基于物理信息的神经网络在橡胶压延过程中的应用
Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering process
摘要：
物理信息神经网络（PINN）由于能够将物理定律融入模型中而在工程的各个领域得到了广泛的关注。然而，PINN在涉及机械和热场之间耦合的工业应用中的评估仍然是一个活跃的研究课题。在这项工作中，我们提出了一个应用程序的PINNs的非牛顿流体的热力学问题，这是经常被认为是在橡胶压延过程中。我们证明了PINNs的有效性时，处理逆和不适定的问题，这是不切实际的解决经典的数值离散化方法。我们研究了传感器的位置和无监督点的分布对PINN的性能的影响，从一些部分数据中推断隐藏的物理场的问题。我们还研究了PINN从传感器捕获的测量中识别未知物理参数的能力。噪声测量的影响也被认为是整个这项工作。本文的结果表明，在识别问题中，PINNs可以成功地估计未知参数仅使用传感器上的测量。在边界条件没有完全定义的不适定问题中，即使传感器的位置和无监督点的分布对PINN的性能有很大的影响，我们表明该算法能够从局部测量中推断出隐藏的物理特性。
英文摘要：
Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. However, the assessment of PINNs in industrial applications involving coupling between mechanical and thermal fields is still an active research topic. In this work, we present an application of PINNs to a non-Newtonian fluid thermo-mechanical problem which is often considered in the rubber calendering process. We demonstrate the effectiveness of PINNs when dealing with inverse and ill-posed problems, which are impractical to be solved by classical numerical discretization methods. We study the impact of the placement of the sensors and the distribution of unsupervised points on the performance of PINNs in a problem of inferring hidden physical fields from some partial data. We also investigate the capability of PINNs to identify unknown physical parameters from the measurements captured by sensors. The effect of noisy measurements is also considered throughout this work. The results of this paper demonstrate that in the problem of identification, PINNs can successfully estimate the unknown parameters using only the measurements on the sensors. In ill-posed problems where boundary conditions are not completely defined, even though the placement of the sensors and the distribution of unsupervised points have a great impact on PINNs performance, we show that the algorithm is able to infer the hidden physics from local measurements.
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