mlsanityData to 14 Oct 2026

A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling

arXiv 2110.03442 ↗First posted 5 Oct 2021cs.LG cs.NA math.NAcited by 22

Not on the map. Why?

Abstract (arXiv)

The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). Builds on 17 of its 29 references that are in the map. First posted on arXiv 5 Oct 2021.

Builds on

17 of 29 references.

References · 17

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  4. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  5. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,401
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  7. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
  8. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  9. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  10. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  11. 2019Simplifying Graph Convolutional Networkscited by 1,477
  12. 2020Simple and Deep Graph Convolutional Networkscited by 860
5 more
  1. 2017Residual Gated Graph ConvNetscited by 346
  2. 2016A guide to convolution arithmetic for deep learningcited by 185
  3. 2020A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEscited by 105
  4. 2020Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flowscited by 36
  5. 2019PAN: Path Integral Based Convolution for Deep Graph Neural Networkscited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 9; 2024: 4; 2025: 2; 2026: 4.

22 papers.

Sort:

  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 31
  3. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  4. 2023RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operatorcited by 19
  5. 2023Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learningcited by 18
  6. 2022Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencodercited by 15
  7. 2023Canonical and Noncanonical Hamiltonian Operator Inferencecited by 15
  8. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  9. 2023Latent assimilation with implicit neural representations for unknown dynamicscited by 9
  10. 2023Generative Adversarial Reduced Order Modellingcited by 7
  11. 2023Low-dimensional Data-based Surrogate Model of a Continuum-mechanical Musculoskeletal System Based on Non-intrusive Model Order Reductioncited by 6
  12. 2022An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipescited by 3
10 more
  1. 2022AI-enhanced iterative solvers for accelerating the solution of large scale parametrized systemscited by 3
  2. 2024Data-driven identification of latent port-Hamiltonian systemscited by 3
  3. 2024A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEscited by 2
  4. 2025Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systemscited by 2
  5. 2025Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decompositioncited by 2
  6. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  7. 2024Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networkscited by 1
  8. 2026Nonlinear model reduction for transport-dominated problemscited by 1
  9. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  10. 2026Deep Wave Network for Modeling Multi-Scale Physical Dynamicscited by 0