Related papers: Approximation of slow and fast dynamics in multisc…

A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

We propose a new framework to discuss the transition from exponential relaxation in a liquid to the regime of slow dynamics. For the purposes of stress relaxation, we show that a liquid can be treated as an elastic medium. We discuss that,…

We propose using the dynamical invariant also known as the Lewis-Riesenfeld invariant, to speed-up the equilibration of a driven open quantum system. This allows us to reverse engineer the time-dependent master equation that describes the…

We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition…

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…

We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…

Learning dynamical systems is a promising avenue for scientific discoveries. However, capturing the governing dynamics in multiple environments still remains a challenge: model-based approaches rely on the fidelity of assumptions made for a…

This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model…

This is the first part of four series papers, aiming at the problem of actuator dynamics compensation for linear systems. We consider the stabilization of a type of cascade abstract linear systems which model the actuator dynamics…

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…

The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed…

This study investigates the use of continuous-time dynamical systems for sparse signal recovery. The proposed dynamical system is in the form of a nonlinear ordinary differential equation (ODE) derived from the gradient flow of the Lasso…

Discretizing a distribution function in a phase space for an efficient quantum dynamics simulation is a non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum…

In the current paper the so-called REaction-DIffusion Manifold (REDIM) method of model reduction is discussed within the framework of standard singular perturbation theory. According to the REDIM a reduced model for the system describing a…

Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…