scholarly journals Assessing the Interplay of Shape and Physical Parameters by Unsupervised Nonlinear Dimensionality Reduction Methods

2019 ◽  
Author(s):  
Andrea Serani ◽  
Danny D’Agostino ◽  
Emilio Fortunato Campana ◽  
Matteo Diez
Keyword(s):  
Dimensionality Reduction ◽  
Shape Optimization ◽  
Design Space ◽  
Mean Squared Error ◽  
Physical Parameters ◽  
Nonlinear Dimensionality Reduction ◽  
Data Set ◽  
Reduced Dimensionality ◽  
Nonlinear Design ◽  
Reduction Methods

The article presents an exploratory study on the application to ship hydrodynamics of unsupervised nonlinear design-space dimensionality reduction methods, assessing the interaction of shape and physical parameters. Nonlinear extensions of the principal component analysis (PCA) are applied, namely local PCA (LPCA) and kernel PCA (KPCA). An artificial neural network approach, specifically a deep autoencoder (DAE) method, is also applied and compared with PCA-based approaches. The data set under investigation is formed by the results of 9000 potential flow simulations coming from an extensive exploration of a 27-dimensional design space, associated with a shape optimization problem of the DTMB 5415 model in calm water at 18 kn (Froude number, <inline-formula><mml:math><mml:mrow><mml:mtext>Fr</mml:mtext><mml:mo>=</mml:mo><mml:mn>.25</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="JOSR09180056inf1.tif"/></inline-formula>). Data include three heterogeneous distributed and suitably discretized parameters (shape modification vector, pressure distribution on the hull, and wave elevation pattern) and one lumped parameter (wave resistance coefficient), for a total of <inline-formula><mml:math><mml:mrow><mml:mn>9000</mml:mn><mml:mtext> </mml:mtext><mml:mo>×</mml:mo><mml:mtext> </mml:mtext><mml:mn>5101</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="JOSR09180056inf2.tif"/></inline-formula> elements. The reduced-dimensionality representation of shape and physical parameters is set to provide a normalized mean squared error smaller than 5%. The standard PCA meets the requirement using 19 principal components/parameters. LPCA and KPCA provide the most promising compression capability with 14 parameters required by the reduced-dimensionality parametrizations, indicating significant nonlinear interactions in the data structure of shape and physical parameters. The DAE achieves the same error with 17 components. Although the focus of the current work is on design-space dimensionality reduction, the formulation goes beyond shape optimization and can be applied to large sets of heterogeneous physical data from simulations, experiments, and real operation measurements.

scholarly journals Nonlinear dimensionality reduction methods for synthetic biology biobricks’ visualization

2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Jiaoyun Yang ◽  
Haipeng Wang ◽  
Huitong Ding ◽  
Ning An ◽  
Gil Alterovitz
Keyword(s):  
Synthetic Biology ◽  
Dimensionality Reduction ◽  
Nonlinear Dimensionality Reduction ◽  
Reduction Methods

scholarly journals A GAN-based dimensionality reduction technique for aerodynamic shape optimization

2021 ◽  
Author(s):  
Jun Zhang ◽  
Wenzheng Wang ◽  
Qiuyu Wu ◽  
Liwei Hu
Keyword(s):  
Dimensionality Reduction ◽  
Shape Optimization ◽  
Design Space ◽  
Reduction Technique ◽  
Aerodynamic Shape Optimization ◽  
Generative Adversarial Network ◽  
Aerodynamic Shape ◽  
Adversarial Network ◽  
Dimensionality Reduction Technique ◽  
Dynamics Simulations

Abstract Aerodynamic shape optimization (ASO) based on computational fluid dynamics simulations is extremely computationally demanding because a search needs to be performed in a high-dimensional design space. One solution to this problem is to reduce the dimensionality of the design space for aircraft optimization. Hence, in this study, a dimensionality reduction technique is designed based on a generative adversarial network (GAN) to facilitate ASO. The novel GAN model is developed by combining the GAN with airfoil curve parameterization and can directly produce realistic and highly accurate airfoil curves from input data of aerodynamic shapes. In addition, the respective interpretable characteristic airfoil variables can be obtained by extracting latent codes with physical meaning, while reducing the dimensionality of the airfoil design space. The results of simulation experiments show that the proposed technique can significantly improve the optimization convergence rate of the ASO process.

scholarly journals Ensembles of Random Projections for Nonlinear Dimensionality Reduction

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Amir Hossein Karimi ◽  
Mohammad Javad Shafiee ◽  
Ali Ghodsi ◽  
Alexander Wong
Keyword(s):  
Dimensionality Reduction ◽  
Experimental Analysis ◽  
Random Projections ◽  
Nonlinear Dimensionality Reduction ◽  
Generalization Performance ◽  
Highly Efficient ◽  
Efficiency Of Algorithms ◽  
Reduction Methods ◽  
Embedding Performance

Dimensionality reduction methods are widely used in informationprocessing systems to better understand the underlying structuresof datasets, and to improve the efficiency of algorithms for bigdata applications. Methods such as linear random projections haveproven to be simple and highly efficient in this regard, however,there is limited theoretical and experimental analysis for nonlinearrandom projections. In this study, we review the theoretical frameworkfor random projections and nonlinear rectified random projections,and introduce ensemble of nonlinear maximum random projections.We empirically evaluate the embedding performance on 3commonly used natural datasets and compare with linear randomprojections and traditional techniques such as PCA, highlightingthe superior generalization performance and stable embedding ofthe proposed method.

scholarly journals Multiple Kernel Dimensionality Reduction via Ratio-Trace and Marginal Fisher Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Hui Xu ◽  
Yongguo Yang ◽  
Xin Wang ◽  
Mingming Liu ◽  
Hongxia Xie ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Convex Combination ◽  
Multiple Kernel Learning ◽  
Nonlinear Dimensionality Reduction ◽  
Kernel Discriminant Analysis ◽  
Restrictive Assumption ◽  
Optimal Weights ◽  
Multiple Kernel ◽  
Benchmark Datasets ◽  
Reduction Methods

Traditional supervised multiple kernel learning (MKL) for dimensionality reduction is generally an extension of kernel discriminant analysis (KDA), which has some restrictive assumptions. In addition, they generally are based on graph embedding framework. A more general multiple kernel-based dimensionality reduction algorithm, called multiple kernel marginal Fisher analysis (MKL-MFA), is presented for supervised nonlinear dimensionality reduction combined with ratio-race optimization problem. MKL-MFA aims at relaxing the restrictive assumption that the data of each class is of a Gaussian distribution and finding an appropriate convex combination of several base kernels. To improve the efficiency of multiple kernel dimensionality reduction, the spectral regression frameworks are incorporated into the optimization model. Furthermore, the optimal weights of predefined base kernels can be obtained by solving a different convex optimization. Experimental results on benchmark datasets demonstrate that MKL-MFA outperforms the state-of-the-art supervised multiple kernel dimensionality reduction methods.

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