Related papers: Deterministic and stochastic surrogate models for …
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…
Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…
We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and…
The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the synthetic data of the Lorenz system, the network measures show a comparable…
Linear response theory has developed into a formidable set of tools for studying the forced behaviour of a large variety of systems - including out of equilibrium ones. In this paper we provide a new angle on the problem, by studying under…
We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected…
This paper develops a surrogate model refinement approach for the simulation of dynamical systems and the solution of optimization problems governed by dynamical systems in which surrogates replace expensive-to-compute state- and…
The governed equations for the order parameter, one-time and two-time correlators are obtained on the basis of the Langevin equation with the white multiplicative noise which amplitude $x^{a}$ is determined by an exponent $0<a<1$ ($x$ being…
In climate systems, physiological models, optics, and many more, surrogate models are developed to reconstruct chaotic dynamical systems. We introduce four data-driven measures using global attractor properties to evaluate the quality of…
Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are…
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…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of…
A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future…
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from…
The transition of the power grid requires new technologies and methodologies, which can only be developed and tested in simulations. Especially larger simulation setups with many levels of detail can become quite slow. Therefore, the number…