Partial Differential Equations (PDEs) are notoriously difficult to solve . In general, closed-form solutions are not available and numerical approximationschemes are computationally expensive . In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches . We leverage theadvantages of both of these approaches by using Hermite spline kernels in orderto continuously interpolate a grid-based state representation . This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains . Our models are able to learn several intriguing phenomenasuch as Karman vortex streets, the Magnus effect, the Doppler effect and wave reflections. Our quantitative assessment and an interactivereal-time demo show that we are narrowing the gap in accuracy of unsupervisedML based methods to industrial CFD solvers while being orders of magnitudefaster. Our method is narrowing in accuracy to industrial CED solvers and is orders of magnitudeefaster .

Author(s) : Nils Wandel, Michael Weinmann, Michael Neidlin, Reinhard Klein

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Keywords : based - pdes - spline - informed - industrial -

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