DISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA

Rico-Martı́nez, Ramiro; Krischer, Katharina; Kevrekidis, Ioannis G.; Kube, M.; Hudson, John L.

doi:10.1080/00986449208936084

Cited by 129 publications

(84 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To identify this nonlinear mapping we employ an artificial neural network (ANN). Generally, the neural network approach is used as a "black-box" tool in order to develop a dynamic model based only on observations of the system's input-output behavior [23,24]. In the learning process the network adjusts its internal parameters to minimize the squared error between the network output and the desired outputs.…”

Section: Model Reconstruction and Short-term Earthquake Forecastingmentioning

confidence: 99%

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault

Anghel¹,

Ben‐Zion²,

Rico-Martı́nez³

2004

Computational Earthquake Science Part I

View full text Add to dashboard Cite

We present a method of constructing low-dimensional nonlinear models describing the main dynamical features of a discrete 2D cellular fault zone, with many degrees of freedom, embedded in a 3D elastic solid. A given fault system is characterized by a set of parameters that describe the dynamics, rheology, property disorder, and fault geometry. Depending on the location in the system parameter space we show that the coarse dynamics of the fault can be confined to an attractor whose dimension is significantly smaller than the space in which the dynamics takes place. Our strategy of system reduction is to search for a few coherent structures that dominate the dynamics and to capture the interaction between these coherent structures. The identification of the basic interacting structures is obtained by applying the Proper Orthogonal Decomposition (POD) to the surface deformations fields that accompany strike-slip faulting accumulated over equal time intervals. We use a feed-forward artificial neural network (ANN) architecture for the identification of the system dynamics projected onto the subspace (model space) spanned by the most energetic coherent structures. The ANN is trained using a standard back-propagation algorithm to predict (map) the values of the observed model state at a future time given the observed model state at the present time.This ANN provides an approximate, large scale, dynamical model for the fault. The map can be evaluated once to provide short term predictions or iterated to obtain prediction for the long term fault dynamics.

show abstract

Section: Model Reconstruction and Short-term Earthquake Forecastingmentioning

confidence: 99%

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault

Anghel¹,

Ben‐Zion²,

Rico-Martı́nez³

2004

Computational Earthquake Science Part I

View full text Add to dashboard Cite

show abstract

“…To identify this nonlinear mapping we employ an artificial neural network (ANN). Generally, the neural network approach is used as a ''black-box'' tool in order to develop a dynamic model based only on observations of the system's input-output behavior (RICO-MARTINEZ et al, 1992. In the learning process the network adjusts its internal parameters to minimize the squared error between the network output and the desired outputs.…”

Section: Model Reconstruction and Short-term Earthquake Forecastingmentioning

confidence: 99%

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault

Anghel

Ben‐Zion

Rico-Martı́nez

2004

Pure appl. geophys.

View full text Add to dashboard Cite

We present a method of constructing low-dimensional nonlinear models describing the main dynamical features of a discrete 2-D cellular fault zone, with many degrees of freedom, embedded in a 3-D elastic solid. A given fault system is characterized by a set of parameters that describe the dynamics, rheology, property disorder, and fault geometry. Depending on the location in the system parameter space, we show that the coarse dynamics of the fault can be confined to an attractor whose dimension is significantly smaller than the space in which the dynamics takes place. Our strategy of system reduction is to search for a few coherent structures that dominate the dynamics and to capture the interaction between these coherent structures. The identification of the basic interacting structures is obtained by applying the Proper Orthogonal Decomposition (POD) to the surface deformation fields that accompany strike-slip faulting accumulated over equal time intervals. We use a feed-forward artificial neural network (ANN) architecture for the identification of the system dynamics projected onto the subspace (model space) spanned by the most energetic coherent structures. The ANN is trained using a standard back-propagation algorithm to predict (map) the values of the observed model state at a future time, given the observed model state at the present time. This ANN provides an approximate, large-scale, dynamical model for the fault. The map can be evaluated once to provide a short-term predictions or iterated to obtain a prediction for the long-term fault dynamics.

show abstract

“…If such a decomposition into a few dominating modes is possible this method turns out to be very efficient. Prom the temporal evolution of the (few) coefficients {c£} (k = 1,..., K), low dimensional models can be derived and may be used for analyzing and predicting the STTS [Ciliberto & Nicolaenko, 1991;Rico-Martinez et al, 1992;Chauve & Le Gal, 1992;Berry et al, 1994].…”

Section: Spatio-temporal Datamentioning

confidence: 99%

2000 Physical Acoustics Summer School (PASS 00). Volume III: Background Materials

Bass¹,

Furr²

2001

View full text Add to dashboard Cite

DISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA

Cited by 129 publications

References 28 publications

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault

2000 Physical Acoustics Summer School (PASS 00). Volume III: Background Materials

Contact Info

Product

Resources

About