Related papers: Constructing differential equations using only a s…

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

Recurrence networks are powerful tools used effectively in the nonlinear analysis of time series data. The analysis in this context is done mostly with unweighted and undirected complex networks constructed with specific criteria from the…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

A method of network reconstruction from the dynamical time series is introduced, relying on the concept of derivative-variable correlation. Using a tunable observable as a parameter, the reconstruction of any network with known interaction…

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…

This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…

This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields. This task becomes prohibitive when such data is moreover highly corrupted, for example, due to the…

Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…

An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are…

In many real-world applications, optimization problems evolve continuously over time and are often subject to stochastic noise. We consider a stochastic time-varying optimization problem in which the objective function $f(x;t)$ changes…

We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…

We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…

This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…