Related papers: Surrogate-assisted network analysis of nonlinear t…
The effect differencing has on the estimated correlation dimension of a nongaussian time series is discussed. Two different methods for generating surrogate data sets are compared. The results suggest that any filtering should be applied to…
Randomizing the Fourier-transform (FT) phases of temporal-spatial data generates surrogates that approximate examples from the data-generating distribution. We propose such FT surrogates as a novel tool to augment and analyze training of…
We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…
We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…
In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…
This work proposes a data-driven surrogate modeling framework for cost-effectively inferring the torque of a permanent magnet synchronous machine under geometric design variations. The framework is separated into a reduced-order modeling…
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…
Evaluation metrics in machine learning are often hardly taken as loss functions, as they could be non-differentiable and non-decomposable, e.g., average precision and F1 score. This paper aims to address this problem by revisiting the…
Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…
Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system. The same approach can be used to correct the…
We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a…
We present a methodology for detecting non-linearities in data sets based on the characterization of the structural features of the Fourier phase maps. A Fourier phase map is a 2D set of points $M= \{(\phi_{\vec{k}}, \phi_{\vec{k} +…
Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where…
Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data…
Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems…
The statistical properties of nonlinear phase noise, often called the Gordon-Mollenauer effect, is studied analytically when the number of fiber spans is very large. The joint characteristic functions of the nonlinear phase noise with…
We describe two families of statistical tests to detect partial correlation in vectorial timeseries. The tests measure whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z…
We introduce the concept of decision-focused surrogate modeling for solving computationally challenging nonlinear optimization problems in real-time settings. The proposed data-driven framework seeks to learn a simpler, e.g. convex,…
Accurate gene regulatory networks can be used to explain the emergence of different phenotypes, disease mechanisms, and other biological functions. Many methods have been proposed to infer networks from gene expression data but have been…
We report about probabilistic likelihood estimates that are performed on time series using an echo state network with orthogonal recurrent connectivity. The results from tests using synthetic stochastic input time series with temporal…