An Image Generator Enhanced Deep Operator Network for Predicting the Geometry Deformations in Contact Problems With Random Rough Surfaces

Abstract Optimizing the geometry deformation characteristics in contact problems with random rough surfaces is an important component of improving product performance, such as assembly accuracy, sealing percolation, contact thermal resistance, and electrical resistance. Traditionally, the deformation is computed by numerically solving the partial differential equations that govern the contact problems. In the optimization process, the deformations under a variety of random rough surfaces need to be solved. It is computationally intensive and necessitates a surrogate model to approximate the numerical solutions. This study employs non-uniform rational B-splines (NURBS) to represent the geometries involved in the contact problem and proposes treating the NURBS control points as image pixels, treating the deformations of these points as image pixel values. Furthermore, an image generator-enhanced deep operator network (IGE-DeepONet) that leverages an image generator as a trunk net is proposed to predict the deformations and a concatenation-based information fusion mechanism between the trunk net and branch net of the DeepONet was developed to improve the prediction accuracy. Based on the contact problem between a smooth elastomer cube and a rigid cuboid with a random rough surface, it was demonstrated that the proposed IGE-DeepONet has smaller test error and reduced training time compared to the standalone image generator and the traditional DeepONet which uses a fully connected neural network as trunk net.