Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques

Abstract

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of $\mathrm{C}{\mathrm{O}}_2$ sequestration). Here, we present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. We present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of $7\times 10^6$ because our framework is not bound by the Courant-Friedrichs-Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model's accuracy still lies within a mean squared error of 0.07 (two-order of magnitude lower than the maximum value of the finite element results) in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) or t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

References in corpus (19)

• Semi-Supervised Classification with Graph Convolutional Networks
• A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
• Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations
• Assessment of unsteady flow predictions using hybrid deep learning based reduced order models
• An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion
• Non-Intrusive Reduced-Order Modeling Using Uncertainty-Aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to Flood Modeling
• Component-wise reduced order model lattice-type structure design
• Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction
• Reduced order models for Lagrangian hydrodynamics
• Accelerating design optimization using reduced order models
• A Locally Conservative Mixed Finite Element Framework for Coupled Hydro-Mechanical-Chemical Processes in Heterogeneous Porous Media
• Efficient nonlinear manifold reduced order model
• On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis
• An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques
• Applying Convolutional Neural Networks to Data on Unstructured Meshes with Space-Filling Curves
• Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation
• A non-intrusive data-driven ROM framework for hemodynamics problems
• Non-intrusive Surrogate Modeling for Parametrized Time-dependent PDEs using Convolutional Autoencoders
• Learning to regularize with a variational autoencoder for hydrologic inverse analysis

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