Nonlinear Multi-Fidelity Reduced Order Modeling Method using Manifold Alignment

TL;DR: In this article , a parametric reduced order modeling method was proposed to enable the prediction of uncertain high-dimensional outputs with complex, nonlinear features and limited sampling budgets, where a Proper Orthogonal Decomposition (POD) procedure was utilized to reduce the dimensionality of the highdimensional space and identify a low-dimensional latent space.

TL;DR: The proposed ROM is validated to predict nonlinear transonic flows over RAE 2822 airfoil and undeflected NASA Common Research Model with aspect ratio 9, in which nonlinearities are induced by shock waves, and results confirm that the ROM replicates CFD solutions accurately at fraction of the cost of CFD calculation or the full-order modeling.

TL;DR: In this article , a multifidelity reduced-order model was proposed to emulate aerodynamic flow fields with nonlinear and discontinuous features, which can leverage an abundance of inexpensive low-fidelity data to improve the model's predictive accuracy.

TL;DR: Scikit-learn as mentioned in this paper is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems.

TL;DR: SciPy as discussed by the authors is an open source scientific computing library for the Python programming language, which includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics.

TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.

TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.