Related papers: Variational approach for learning Markov processes…

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…

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…

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…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…

Finding low dimensional representation of data from long-timescale trajectories of biomolecular processes such as protein-folding or ligand-receptor binding is of fundamental importance and kinetic models such as Markov modeling have proven…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly-varying collective variables, where subsequent analyses are made, such as…

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…

Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…

We revisit macroeconomic time-varying parameter vector autoregressions (TVP-VARs), whose persistent coefficients may adapt too slowly to large, abrupt shifts such as those during major crises. We explore the performance of an…

In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Vector autoregressive (VAR) models are widely used in practical studies, e.g., forecasting, modelling policy transmission mechanism, and measuring connection of economic agents. To better capture the dynamics, this paper introduces a new…

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…

Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly…

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into…

Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task.…

Designing control inputs for a system that involves dynamical responses in multiple timescales is nontrivial. This paper proposes a parameterized time-warping function to enable a non-uniformly sampling along a prediction horizon given some…