mlsanityData to 7 Oct 2026

Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks

arXiv 2204.07413 ↗First posted 15 Apr 2022math.NA cs.LG cs.NAcited by 4

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Abstract (arXiv)

We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process, and to provide error correction and stabilization mechanisms. In addition, to compensate for decrease of observer's performance due to the presence of unknown destabilizing forcing, the network is designed to estimate the contribution of the unknown forcing implicitly from the data over the course of training. By running a set of numerical experiments, we demonstrate that the proposed network does recover unknown forcing from data and is capable of predicting turbulent flows in high resolution from low resolution noisy observations.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 9 of its 18 references that are in the map. First posted on arXiv 15 Apr 2022.

Builds on

9 of 18 references.

References · 9

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  5. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  6. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
  7. 2020Understanding and mitigating gradient pathologies in physics-informed neural networkscited by 134
  8. 2016Accelerating Eulerian Fluid Simulation With Convolutional Networkscited by 128
  9. 2020MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Frameworkcited by 78

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Cited by year

Citing papers per year: 2023: 2; 2024: 2.

4 papers.

  1. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  2. 2024Wavelet Diffusion Neural Operatorcited by 28
  3. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  4. 2023A 3D super-resolution of wind fields via physics-informed pixel-wise self-attention generative adversarial networkcited by 0