Reduced basis methods for time-dependent problems
Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …
study of real-world phenomena in applied science and engineering. Computational methods …
[HTML][HTML] Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression
Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation,
entail a huge computational complexity when dealing with input-output maps involving the …
entail a huge computational complexity when dealing with input-output maps involving the …
[HTML][HTML] Nonlinear model order reduction for problems with microstructure using mesh informed neural networks
Many applications in computational physics involve approximating problems with
microstructure, characterized by multiple spatial scales in their data. However, these …
microstructure, characterized by multiple spatial scales in their data. However, these …
Model reduction techniques for parametrized nonlinear partial differential equations
NC Nguyen - Error Control, Adaptive Discretizations, and …, 2024 - books.google.com
2. Hyper-reduction methods 2.1 Parametrized integrals 2.2 Empirical quadrature methods
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …
Optimal Transport-inspired Deep Learning Framework for Slow-Decaying Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel
Reduced order models (ROMs) are widely used in scientific computing to tackle high-
dimensional systems. However, traditional ROM methods may only partially capture the …
dimensional systems. However, traditional ROM methods may only partially capture the …
A physics-based reduced order model for urban air pollution prediction
This article presents an innovative approach for developing an efficient reduced-order
model to study the dispersion of urban air pollutants. The need for real-time air quality …
model to study the dispersion of urban air pollutants. The need for real-time air quality …
Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy
Forward uncertainty quantification (UQ) for partial differential equations is a many-query task
that requires a significant number of model evaluations. The objective of this work is to …
that requires a significant number of model evaluations. The objective of this work is to …
High-order empirical interpolation methods for real time solution of parametrized nonlinear PDEs
NC Nguyen - arXiv preprint arXiv:2410.02100, 2024 - arxiv.org
We present novel model reduction methods for rapid solution of parametrized nonlinear
partial differential equations (PDEs) in real-time or many-query contexts. Our approach …
partial differential equations (PDEs) in real-time or many-query contexts. Our approach …
Fourier neural operator for large eddy simulation of compressible Rayleigh-Taylor turbulence
The Fourier neural operator (FNO) framework is applied to the large eddy simulation (LES)
of three-dimensional compressible Rayleigh-Taylor (RT) turbulence with miscible fluids at …
of three-dimensional compressible Rayleigh-Taylor (RT) turbulence with miscible fluids at …
Reservoir computing in reduced order modeling for chaotic dynamical systems
AC Nogueira Jr, FCT Carvalho, JLS Almeida… - … Computing: ISC High …, 2021 - Springer
The mathematical concept of chaos was introduced by Edward Lorenz in the early 1960s
while attempting to represent atmospheric convection through a two-dimensional fluid flow …
while attempting to represent atmospheric convection through a two-dimensional fluid flow …