Related papers: A deep learning based reduced order modeling for s…

In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational…

In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3D heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural…

In this paper, we present two adaptive methods for the basis enrichment of the mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving the flow problem in heterogeneous media. We develop an a-posteriori error indicator which…

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

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…

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved…

Federated learning increasingly operates in a large-model regime where communication, memory, and computation are all scarce. Typically, non-IID client data induce drift that degrades the stability and performance of local training.…

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

In this paper, we present two deep learning-based hybrid data-driven reduced order models for the prediction of unsteady fluid flows. The first model projects the high-fidelity time series data from a finite element Navier-Stokes solver to…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…

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…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…

We present a method to construct reduced-order models for duct flows of Bingham media. Our method is based on proper orthogonal decomposition (POD) to find a low-dimensional approximation to the velocity and artificial neural network to…

In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…