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Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important…
In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD)…
UAV trajectory planning is often done in a two-step approach, where a low-dimensional path is refined to a dynamic trajectory. The resulting trajectories are only locally optimal, however. On the other hand, direct planning in…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Quantitative assessment of the uncertainties tainting the results of computer simulations is nowadays a major topic of interest in both industrial and scientific communities. One of the key issues in such studies is to get information about…
Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…
The paper presents the study of the effect of a mesh refinement on numerical results of 3D RANS computations of turbomachinery flows. The CFD solver F, which based on the second-order accurate ENO scheme, is used in this study. The…
Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…
Feature embeddings are one of the most essential steps when training deep learning based Click-Through Rate prediction models, which map high-dimensional sparse features to dense embedding vectors. Classic human-crafted embedding size…
Multi-directional 3D printing has the capability of decreasing or eliminating the need for support structures. Recent work proposed a beam-guided search algorithm to find an optimized sequence of plane-clipping, which gives volume…
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…
Accurate machine-learning models for aerodynamic prediction are essential for accelerating shape optimization, yet remain challenging to develop for complex three-dimensional configurations due to the high cost of generating training data.…
We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…
In aerodynamic shape optimization, the convergence and computational cost are greatly affected by the representation capacity and compactness of the design space. Previous research has demonstrated that using a deep generative model to…
Design optimization of mechanisms is a promising research area as it results in more energy-efficient machines without compromising performance. However, machine builders do not actually use the potential described in the literature as…