Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems. They have been particularly effective in the area of inverse problems, where boundary conditions may be ill-defined, and data-absent scenarios, where typical supervised learning approaches will fail. Here, we further explore the use of this modeling methodology to surrogate modeling of a fluid dynamical system, and demonstrate additional undiscussed and interesting advantages of such a modeling methodology over conventional data-driven approaches: 1) improving the model's predictive performance even with incomplete description of the underlying physics; 2) improving the robustness of the model to noise in the dataset; 3) reduced effort to convergence during optimization for a new, previously unseen scenario by transfer optimization of a pre-existing model. Hence, we noticed the inclusion of a physics-based regularization term can substantially improve the equivalent data-driven surrogate model in many substantive ways, including an order of magnitude improvement in test error when the dataset is very noisy, and a 2-3x improvement when only partial physics is included. In addition, we propose a novel transfer optimization scheme for use in such surrogate modeling scenarios and demonstrate an approximately 3x improvement in speed to convergence and an order of magnitude improvement in predictive performance over conventional Xavier initialization for training of new scenarios.
翻译:最近,物理学和内建神经网络(内建神经网络)作为将物理领域知识,包括基本治理方程式纳入许多复杂工程系统神经网络模型的一种方式,显示出了巨大的希望,这种将物理领域知识,包括基本治理方程式,纳入许多复杂工程系统神经网络模型的方法,在反面问题领域特别有效,边界条件可能定义不当,数据缺漏情景,典型的受监督的学习方法将失败。在这里,我们进一步探索使用这种模型方法来替代流动动态系统模型,并表明这种模型方法比传统数据驱动方法具有更多未经讨论和令人感兴趣的优势:(1) 改进模型的预测性功能,即使对基础物理学的描述不完整;(2) 提高模型对数据集噪音的稳健性;(3) 通过转移现有模型的优化,减少对以前看不见的新情景进行优化时的趋同努力。