Related papers: A Methodology for Projection-Based Model Reduction…
We present a model reduction approach for the real-time solution of time-dependent nonlinear partial differential equations (PDEs) with parametric dependencies. The approach integrates several ingredients to develop efficient and accurate…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective…
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…
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…
A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…
This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon the prior research incorporating a data-driven finite-difference approximation of smooth solutions…
We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
Despite the success of model predictive control (MPC), its application to high-dimensional systems, such as flexible structures and coupled fluid/rigid-body systems, remains a largely open challenge due to excessive computational…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Often, such systems arise from the discretization of operator…
We present a model predictive control (MPC) framework for linear switched evolution equations arising from a parabolic partial differential equation (PDE). First-order optimality conditions for the resulting finite-horizon optimal control…
Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…