Related papers: Reduced Markovian Models of Dynamical Systems
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially…
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…
Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Energy distribution networks are crucial for human societies and since they often cover large geographical areas, their physical analysis is challenging. Modeling and simulation can be used to analyze such complex energy networks. In this…
Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD)…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems.…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
Modelling rarefied gas flow via the Boltzmann equation plays a vital role in many areas. Due to the high dimensionality of this kinetic equation and the coexistence of multiple characteristic scales in the transport processes, conventional…
This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using multi-agents with Markov switched network dynamics and noisy inter-agent communications. Unlike…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…