The design of strongly coupled multidisciplinary engineering systems is challenging since it is characterized by the complex interaction of different disciplines. Such complexity cannot be easily captured by explicit analytical solutions, which motivates the development of a surrogate model. Deep learning (DL) has gained considerable interest among existing surrogate modeling techniques because of the flexible non-linear formulation, comparability to data format diversity, and applicability to data-driven analysis. Notably, a convolution neural network (CNN) has been employed in multifold research to ameliorate the prediction accuracy of the surrogate model once images representing physical phenomena are utilized. Nevertheless, it is still questionable to guarantee the feasibility of the CNN-based surrogate model in the multi-physics domain due to (1) unreliable correlation representation between multi-domain design parameters and the coupled responses and (2) massive training costs.

To address those issues, therefore, this research proposes a framework of CNN-based deep surrogate model (DSM), developing a novel input structure called physics-informed artificial image (PiAI). PiAI incubates (1) geometry-informed CAD representing physical uncertainties of engineering systems, (2) location-clarified filter improving CNN training accuracy, and (3) simulation conditions essentially required in the multi-physics analysis, which reinforces the prediction credibility. Moreover, in lieu of employing multi-modalities or multiple image channels, the proposed method applies unimodal-based single image inputs to escalate computational efficiency. The proposed framework’s efficacy and applicability are addressed in practical engineering design applications: a cantilever beam and a stretchable strain sensor.

强耦合多学科工程系统的设计具有挑战性，因为它的特点是不同学科之间的复杂相互作用。这种复杂性无法通过显式分析解决方案轻松捕获，这激发了代理模型的开发。由于灵活的非线性公式、与数据格式多样性的可比性以及对数据驱动分析的适用性，深度学习 (DL) 在现有代理建模技术中引起了极大的兴趣。值得注意的是，一旦利用代表物理现象的图像，卷积神经网络 (CNN) 已被用于多项研究，以提高替代模型的预测精度。尽管如此，

因此，为了解决这些问题，本研究提出了一个基于 CNN 的深度代理模型 (DSM) 框架，开发了一种称为物理信息人工图像 (PiAI) 的新型输入结构。PiAI 孵化 (1) 表示工程系统物理不确定性的几何信息 CAD，(2) 提高 CNN 训练精度的位置澄清滤波器，以及 (3) 多物理分析中必不可少的模拟条件，这增强了预测的可信度。此外，代替采用多模态或多个图像通道，所提出的方法应用基于单模态的单图像输入来提高计算效率。所提出的框架的功效和适用性在实际工程设计应用中得到解决：悬臂梁和可拉伸应变传感器。