mlsanityData to 7 Oct 2026

Applying Machine Learning to Study Fluid Mechanics

arXiv 2110.02083 ↗First posted 5 Oct 2021physics.flu-dyn cs.LGcited by 13

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Abstract (arXiv)

This paper provides a short overview of how to use machine learning to build data-driven models in fluid mechanics. The process of machine learning is broken down into five stages: (1) formulating a problem to model, (2) collecting and curating training data to inform the model, (3) choosing an architecture with which to represent the model, (4) designing a loss function to assess the performance of the model, and (5) selecting and implementing an optimization algorithm to train the model. At each stage, we discuss how prior physical knowledge may be embedding into the process, with specific examples from the field of fluid mechanics.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 32 of its 113 references that are in the map. First posted on arXiv 5 Oct 2021.

Builds on

32 of 113 references.

References · 32

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2021Convex optimizationcited by 2,479
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
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20 more
  1. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
  2. 2018Techniques for Interpretable Machine Learningcited by 237
  3. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 7; 2024: 3; 2025: 0; 2026: 1.

13 papers.

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  1. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  2. 2023A multifidelity approach to continual learning for physical systemscited by 13
  3. 2023XLB: A differentiable massively parallel lattice Boltzmann library in Pythoncited by 11
  4. 2023Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systemscited by 7
  5. 2023How to Control Hydrodynamic Force on Fluidic Pinball via Deep Reinforcement Learningcited by 5
  6. 2024Additive-feature-attribution methods: a review on explainable artificial intelligence for fluid dynamics and heat transfercited by 4
  7. 2022Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networkscited by 3
  8. 2023Physics-Informed Machine Learning of Argon Gas-Driven Melt Pool Dynamicscited by 2
  9. 2022Deep convolutional surrogates and degrees of freedom in thermal designcited by 0
  10. 2023A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulationcited by 0
  11. 2024Towards a Real-Time Simulation of Elastoplastic Deformation Using Multi-Task Neural Networkscited by 0
  12. 2024Upstream flow geometries can be uniquely learnt from single-point turbulence signaturescited by 0
1 more
  1. 2026Physics-guided surrogate learning enables zero-shot control of turbulent wingscited by 0