线性弹性的物理感知深度学习框架
Physics-aware deep learning framework for linear elasticity
摘要：
本文提出了一个高效和强大的数据驱动的深度学习（DL）计算框架开发的线性连续弹性问题。该方法基于物理信息神经网络（PINNs）的基本原理。为了准确地表示场变量，提出了多目标损失函数。它由对应于偏微分方程（PDE）的剩余部分的项，从管理物理学导出的本构关系，各种边界条件，以及数据驱动的物理知识拟合项在问题域中随机选择的配置点。为此，多个密集连接的独立人工神经网络（ANN），每个近似一个字段变量，进行训练，以获得准确的解决方案。几个基准问题，包括Airy解决弹性和Kirchhoff-Love板问题的解决。在准确性和鲁棒性方面的性能说明了当前框架的优越性，显示出与分析解决方案的良好一致性。目前的工作结合了经典方法的优势，这取决于物理信息的分析关系与DL技术在数据驱动的轻量级，但准确和强大的神经网络建设的优越能力。本文开发的模型可以使用最小的网络参数显着提高计算速度，并且易于在不同的计算平台上适应。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
