Related papers: Modelling Chaotic Data
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information…
Template and prunning front are calculated for an experimental chaotic time series from a mechanical string experiment. An empirical synchronized model is also created for the data set. To appear in Physical Review E.
In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…
Deep learning time-series models are often used to make forecasts that inform downstream decisions. Since these decisions can differ from those in the training set, there is an implicit requirement that time-series models will generalize…
In the current context of Big Data, the nature of many forecasting problems has changed from predicting isolated time series to predicting many time series from similar sources. This has opened up the opportunity to develop competitive…
In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
Imbalanced problems can arise in different real-world situations, and to address this, certain strategies in the form of resampling or balancing algorithms are proposed. This issue has largely been studied in the context of classification,…
Most research designing novel predictive models, or employing existing ones, assumes that training and testing data are independent and identically distributed. In practice, the data encountered at serving time often deviate from the…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…