High-order differentiable autoencoder for nonlinear model reduction
High-order differentiable autoencoder for nonlinear model reduction
复制标题
用于非线性模型简化的高阶可微自动编码器
DOI：
10.1145/3450626.3459754
复制
发表时间：
2021
影响因子：
6.2
通讯作者：
Zhou, Kun
中科院分区：
文献类型：
--
作者：
Shen, Siyuan;Yang, Yin;Shao, Tianjia;Wang, He;Jiang, Chenfanfu;Lan, Lei;Zhou, Kun
本文为利用深度神经网络改进基于物理的模拟提供了一条新的途径。具体地说，我们将经典的拉格朗日力学与深度自动编码器相结合，以加速对可变形实体的弹性模拟。由于惯性效应的影响，如果不评估深度自动编码器网络的二阶导数，就无法建立动态平衡。这超出了主要关注梯度评估的现成自动判别包和算法的能力。如果要使用标准的牛顿方法，求解非线性力平衡就更具挑战性。这是因为我们需要计算网络的三阶导数来获得变分黑森。我们通过利用复步有限差分结合反向自动微分来解决这些困难。这一策略使我们能够享受复步有限差分的便利性和准确性，同时，尽可能集中地部署复值摄动，以节省过多的网络遍数。通过基于GPU的实现，我们能够实时地使用具有相对高维潜在空间的深度自动编码器(例如，层)。沿着这条管道，我们还设计了一个采样网络和一个加权网络来实现变权立方体积分，以便在模型降阶中引入非线性。我们相信，这项工作将启发和有益于未来在非线性简化物理模拟问题方面的研究工作。
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids. Due to the inertia effect, the dynamic equilibrium cannot be established without evaluating the second-order derivatives of the deep autoencoder network. This is beyond the capability of off-the-shelf automatic differentiation packages and algorithms, which mainly focus on the gradient evaluation. Solving the nonlinear force equilibrium is even more challenging if the standard Newton's method is to be used. This is because we need to compute a third-order derivative of the network to obtain the variational Hessian. We attack those difficulties by exploiting complex-step finite difference, coupled with reverse automatic differentiation. This strategy allows us to enjoy the convenience and accuracy of complex-step finite difference and in the meantime, to deploy complex-value perturbations as collectively as possible to save excessive network passes. With a GPU-based implementation, we are able to wield deep autoencoders (e.g.,layers) with a relatively high-dimension latent space in real-time. Along this pipeline, we also design a sampling network and a weighting network to enable \emph{weight-varying} Cubature integration in order to incorporate nonlinearity in the model reduction. We believe this work will inspire and benefit future research efforts in nonlinearly reduced physical simulation problems.