Related papers: Deciphering Dynamical Nonlinearities in Short Time…

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…

Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace…

Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

In this work we present a novel recurrent neural network architecture designed to model systems characterized by multiple characteristic timescales in their dynamics. The proposed network is composed by several recurrent groups of neurons…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

We propose a framework for surrogate modelling of spiking systems. These systems are often described by stiff differential equations with high-amplitude oscillations and multi-timescale dynamics, making surrogate models an attractive tool…

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…

Detecting structure in noisy time series is a difficult task. One intuitive feature is the notion of trend. From theoretical hints and using simulated time series, we empirically investigate the efficiency of standard recurrent neural…

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.…

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…

One-shot decision making is required in situations in which we can evaluate a fixed number of solution candidates but do not have any possibility for further, adaptive sampling. Such settings are frequently encountered in neural network…

Standard tests for nonlinearity reject the null hypothesis of a Gaussian linear process whenever the data is non-stationary. Thus, they are not appropriate to distinguish nonlinearity from non-stationarity. We address the problem of…

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…

Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…