2021/03/19 by Lukas Harsch, Harsch, Lukas, Johannes Burgbacher +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Artificial Intelligence (cs.AI) #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2103.10805
openalex publication_date 2021/03/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The interaction of neural networks with physical equations offers a wide\nrange of applications. We provide a method which enables a neural network to\ntransform objects subject to given physical constraints. Therefore an U-Net\narchitecture is used to learn the underlying physical behaviour of fluid flows.\nThe network is used to infer the solution of flow simulations, which will be\nshown for a wide range of generic channel flow simulations. Physical meaningful\nquantities can be computed on the obtained solution, e.g. the total pressure\ndifference or the forces on the objects. A Spatial Transformer Network with\nthin-plate-splines is used for the interaction between the physical constraints\nand the geometric representation of the objects. Thus, a transformation from an\ninitial to a target geometry is performed such that the object is fulfilling\nthe given constraints. This method is fully differentiable i.e., gradient\ninformations can be used for the transformation. This can be seen as an inverse\ndesign process. The advantage of this method over many other proposed methods\nis, that the physical constraints are based on the inferred flow field\nsolution. Thus, we have a transferable model which can be applied to varying\nproblem setups and is not limited to a given set of geometry parameters or\nphysical quantities.\n