Related papers: Nonlinear Model Order Reduction via Lifting Transf…
Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…
Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…
This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…
A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Deep-learning-based nonlinear system identification has shown the ability to produce reliable and highly accurate models in practice. However, these black-box models lack physical interpretability, and a considerable part of the learning…
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear…
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…
Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…