Related papers: Uncertainty quantification for nonlinear solid mec…
Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…
Reduced Order Modeling (ROM) for engineering applications has been a major research focus in the past few decades due to the unprecedented physical insight into turbulence offered by high-fidelity CFD. The primary goal of a ROM is to model…
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires…
Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition…
A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the…
We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated…
High-fidelity simulations of mixing and combustion processes are generally computationally demanding and time-consuming, hindering their wide application in industrial design and optimization. The present study proposes parametric reduced…
Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…
Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is…
In Laser Powder Bed Fusion (LPBF), the applied laser energy produces high thermal gradients that lead to unacceptable final part distortion. Accurate distortion prediction is essential for optimizing the 3D printing process and…
Robust optimization is a method for optimization under uncertainties in engineering systems and designs for applications ranging from aeronautics to nuclear. In a robust design process, parameter variability (or uncertainty) is incorporated…
Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…
In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…
In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…
A long-standing topic in artificial intelligence is the effective recognition of patterns from noisy images. In this regard, the recent data-driven paradigm considers 1) improving the representation robustness by adding noisy samples in…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
Non-intrusive reduced-order modeling techniques are necessary for systems that are simulated using black-box solvers or known only from data. For systems exhibiting large transients and operating far away from equilibria, current…