Training Variation of Physically-Informed Deep Learning Models
This work addresses the reproducibility and fairness in comparing training methods for physics-informed deep learning, which is important for researchers in computational physics and machine learning, though it is incremental in nature.
The study investigated the reliability of physics-informed loss functions in training deep learning models to enforce boundary conditions, using a Pix2Pix network for stress field prediction in composites as a case study, and found that different loss functions led to varying levels of convergence, accuracy, and equilibrium enforcement across training sessions.
A successful deep learning network is highly dependent not only on the training dataset, but the training algorithm used to condition the network for a given task. The loss function, dataset, and tuning of hyperparameters all play an essential role in training a network, yet there is not much discussion on the reliability or reproducibility of a training algorithm. With the rise in popularity of physics-informed loss functions, this raises the question of how reliable one's loss function is in conditioning a network to enforce a particular boundary condition. Reporting the model variation is needed to assess a loss function's ability to consistently train a network to obey a given boundary condition, and provides a fairer comparison among different methods. In this work, a Pix2Pix network predicting the stress fields of high elastic contrast composites is used as a case study. Several different loss functions enforcing stress equilibrium are implemented, with each displaying different levels of variation in convergence, accuracy, and enforcing stress equilibrium across many training sessions. Suggested practices in reporting model variation are also shared.