Related papers: Deep-HyROMnet: A deep learning-based operator appr…

A new deep-learning-based reduced-order modeling (ROM) framework is proposed for application in subsurface flow simulation. The reduced-order model is based on an existing embed-to-control (E2C) framework and includes an auto-encoder, which…

Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…

Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order…

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…

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…

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…

We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies…

Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlinear conservation laws utilize full order models (FOMs) based…

Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…

In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in…

Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle high-dimensional data, approximate highly nonlinear…

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…

Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of high-dimensional, parametric systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs…

The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…

This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…