Transferable Model for Shape Optimization subject to Physical Constraints

TL;DR

This paper introduces a transferable neural network model that integrates physical constraints into shape optimization for fluid flows, enabling inverse design and adaptable applications across different geometries and physical scenarios.

Contribution

The authors develop a fully differentiable model combining U-Net and Spatial Transformer Networks to incorporate physical constraints into shape optimization, allowing for versatile inverse design in fluid dynamics.

Findings

The model accurately predicts flow solutions for various channel geometries.

Physical constraints based on flow solutions improve shape optimization.

The approach is transferable across different physical setups.

Abstract

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture is used to learn the underlying physical behaviour of fluid flows. The network is used to infer the solution of flow simulations, which will be shown for a wide range of generic channel flow simulations. Physical meaningful quantities can be computed on the obtained solution, e.g. the total pressure difference or the forces on the objects. A Spatial Transformer Network with thin-plate-splines is used for the interaction between the physical constraints and the geometric representation of the objects. Thus, a transformation from an initial to a target geometry is performed such that the object is fulfilling the given constraints. This method is fully differentiable i.e., gradient informations can be used for the transformation. This can be seen as an inverse design process. The advantage of this method over many other proposed methods is, that the physical constraints are based on the inferred flow field solution. Thus, we have a transferable model which can be applied to varying problem setups and is not limited to a given set of geometry parameters or physical quantities.