Related papers: Model Reduction for Large Scale Systems
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced…
There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which proposes the use of pre-trained predictive…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin and stochastic collocations methods. This work is…
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment or blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale…
High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization,…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…
Protein structure prediction has been a grand challenge for over 50 years, owing to its broad scientific and application interests. There are two primary types of modeling algorithms, template-free modeling and template-based modeling. The…
Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried…
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…
We consider the problem of model reduction of parametrized PDEs where the goal is to approximate any function belonging to the set of solutions at a reduced computational cost. For this, the bottom line of most strategies has so far been…
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…
Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential…
Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…
The Kolmogorov $n$-width is an established benchmark to judge the performance of reduced basis and similar methods that produce linear reduced spaces. Although immensely successful in the elliptic regime, this width, shows unsatisfactory…
This paper presents a novel theoretical framework for reducing the computational complexity of multi-model adaptive control/estimation systems through systematic transformation to controllable canonical form. While traditional multi-model…