NNWarp is a highly re-usable and efficient neural network (NN) based nonlinear deformable simulation framework. Unlike other machine learning applications such as image recognition, where different inputs have a uniform and consistent format (e.g. an array of all the pixels in an image), the input for deformable simulation is quite variable, high-dimensional, and parametrization-unfriendly. Consequently, even though the neural network is known for its rich expressivity of nonlinear functions, directly using an NN to reconstruct the force-displacement relation for general deformable simulation is nearly impossible. NNWarp obviates this difficulty by partially restoring the force-displacement relation via warping the nodal displacement simulated using a simplistic constitutive model - the linear elasticity. In other words, NNWarp yields an incremental displacement fix per mesh node based on a simplified (therefore incorrect) simulation result other than synthesizing the unknown displacement directly. We introduce a compact yet effective feature vector including geodesic, potential and digression to sort training pairs of per-node linear and nonlinear displacement. NNWarp is robust under different model shapes and tessellations. With the assistance of deformation substructuring, one NN training is able to handle a wide range of 3D models of various geometries. Thanks to the linear elasticity and its constant system matrix, the underlying simulator only needs to perform one pre-factorized matrix solve at each time step, which allows NNWarp to simulate large models in real time.

中文翻译：

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NNWarp：基于神经网络的非线性变形。

NNWarp是一个基于高度可重用和高效的神经网络（NN）的非线性可变形仿真框架。与其他机器学习应用程序（例如图像识别）不同，在这些应用程序中，不同的输入具有统一且一致的格式（例如，图像中所有像素的阵列），用于可变形模拟的输入具有很大的可变性，高维和参数化不友好。因此，即使神经网络以其丰富的非线性函数表达能力而闻名，直接使用NN来重构力-位移关系以进行一般的可变形仿真也是几乎不可能的。NNWarp通过扭曲使用简单本构模型（线性弹性）模拟的节点位移来部分恢复力-位移关系，从而避免了这一难题。换一种说法，NNWarp基于简化（因此不正确）的模拟结果，而不是直接合成未知位移，会为每个网格节点生成增量位移固定。我们引入了一个紧凑但有效的特征向量，包括测地线，势能和离题，以对每个节点的线性和非线性位移的训练对进行排序。NNWarp在不同的模型形状和曲面细分下具有鲁棒性。借助变形子结构，一次NN训练就能处理各种几何形状的3D模型。得益于线性弹性及其恒定的系统矩阵，底层的仿真器仅需在每个时间步执行一个预先分解的矩阵求解，即可使NNWarp实时仿真大型模型。