Related papers: A Quadratic Manifold for Model Order Reduction of …
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
This paper presents the first application of the direct parametrisation method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field.…
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,…
Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…
In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…
Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…
In this work, Galerkin projection is used to build Reduced Order Models (ROM) for two-dimensional Rayleigh-B\'enard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…
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…
We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…
I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…
Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…