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@ARTICLE{Sarma:1031510,
      author       = {Sarma, Rakesh and Hübenthal, Fabian and Inanc, Eray and
                      Lintermann, Andreas},
      title        = {{P}rediction of {T}urbulent {B}oundary {L}ayer {F}low
                      {D}ynamics with {T}ransformers},
      journal      = {Mathematics},
      volume       = {12},
      number       = {19},
      issn         = {2227-7390},
      address      = {Basel},
      publisher    = {MDPI},
      reportid     = {FZJ-2024-05711},
      pages        = {2998},
      year         = {2024},
      abstract     = {Time-marching of turbulent flow fields is computationally
                      expensive using traditional Computational Fluid Dynamics
                      (CFD) solvers. Machine Learning (ML) techniques can be used
                      as an acceleration strategy to offload a few time-marching
                      steps of a CFD solver. In this study, the Transformer (TR)
                      architecture, which has been widely used in the Natural
                      Language Processing (NLP) community for prediction and
                      generative tasks, is utilized to predict future velocity
                      flow fields in an actuated Turbulent Boundary Layer (TBL)
                      flow. A unique data pre-processing step is proposed to
                      reduce the dimensionality of the velocity fields, allowing
                      the processing of full velocity fields of the actuated TBL
                      flow while taking advantage of distributed training in a
                      High Performance Computing (HPC) environment. The trained
                      model is tested at various prediction times using the
                      Dynamic Mode Decomposition (DMD) method. It is found that
                      under five future prediction time steps with the TR, the
                      model is able to achieve a relative Frobenius norm error of
                      less than $5\%,$ compared to fields predicted with a Large
                      Eddy Simulation (LES). Finally, a computational study shows
                      that the TR achieves a significant speed-up, offering
                      computational savings approximately 53 times greater than
                      those of the baseline LES solver. This study demonstrates
                      one of the first applications of TRs on actuated TBL flow
                      intended towards reducing the computational effort of
                      time-marching. The application of this model is envisioned
                      in a coupled manner with the LES solver to provide few
                      time-marching steps, which will accelerate the overall
                      computational process.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / RAISE - Research on
                      AI- and Simulation-Based Engineering at Exascale (951733)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(EU-Grant)951733},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001331954100001},
      doi          = {10.3390/math12192998},
      url          = {https://juser.fz-juelich.de/record/1031510},
}