This paper focuses on surrogate modeling for fast inference of nonlinear boundary value problems in mechanical engineering, especially applications involving contact of deformable bodies. Existing methods are limited to rigid contact or contact between rigid and soft bodies with well-defined contact surfaces, and have limitations in using contact or collision detection filters that only use necessary conditions rather than sufficient conditions. In this study, we present a graph neural network architecture that utilizes continuous collision detection and incorporates sufficient conditions designed for contact between deformable and soft bodies for the first time. We test the performance on two benchmark problems, such as prediction of the closure state of a biomedical aortic valve, and verify the regularization effect that improves generalization performance by adding an additional contact term to the loss function. Although it shows that it can handle a variety of reference geometries, it suffers from high computational cost during training, which trades off with the speedup of inference. We quantitatively analyze the training cost and the speedup of inference on various hardware architectures, and achieve up to 1000x speedup on benchmark problems.
