mlsanityData to 7 Oct 2026

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

arXiv 2107.11460 ↗First posted 23 Jul 2021cs.CE cs.LG cs.NAcited by 23

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Abstract (arXiv)

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO2 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 × 106 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.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 22 of its 116 references that are in the map. First posted on arXiv 23 Jul 2021.

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22 of 116 references.

References · 22

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10 more
  1. 2020An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusioncited by 19
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 7; 2024: 2; 2025: 1; 2026: 4.

23 papers.

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  2. 2023Weak-Form Latent Space Dynamics Identificationcited by 20
  3. 2022Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materialscited by 17
  4. 2022Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencodercited by 15
  5. 2023Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifoldscited by 13
  6. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  7. 2022Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learningcited by 12
  8. 2023Reduced-order modeling for parameterized PDEs via implicit neural representationscited by 7
  9. 2022textitFastSVD-ML-ROM: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applicationscited by 5
  10. 2022Certified data-driven physics-informed greedy auto-encoder simulatorcited by 4
  11. 2022An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipescited by 3
  12. 2022AI-enhanced iterative solvers for accelerating the solution of large scale parametrized systemscited by 3
11 more
  1. 2023Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencodercited by 3
  2. 2024System stabilization with policy optimization on unstable latent manifoldscited by 2
  3. 2025Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decompositioncited by 2
  4. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  5. 2022Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compressioncited by 1
  6. 2023Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfercited by 0
  7. 2023Efficient machine-learning surrogates for large-scale geological carbon and energy storagecited by 0
  8. 2023Online Two-stage Thermal History Prediction Method for Metal Additive Manufacturing of Thin Wallscited by 0
  9. 2026Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approachcited by 0
  10. 2026Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamicscited by 0
  11. 2026HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networkscited by 0