Related papers: Identifying statistical indicators of temporal asy…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…

We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…

Time reversal of vast classes of phenomena has direct implications with predictability, causality and the second principle of thermodynamics. We analyze in detail time reversibility of a paradigmatic dissipative nonlinear dynamical system,…

The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…

Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…

Among existing subgrid scale models for large-eddy simulation (LES) some are time-reversible in the sense that the dynamics evolve backwards in time after a transformation $\bm u \rightarrow -\bm u$ at every point in space. In practice,…

Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data---which results from the dimension,…

This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…

Within Tsallis statistics, a picture is elaborated to address self--similar time series as a thermodynamic system. Thermodynamic--type characteristics relevant to temperature, pressure, entropy, internal and free energies are introduced and…

We propose and investigate a method for identifying timescales of dissipation in nonequilibrium steady states modeled as discrete-state Markov jump processes. The method is based on how the irreversibility-measured by the statistical…

Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…

We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…

Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…