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We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity…

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

Computational physics simulation can be a powerful tool to accelerate industry deployment of new scientific technologies. However, it must address the challenge of computationally tractable, moderately accurate prediction at large industry…

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…

We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a…

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 analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

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…

This work aims to advance computational methods for projection-based reduced order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a…

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…

Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…