NNWarp: Neural Network-Based Nonlinear Deformation
NNWarp: Neural Network-Based Nonlinear Deformation
复制标题
NNWarp：基于神经网络的非线性变形
DOI：
10.1109/tvcg.2018.2881451
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发表时间：
2020-04-01
影响因子：
5.2
通讯作者：
Yang, Yin
中科院分区：
文献类型：
--
作者：
Luo, Ran;Shao, Tianjia;Yang, Yin
NNWarp是一个高度可重用且高效的基于神经网络（NN）的非线性可变形仿真框架。与图像识别等其他机器学习应用不同，不同的输入具有统一和一致的格式（例如，图像中所有像素的阵列），用于可变形模拟的输入是相当可变的、高维的并且参数化不友好。因此，即使神经网络以其丰富的非线性函数的表达能力而闻名，直接使用神经网络来重建一般变形模拟的力-位移关系几乎是不可能的。NNWarp通过扭曲使用简单的本构模型-线弹性模拟的节点位移来部分恢复力-位移关系，从而避免了这一困难。换句话说，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，为每个网格节点生成增量位移固定。我们引入了一个紧凑而有效的特征向量，包括测地线，潜在的和离题排序训练对每个节点的线性和非线性位移。NNWarp在不同的模型形状和细分下都是鲁棒的。在变形子结构的帮助下，一个NN训练能够处理各种几何形状的各种3D模型。由于线性弹性及其恒定的系统矩阵，底层模拟器只需在每个时间步长执行一次预分解矩阵求解，这使得NNWarp能够真实的模拟大型模型。
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.