Physics-Informed Neural Networks for Engineering Problems: Challenges of the Application to 3D Stirred Tank Reactors
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Physics-Informed Neural Networks (PINNs), first proposed by Raissi et al. [1], have been the subject of extensive research due to their ability to simultaneously exploit both the available data and the knowledge of the underlying physics of the problem at hand. In PINNs, the governing equations are embedded in the loss function of the neural network, which makes them attractive for applications where data is typically sparse and costly to obtain and the governing equations are known. In the recent years, a variety of extensions and modifications to the vanilla PINN have been proposed [2]. However, their capabilities and eficiency are mostly demonstrated on benchmark test cases in computational domains with simple geometries. The application of PINNs to engineering problems in complex 3D domains remains a challenge. Stirred Tank Reactors (STRs) play a central role in biotechnological process development and manufacturing. Models of STRs can be used both to minimize the amount of supporting experimental studies required during process design and scale-up, and to deepen the understanding of conditions inside a reactor, where little information is available due to the lack of appropriate measurement techniques. For this purpose, Computational Fluid Dynamics (CFD) tools are already widely used in the industry. However, the high computational cost of high fidelity simulations, especially in scenarios, where the same model must be solved repeatedly for different parameter values (such as stirring rate), motivates the construction of less computationally intensive Reduced Order Models (ROMs) to approximate solutions. This use case represents a particular challenge for PINNs due to the geometric complexity of the computational domain and the large variety of phenomena involved in the process (e.g., turbulence,mass transfer). Building on the investigation of strategies to improve the predictive accuracy of the model, for example by imposing boundary constraints in a postprocessing step using an interpolation spline as proposed in [3] or by leveraging additional knowledge of the problem, such as domain decomposition based on the different character of the flow in different parts of the domain, we aim to apply the approaches tested in 2D to more realistic 3D models. Our overarching goal is to explore the feasibility of PINNs as robust and reproducible ROMs for addressing complex 3D engineering problems.