We present a non-intrusive gradient algorithm for parameter estimation problems in non-stationary elasticity. To avoid multiple (and potentially expensive) solutions of the underlying partial differential equation (PDE), we approximate the PDE solver by a neural network within the gradient algorithm. The network is trained offline for a given set of parameters. The algorithm is applied to an unsteady linear-elastic contact problem; its convergence and approximation properties are investigated numerically.

翻译：本文提出了一种用于非平稳弹性参数估计问题的非侵入式梯度算法。为避免重复（且可能代价高昂地）求解底层偏微分方程，我们在梯度算法中利用神经网络近似替代偏微分方程求解器。该网络针对给定参数集进行离线训练。本算法应用于非稳态线弹性接触问题，并通过数值实验验证了其收敛性与逼近性能。