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Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…

Markov state models (MSMs) and Master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering.…

Poor scaling of dynamics simulations with number of dimensions is currently a major limiting factor in the simulation of photochemical processes. In this work, we investigate ways to reduce the dimensionality of many-atom systems with a…

Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavour, determining nucleation mechanisms and rates for phase separation requires an…

The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions…

Transfer operators such as Perron-Frobenius or Koopman operator play a key role in modeling and analysis of complex dynamical systems, which allow linear representations of nonlinear dynamics by transforming the original state variables to…

A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or…

The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…

Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to…

We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…

Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained…

There is an increasing demand for computing the relevant structures, equilibria and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ…

We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even…

Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

The thermodynamic approach to non-equilibrium dynamics describes the state of macroscopic systems by means of a collection of intensities or intensive variables. The latter are by definition the differentials of the entropy with respect to…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behavior as well as the occurrence of singularities. The study brings together the various ways to identify and quantify…

This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics…