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A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems

arXiv 2505.10919 ↗First posted 16 May 2025physics.flu-dyn cs.LG stat.MLcited by 0

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Abstract (arXiv)

Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a novel physics-informed spatiotemporal surrogate model for Rayleigh-Benard convection (RBC), a canonical example of convective fluid flow. Our approach combines convolutional neural networks, for spatial dimension reduction, with an innovative recurrent architecture, inspired by large language models, to model long-range temporal dynamics. Inference is penalized with respect to the governing partial differential equations to ensure physical interpretability. Since RBC exhibits turbulent behavior, we quantify uncertainty using a conformal prediction framework. This model replicates key physical features of RBC dynamics while significantly reducing computational cost, offering a scalable alternative to DNS for long-term simulations.

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References · 17

  1. 2014Sequence to Sequence Learning with Neural Networkscited by 2,986
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2015Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcastingcited by 1,436
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  5. 2021Modern Koopman Theory for Dynamical Systemscited by 276
  6. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 150
  7. 2020Understanding and mitigating gradient pathologies in physics-informed neural networkscited by 135
  8. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 126
  9. 2013Learning by Transductioncited by 121
  10. 2019Shape and Time Distortion Loss for Training Deep Time Series Forecasting Modelscited by 70
  11. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
  12. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
5 more
  1. 2020Physics-informed deep learning for incompressible laminar flowscited by 54
  2. 2018Deep Echo State Networks with Uncertainty Quantification for Spatio-Temporal Forecastingcited by 16
  3. 2022Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convectioncited by 10
  4. 2025Solving Turbulent Rayleigh-B'enard Convection using Fourier Neural Operatorscited by 5
  5. 2024On the Efficiency of Convolutional Neural Networkscited by 2

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