mlsanityData to 14 Oct 2026

Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder

arXiv 2307.06816 ↗First posted 10 Jul 2023cs.LG physics.data-an physics.flu-dyncited by 3

Not on the map. Why?

Abstract (arXiv)

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing nonlinear MOR for the parametric interpolation of a nonlinear dynamic system with a significant number of degrees of freedom. LSH-VAE exploits two major changes to the existing networks: a hierarchical deep structure and a hybrid weighted, probabilistic loss function. The enhancements result in a significantly improved accuracy and stability compared against the conventional nonlinear MOR methods, autoencoder, and variational autoencoder. Upon LSH-VAE, a parametric MOR framework is presented based on the spherically linear interpolation of the latent manifold. The present framework is validated and evaluated on three nonlinear and multiphysics dynamic systems. First, the present framework is evaluated on the fluid-structure interaction benchmark problem to assess its efficiency and accuracy. Then, a highly nonlinear aeroelastic phenomenon, limit cycle oscillation, is analyzed. Finally, the present framework is applied to a three-dimensional fluid flow to demonstrate its capability of efficiently analyzing a significantly large number of degrees of freedom. The performance of LSH-VAE is emphasized by comparing its results against that of the widely used nonlinear MOR methods, convolutional autoencoder, and β-VAE. The present framework exhibits a significantly enhanced accuracy to the conventional methods while still exhibiting a large speed-up factor.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 25 of its 59 references that are in the map. First posted on arXiv 10 Jul 2023.

Builds on

25 of 59 references.

References · 25

  1. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  2. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 640
  3. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  4. 2015Generating Sentences from a Continuous Spacecited by 612
  5. 2014Semi-Supervised Learning with Deep Generative Modelscited by 496
  6. 2015Autoencoding beyond pixels using a learned similarity metriccited by 407
  7. 2019Machine Learning for Fluid Mechanicscited by 385
  8. 2016Ladder Variational Autoencoderscited by 318
  9. 2019Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishingcited by 191
  10. 2018Hyperspherical Variational Auto-Encoderscited by 189
  11. 2018Understanding and Improving Interpolation in Autoencoders via an Adversarial Regularizercited by 88
  12. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
13 more
  1. 2023β-Variational autoencoders and transformers for reduced-order modelling of fluid flowscited by 77
  2. 2018Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systemscited by 54
  3. 2019Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamicscited by 45
  4. 2021Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flowscited by 45
  5. 2019Dirichlet Variational Autoencodercited by 43
  6. 2020Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flowscited by 36
  7. 2019Tutorial: Deriving the Standard Variational Autoencoder (VAE) Loss Functioncited by 26
  8. 2021Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniquescited by 23
  9. 2020Efficient nonlinear manifold reduced order modelcited by 17
  10. 2022Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencodercited by 15
  11. 2019Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoderscited by 14
  12. 2017Optimal transport maps for distribution preserving operations on latent spaces of Generative Modelscited by 13
  13. 2023Low-dimensional Data-based Surrogate Model of a Continuum-mechanical Musculoskeletal System Based on Non-intrusive Model Order Reductioncited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 2.

3 papers.

  1. 2024Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networkscited by 1
  2. 2026An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interactioncited by 0
  3. 2026HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networkscited by 0