
Towards 3D Surrogate Model of Flow in Stirred Tank Reactors Using Physics-Informed Neural Networks
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Stirred Tank Reactors (STRs) are essential in biotechnological production and process development. Due to limitations in experimental measurement techniques within these reactors, accurately modeling flow behavior is critical for optimizing process design and scale-up. While Computational Fluid Dynamics (CFD) simulations are widely used for this purpose, their high computational cost – especially when solving the same model for varying operating conditions (e.g., stirring rate) – highlights the need for surrogate models that can provide both efficient and accurate flow field approximations. Physics-Informed Neural Networks (PINNs), first introduced by Raissi et al. [1], have shown significant potential as surrogate models for engineering problems by integrating both data and governing physics through the neural network’s loss function. Although numerous modifications and enhancements to the original PINN framework have been proposed, e.g., [2], applying PINNs to complex 3D engineering problems, particularly in geometrically intricate domains, remains a challenge. This work focuses on developing a 3D surrogate model of the flow field in a stirred tank reactor using PINNs. The modeling of impeller rotation, the complexity of the domain geometry and the distinct flow characteristics across different regions of the reactor pose significant challenges. To address these, we investigate techniques such as adaptive loss scaling to balance competing terms in the loss function, hard enforcement of boundary conditions, and domain decomposition strategies. Building on previous studies conducted with a simplified 2D test case [3], our goal is to assess the feasibility of constructing a robust and efficient 3D surrogate model that accurately approximates the flow field in stirred tanks using PINNs. REFERENCES [1] M. Raissi, P. Perdikaris, and G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686-707, 2019. [2] S. Wang, S. Sankaran, H. Wang, and P. Perdikaris, An Expert's Guide to Training Physics-informed Neural Networks. arXiv:2308.08468v1, 2023. [3] V. Trávníková, D. Wolff, N. Dirkes, S. Elgeti, E. von Lieres and M. Behr, A model hierarchy for predicting the flow in stirred tanks with physics-informed neural networks. Advances in Computational Science and Engineering, 2:91-129, 2024.