Related papers: Reduced-order modeling for stochastic large-scale …
Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modeling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To…
Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…
In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-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…
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…
Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…
We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…
In this work, a new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. This algorithm is based on a dimensionality reduction using Proper Orthogonal Decomposition (POD) combined with deep learning…
In recent years, deep learning has gained increasing popularity in the fields of Partial Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain practitioners with new powerful data-driven techniques such as…
We propose a novel stochastic reduced-order model (SROM) for complex systems by combining clustering and classification strategies. Specifically, the distance and centroid of centroidal Voronoi tessellation (CVT) are redefined according to…
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…
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…
This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced…
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…
A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
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…