve crime activates. Study shows…

The unparalleled ability of machine learning algorithms to learn patterns from data also enables them to incorporate biases embedded within. A biased model can then make decisions that disproportionately harm certain groups in society. Much…

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…

There are insights of chaotic properties in economic systems and data. To prove the existence of chaotic dynamics, the establishment of a deterministic model is mandatory. A global modelling tool (GPoM) is used to search for mathematical…

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical…

The paper describes the use of Bayesian regression for building time series models and stacking different predictive models for time series. Using Bayesian regression for time series modeling with nonlinear trend was analyzed. This approach…

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…

With growing numbers of intelligent autonomous systems in human environments, the ability of such systems to perceive, understand and anticipate human behavior becomes increasingly important. Specifically, predicting future positions of…

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…

Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…

Inference and prediction are fundamental to the study of complex systems, where network data are often incomplete, inaccurate or obtained indirectly. In this paper, we review recent advances in network sampling and comparison, as well as in…