% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{Trvnkov:1048793,
      author       = {Trávníková, Veronika and von Lieres, Eric and Behr,
                      Marek},
      title        = {{Q}uantifying data needs in surrogate modeling for flow
                      fields in two-dimensional stirred tanks with
                      physics-informed neural networks},
      publisher    = {arXiv},
      reportid     = {FZJ-2025-04908},
      year         = {2025},
      abstract     = {Stirred tanks are vital in chemical and biotechnological
                      processes, particularly as bioreactors. Although
                      computational fluid dynamics (CFD) is widely used to model
                      the flow in stirred tanks, its high computational
                      cost$-$especially in multi-query scenarios for process
                      design and optimization$-$drives the need for efficient
                      data-driven surrogate models. However, acquiring
                      sufficiently large datasets can be costly. Physics-informed
                      neural networks (PINNs) offer a promising solution to reduce
                      data requirements while maintaining accuracy by embedding
                      underlying physics into neural network (NN) training. This
                      study quantifies the data requirements of vanilla PINNs for
                      developing surrogate models of a flow field in a 2D stirred
                      tank. We compare these requirements with classical
                      supervised neural networks and boundary-informed neural
                      networks (BINNs). Our findings demonstrate that surrogate
                      models can achieve prediction errors around 3\% across
                      Reynolds numbers from 50 to 5000 using as few as six
                      datapoints. Moreover, employing an approximation of the
                      velocity profile in place of real data labels leads to
                      prediction errors of around 2.5\%. These results indicate
                      that even with limited or approximate datasets, PINNs can be
                      effectively trained to deliver high accuracy comparable to
                      high-fidelity data.},
      keywords     = {Computational Engineering, Finance, and Science (cs.CE)
                      (Other) / FOS: Computer and information sciences (Other) /
                      76-10, 68T07 (Primary) 76D05, 35Q68 (Secondary) (Other)},
      cin          = {IBG-1},
      cid          = {I:(DE-Juel1)IBG-1-20101118},
      pnm          = {2172 - Utilization of renewable carbon and energy sources
                      and engineering of ecosystem functions (POF4-217)},
      pid          = {G:(DE-HGF)POF4-2172},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2507.11640},
      url          = {https://juser.fz-juelich.de/record/1048793},
}