mlsanityData to 7 Oct 2026

A Latent space solver for PDE generalization

arXiv 2104.02452 ↗First posted 6 Apr 2021cs.LGcited by 4

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Abstract (arXiv)

In this work we propose a hybrid solver to solve partial differential equation (PDE)s in the latent space. The solver uses an iterative inferencing strategy combined with solution initialization to improve generalization of PDE solutions. The solver is tested on an engineering case and the results show that it can generalize well to several PDE conditions.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 12 of its 29 references that are in the map. First posted on arXiv 6 Apr 2021.

Builds on

12 of 29 references.

References · 12

  1. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  2. 2021Machine learning accelerated computational fluid dynamicscited by 461
  3. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  4. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  5. 2020Learning to Control PDEs with Differentiable Physicscited by 131
  6. 2018Deep Fluids: A Generative Network for Parameterized Fluid Simulationscited by 121
  7. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  8. 2020Physics-informed deep learning for incompressible laminar flowscited by 54
  9. 2020DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretizationcited by 35
  10. 2020Differentiable Molecular Simulations for Control and Learningcited by 25
  11. 2020Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flowcited by 13
  12. 2020An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradientcited by 13

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 1; 2023: 1; 2024: 1.

4 papers.

  1. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
  2. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  3. 2023LatentPINNs: Generative physics-informed neural networks via a latent representation learningcited by 5
  4. 2021A composable autoencoder-based iterative algorithm for accelerating numerical simulationscited by 3