Sparse Design Field Construction using PINNs
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Surrogate model are widely used methods in aerodynamics for design space exploration and optimization processes. Traditional methods for generating surrogate models, like statistical methods, deep learning based methods, rely on a large amount of data. This makes them computationally expensive and time consuming. To overcome this data burden, we offer a new approach that combines Physics Informed Neural Networks(PINNs) with the classical data based neural networks for constructing surrogate models for design fields that have sparse data. This method allows to construct surrogate models with minimal data. PINNs are introduced as a new approach for solving Partial Differential Equation by adding equations to neural networks as loss function. But they suffer from gradient alignment problem, which this makes PINNs unfeasible for real world problems that contains high frequency features like turbulence, compressibility. We implemented a new training approach using a different splitting scheme from classical methods. In this study we wanted work with a large, industrial scale problem. We worked with a design space for Turbine Cascade Stator blades. Those blades are defined with nine parameters. Our design space splitting as 10/70/20. Only %10 samples are used for data informing, and %70 is used for Physics informing. While &10 represent the sparse data, %70 is defined like a CFD problem with using Dirichlet and Neumann boundary conditions, and flow equations loss at interior in a data free manner. And %20 kept as validation set. We employed PirateNet as our architecture, SOAP as optimizer, for training.
