Deep learning combined with physics-based modeling represents an attractive and efficient approach for producing accurate and robust surrogate modeling. In this paper, a new framework that utilizes Physics Informed Neural Networks (PINN) to solve PDE-based problems for the creation of surrogate models for steady-state flow-thermal engineering design applications is introduced. The surrogate models developed through this framework are demonstrated on several use cases from electronics cooling to biomechanics. Additionally, it is demonstrated how these trained surrogate models can be combined with design optimization methods to improve the efficiency and reduced the cost of the design process. The former is shown through several realistic 3D examples and the latter via a detailed cost-benefit trade off. Overall, the findings of this paper demonstrate that hybrid data-PINN surrogate models combined with optimization algorithms can solve realistic design optimization and have potential in a wide variety of application areas.

翻译：深度学习与基于物理的建模相结合，是生成精确且鲁棒的代理模型的一种有前景且高效的方法。本文提出了一种新框架，利用物理信息神经网络（PINN）求解基于偏微分方程的问题，为稳态流动-热工程设计应用创建代理模型。通过该框架开发的代理模型在从电子冷却到生物力学的多个用例中得到了验证。此外，本文展示了如何将这些训练的代理模型与设计优化方法结合，以提高设计流程效率并降低成本。前者通过多个逼真的三维示例进行验证，后者则通过详细的成本效益权衡分析加以说明。总体而言，本文的研究结果表明，混合数据-PINN代理模型与优化算法相结合，能够解决现实设计优化问题，并在广泛的应用领域中具有潜力。