The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks (PINNs). For an accurate representation of the field variables, a multi-objective loss function is proposed. It consists of terms corresponding to the residual of the governing partial differential equations (PDE), constitutive relations derived from the governing physics, various boundary conditions, and data-driven physical knowledge fitting terms across randomly selected collocation points in the problem domain. To this end, multiple densely connected independent artificial neural networks (ANNs), each approximating a field variable, are trained to obtain accurate solutions. Several benchmark problems including the Airy solution to elasticity and the Kirchhoff-Love plate problem are solved. Performance in terms of accuracy and robustness illustrates the superiority of the current framework showing excellent agreement with analytical solutions. The present work combines the benefits of the classical methods depending on the physical information available in analytical relations with the superior capabilities of the DL techniques in the data-driven construction of lightweight, yet accurate and robust neural networks. The models developed herein can significantly boost computational speed using minimal network parameters with easy adaptability in different computational platforms.

翻译：本文提出了一种高效且鲁棒的数据驱动深度学习计算框架，用于解决线性连续介质弹性问题。该方法基于物理信息神经网络（PINNs）的基本原理。为实现场变量的精确表示，本文提出了一种多目标损失函数，其包含对应于控制偏微分方程（PDE）残差、基于物理特性的本构关系、各类边界条件以及问题域内随机配置点上的数据驱动物理知识拟合项。为此，多个独立的全连接人工神经网络（ANNs）分别逼近每个场变量，通过训练获得精确解。文章求解了多个基准问题，包括弹性力学中的艾里解及基尔霍夫-洛夫板问题。在精度和鲁棒性方面的表现表明，当前框架具有优越性，与解析解吻合良好。本研究将基于物理信息的经典方法优势与深度学习技术在数据驱动构建轻量级、精确且鲁棒神经网络方面的卓越能力相结合。所建立的模型可通过极少的网络参数显著提升计算速度，并易于在不同计算平台上实现适配。