Related papers: Linear model reduction using spectral proper ortho…
A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…
Sparse coding (Sc) has been studied very well as a powerful data representation method. It attempts to represent the feature vector of a data sample by reconstructing it as the sparse linear combination of some basic elements, and a $L_2$…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…
In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…
Strong correlations between explanatory variables are problematic for high-dimensional regularized regression methods. Due to the violation of the Irrepresentable Condition, the popular LASSO method may suffer from false inclusions of…
We address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the unknown system. We assume that the desired PDE is…
Quantum computing is a promising technology for accelerating partial differential equation solvers applied to large-scale real-world problems. However, reconstructing a classical representation of the solution from the quantum state remains…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…
Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…
Many problems in causal inference and economics can be formulated in the framework of conditional moment models, which characterize the target function through a collection of conditional moment restrictions. For nonparametric conditional…
Coordinated optimization dispatch (COD) of transmission system operator (TSO) and distribution system operator (DSO) can effectively ensure system security and efficiency under high-penetration distributed energy resource (DER) integration.…
This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…
This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…
Diffusion models have significantly advanced the state of the art in image, audio, and video generation tasks. However, their applications in practical scenarios are hindered by slow inference speed. Drawing inspiration from the…
The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
We study deep state-space models (Deep SSMs) that contain linear quadratic-output (LQO) systems as internal blocks and present a compression method with a provable output error guarantee. We first derive an upper bound on the output error…
Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design,…