Related papers: Decreasing the temporal complexity for nonlinear, …

In system identification, it is often difficult to find a physical intuition to choose a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, 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…

Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…

We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the…

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

POD--Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam…

When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

In design of optical systems based on LED (Light emitting diode) technology, a crucial task is to handle the unstructured data describing properties of optical elements in standard formats. This leads to the problem of data fitting within…

Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

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…

This paper deals with the problem of predicting the future state of discrete-time input-delayed systems in the presence of unknown disturbances that can affect both the state and the output equations of the plant. Since the disturbance is…

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…

Reducing the computational time required by high-fidelity, full order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. While FOMs,…

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…