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The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…
Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…
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…
Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric…
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…
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…
This paper focuses on addressing challenges posed by non-homogeneous unstructured grids, commonly used in Computational Fluid Dynamics (CFD). Their prevalence in CFD scenarios has motivated the exploration of innovative approaches for…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear…
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…
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…
We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…
Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of $\mathrm{CO_2}$ sequestration). Here, we present a non-intrusive reduced order model of natural…
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…
Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…
Graph self-supervised learning seeks to learn effective graph representations without relying on labeled data. Among various approaches, graph autoencoders (GAEs) have gained significant attention for their efficiency and scalability.…
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…
Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…