Structural chaos and a quasi-crystalline stochastic web in low dimensional nonlinear systems

1999 ◽  
Vol 42 (1) ◽  
pp. 53-58
Author(s):  
A. G. Tret'yakov
Keyword(s):  
Nonlinear Systems ◽  
Low Dimensional ◽  
Stochastic Web

scholarly journals Enlargement of a low-dimensional stochastic web

2009 ◽  
Author(s):  
S. M. Soskin ◽  
I. A. Khovanov ◽  
R. Mannella ◽  
P. V. E. McClintock ◽  
Massimo Macucci ◽  
...  
Keyword(s):  
Low Dimensional ◽  
Stochastic Web

Two-Run Genetic Programming for Predicting Slump Flow of Concrete

2014 ◽  
Vol 590 ◽  
pp. 321-325
Author(s):  
Li Chen ◽  
Chang Huan Kou ◽  
Kuan Ting Chen ◽  
Shih Wei Ma
Keyword(s):  
Nonlinear Systems ◽  
Genetic Programming ◽  
High Performance ◽  
Mean Squared Error ◽  
High Performance Concrete ◽  
Local Optimum ◽  
Root Mean Squared Error ◽  
Squared Error ◽  
Slump Flow ◽  
Low Dimensional

A two-run genetic programming (GP) is proposed to estimate the slump flow of high-performance concrete (HPC) using several significant concrete ingredients in this study. GP optimizes functions and their associated coefficients simultaneously and is suitable to automatically discover relationships between nonlinear systems. Basic-GP usually suffers from premature convergence, which cannot acquire satisfying solutions and show satisfied performance only on low dimensional problems. Therefore it was improved by an automatically incremental procedure to improve the search ability and avoid local optimum. The results demonstrated that two-run GP generates an accurate formula through and has 7.5 % improvement on root mean squared error (RMSE) for predicting the slump flow of HPC than Basic-GP.

Uniform stochastic web in low-dimensional Hamiltonian systems

1997 ◽  
Vol 225 (4-6) ◽  
pp. 274-286 ◽  
Author(s):  
Sergey Pekarsky ◽  
Vered Rom-Kedar
Keyword(s):  
Hamiltonian Systems ◽  
Low Dimensional ◽  
Stochastic Web

INTERMITTENCY, PHASE RANDOMIZATION AND GENERALIZED FRACTAL DIMENSIONS

1993 ◽  
Vol 03 (03) ◽  
pp. 729-736 ◽  
Author(s):  
ANTONELLO PROVENZALE ◽  
BARBARA VILLONE ◽  
ARMANDO BABIANO ◽  
ROBERTO VIO
Keyword(s):  
Time Series ◽  
Nonlinear Systems ◽  
Phase Distribution ◽  
Fractal Dimensions ◽  
Phase Spectrum ◽  
2D Turbulence ◽  
Measured Time ◽  
Linear And Nonlinear ◽  
Low Dimensional ◽  
Phase Randomization

The procedure of Fourier phase randomization has been repeatedly proposed for distinguishing low-dimensional chaos from noise in a measured time series. Here we extend the use of this method and we show that phase randomization is a necessary step for assessing the presence of intermittency in a stochastic and/or turbulent system. This procedure allows us to distinguish between linear and nonlinear signals as well. As an example of application of this approach, we study the time series of positions of passively advected particles in 2D turbulence and we show that their apparent multifractality is not associated with intermittency. The results discussed here confirm the importance of understanding the phase spectrum, and of developing appropriate measures of the phase distribution, in the study of nonlinear systems.

scholarly journals Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Xuping Xie ◽  
Clayton Webster ◽  
Traian Iliescu
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Second Step ◽  
The Novel ◽  
Reduced Order ◽  
Nonlinear Model Reduction ◽  
Learning Framework ◽  
Closure Models ◽  
Low Dimensional ◽  
The Given

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

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