Eighty years of the finite element method: Birth, evolution, and future
This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …
element methods (FEM) since 1941, with a specific emphasis on developments related to …
A review on design of experiments and surrogate models in aircraft real-time and many-query aerodynamic analyses
Full scale aerodynamic wind tunnel testing, numerical simulation of high dimensional (full-
order) aerodynamic models or flight testing are some of the fundamental but complex steps …
order) aerodynamic models or flight testing are some of the fundamental but complex steps …
Deep neural operators as accurate surrogates for shape optimization
Deep neural operators, such as DeepONet, have changed the paradigm in high-
dimensional nonlinear regression, paving the way for significant generalization and speed …
dimensional nonlinear regression, paving the way for significant generalization and speed …
High-performance model reduction techniques in computational multiscale homogenization
A novel model-order reduction technique for the solution of the fine-scale equilibrium
problem appearing in computational homogenization is presented. The reduced set of …
problem appearing in computational homogenization is presented. The reduced set of …
POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations
Numerical simulation of fluid flows requires important computational efforts but it is essential
in engineering applications. Reduced Order Model (ROM) can be employed whenever fast …
in engineering applications. Reduced Order Model (ROM) can be employed whenever fast …
Data‐driven model reduction for the Bayesian solution of inverse problems
One of the major challenges in the Bayesian solution of inverse problems governed by
partial differential equations (PDEs) is the computational cost of repeatedly evaluating …
partial differential equations (PDEs) is the computational cost of repeatedly evaluating …
Machine learning approach to model order reduction of nonlinear systems via autoencoder and LSTM networks
In analyzing and assessing the condition of dynamical systems, it is necessary to account for
nonlinearity. Recent advances in computation have rendered previously computationally …
nonlinearity. Recent advances in computation have rendered previously computationally …
Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization
An adaptive approach to using reduced‐order models (ROMs) as surrogates in partial
differential equations (PDE)‐constrained optimization is introduced that breaks the …
differential equations (PDE)‐constrained optimization is introduced that breaks the …
Deep neural operators can serve as accurate surrogates for shape optimization: a case study for airfoils
Deep neural operators, such as DeepONets, have changed the paradigm in high-
dimensional nonlinear regression from function regression to (differential) operator …
dimensional nonlinear regression from function regression to (differential) operator …
A Review of Model Order Reduction Methods for Large‐Scale Structure Systems
K Lu, K Zhang, H Zhang, X Gu, Y Jin, S Zhao… - Shock and …, 2021 - Wiley Online Library
The large‐scale structure systems in engineering are complex, high dimensional, and
variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors …
variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors …