Related papers: On the use of Nonlinear Normal Modes for Nonlinear…

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources respectively, thus playing an important role in assessing sustainability of these systems. However,…

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…

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…

Nowadays, interest in combining mathematical knowledge about phenomena and data from the physical system is growing. Past research was devoted to developing so-called high-fidelity models, intending to make them able to catch most of the…

A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…

Model order reduction aims to determine a low-order approximation of high-order models with least possible approximation errors. For application to physical systems, it is crucial that the reduced order model (ROM) is robust to any…

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…

The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…

In this paper, we combine convolutional neural networks (CNNs) with reduced order modeling (ROM) for efficient simulations of multiscale problems. These problems are modeled by partial differential equations with high-dimensional random…

A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective…

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

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…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…