Related papers: A micro-macro decomposed reduced basis method for …
A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of…
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…
Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…
High-performance computing (HPC) has revolutionized our ability to perform detailed simulations of complex real-world processes. A prominent contemporary example is from aerospace propulsion, where HPC is used for rotating detonation rocket…
While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to…
We propose and test the first Reduced Radial Basis Function Method (R$^2$BFM) for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
Model reduction attempts to guarantee a desired "model quality", e.g. given in terms of accuracy requirements, with as small a model size as possible. This article highlights some recent developments concerning this issue for the so called…
A multi-fidelity framework is established and demonstrated for prediction of combustion instabilities in rocket engines. The major idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…
This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs…
Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…
Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic…
This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale…
While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…