标题： 接触可变形体的图神经网络代理模型及其必要充分的接触检测 显示英文标题

标题： Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detection

摘要： 用于机械中非线性边值问题快速推断的代理模型在广泛的工程应用中有帮助。 然而，涉及可变形体接触的应用的有效代理建模，特别是在不同几何形状的背景下，仍然是一个开放问题。 特别是，现有方法仅限于刚体接触，或者最多是刚体和具有明确接触平面的柔软物体之间的接触。 此外，它们使用接触或碰撞检测过滤器，作为快速测试，但仅使用必要条件而非充分条件进行检测。 在本工作中，我们提出了一种图神经网络架构，该架构利用连续碰撞检测，并首次引入了为软可变形体之间接触设计的充分条件。 我们在两个基准测试中测试了其性能，包括一个预测生物人工主动脉瓣软组织力学闭合状态的问题。 我们发现，在损失函数中添加额外的接触项具有正则化效果，从而提高了网络的泛化能力。 这些好处适用于相似平面和单元法向角度的简单接触，以及不同平面和单元法向角度的复杂接触。 我们还证明了该框架可以处理不同的参考几何形状。 然而，这种好处伴随着训练期间的高计算成本，导致可能并不总是有利的权衡。 我们量化了在各种硬件架构上的训练成本和由此产生的推理加速。 重要的是，我们的图神经网络实现使我们基准问题的推理速度提高了多达一千倍。 显示英文摘要

摘要： Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable bodies, especially in the context of varying geometries, is still an open issue. In particular, existing methods are confined to rigid body contact or, at best, contact between rigid and soft objects with well-defined contact planes. Furthermore, they employ contact or collision detection filters that serve as a rapid test but use only the necessary and not sufficient conditions for detection. In this work, we present a graph neural network architecture that utilizes continuous collision detection and, for the first time, incorporates sufficient conditions designed for contact between soft deformable bodies. We test its performance on two benchmarks, including a problem in soft tissue mechanics of predicting the closed state of a bioprosthetic aortic valve. We find a regularizing effect on adding additional contact terms to the loss function, leading to better generalization of the network. These benefits hold for simple contact at similar planes and element normal angles, and complex contact at differing planes and element normal angles. We also demonstrate that the framework can handle varying reference geometries. However, such benefits come with high computational costs during training, resulting in a trade-off that may not always be favorable. We quantify the training cost and the resulting inference speedups on various hardware architectures. Importantly, our graph neural network implementation results in up to a thousand-fold speedup for our benchmark problems at inference.