相关论文: Signature-Based Universal Bilinear Approximations …

We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…

We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…

We propose a general --- i.e., independent of the underlying equation --- registration method for parameterized Model Order Reduction. Given the spatial domain $\Omega \subset \mathbb{R}^d$ and a set of snapshots $\{ u^k \}_{k=1}^{n_{\rm…

We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…

In the pursuit of real-time motion planning, a commonly adopted practice is to compute a trajectory by running a planning algorithm on a simplified, low-dimensional dynamical model, and then employ a feedback tracking controller that tracks…

We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the…

Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…

The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…

We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…

We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of…

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

In \cite{ CLEVACKTHI, CLEVACK} an attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness, asymptotic analysis and parameter estimation for fully nonlinear evolutionary game…

During the past decade, Model Order Reduction (MOR) has become key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and computational…

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

Model order reduction (MOR) techniques play a crucial role in the computer-aided design of modern integrated circuits, where they are used to reduce the size of parasitic networks. Unfortunately, the efficient reduction of passive networks…

In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a…

We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…