Related papers: Nonlinear Decomposition Principle and Fundamental …

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…

We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…

The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art…

Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…

A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…

We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving…

Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study…