Related papers: Projection-based model reduction for contact probl…
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact…
The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor…
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…
A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…
In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted…
Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…
In this paper, we consider the problem of model order reduction of stochastic biochemical networks. In particular, we reduce the order of (the number of equations in) the Linear Noise Approximation of the Chemical Master Equation, which is…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
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…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
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…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…