We present a non-intrusive gradient and a non-intrusive BFGS 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 algorithms. The network is trained offline for a given set of parameters. The algorithms are applied to an unsteady linear-elastic contact problem; their convergence and approximation properties are investigated numerically.

翻译：本文针对非稳态弹性参数估计问题，提出了一种无侵入式梯度算法与一种无侵入式BFGS算法。为避免多次（且可能代价高昂地）求解底层偏微分方程，我们在算法中使用神经网络对PDE求解器进行近似。该网络针对给定参数集进行离线训练。算法被应用于非定常线性弹性接触问题；其收敛性与近似特性通过数值实验进行了研究。