HiDeNN-TD: reduced-order hierarchical deep learning neural networks
This paper presents a tensor decomposition (TD) based reduced-order model of the
hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-TD method …
hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-TD method …
Encapsulated PGD algebraic toolbox operating with high-dimensional data
In its original conception, proper generalized decomposition (PGD) provides explicit
parametric solutions, denoted as computational vademecums or digital abacuses, to …
parametric solutions, denoted as computational vademecums or digital abacuses, to …
Nonlinear dimensionality reduction for parametric problems: A kernel proper orthogonal decomposition
Reduced‐order models are essential tools to deal with parametric problems in the context of
optimization, uncertainty quantification, or control and inverse problems. The set of …
optimization, uncertainty quantification, or control and inverse problems. The set of …
Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms
Reduced order models (ROM) are commonly employed to solve parametric problems and to
devise inexpensive response surfaces to evaluate quantities of interest in real-time. There …
devise inexpensive response surfaces to evaluate quantities of interest in real-time. There …
A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties
Understanding the failure of brittle heterogeneous materials is essential in many
applications. Heterogeneities in material properties are frequently modeled through random …
applications. Heterogeneities in material properties are frequently modeled through random …
Nonintrusive parametric NVH study of a vehicle body structure
A reduced order model technique is presented to perform the parametric Noise, Vibration
and Harshness (NVH) study of a vehicle body-in-white (BIW) structure characterized by …
and Harshness (NVH) study of a vehicle body-in-white (BIW) structure characterized by …
A kernel Principal Component Analysis (kPCA) digest with a new backward map** (pre-image reconstruction) strategy
Methodologies for multidimensionality reduction aim at discovering low-dimensional
manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data …
manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data …
Nonintrusive reduced order model for parametric solutions of inertia relief problems
Abstract The Inertia Relief (IR) technique is widely used by industry and produces
equilibrated loads allowing to analyze unconstrained systems without resorting to the more …
equilibrated loads allowing to analyze unconstrained systems without resorting to the more …
Tensorial parametric model order reduction of nonlinear dynamical systems
For a nonlinear dynamical system that depends on parameters, this paper introduces a
novel tensorial reduced-order model (TROM). The reduced model is projection-based, and …
novel tensorial reduced-order model (TROM). The reduced model is projection-based, and …
A staggered high-dimensional proper generalised decomposition for coupled magneto-mechanical problems with application to MRI scanners
Abstract Manufacturing new Magnetic Resonance Imaging (MRI) scanners represents a
computational challenge to industry, due to the large variability in material parameters and …
computational challenge to industry, due to the large variability in material parameters and …