评估物理约束损失函数在训练中的稳定性，提升模型可复现性。
Training Variation of Physically-Informed Deep Learning Models
- 用不同物理损失函数训练网络，对比收敛与精度差异。
- 同一任务下，不同训练会话结果波动明显，反映训练可靠性问题。
- 提出报告模型变异的方法，适合关注训练稳定性的研究者。
深度学习模型的成功不仅依赖训练数据，还取决于训练算法。损失函数、数据集和超参数调优在训练中至关重要，但训练算法的可靠性和可复现性却少有讨论。随着物理信息损失函数日益流行，其在强制施加边界条件时的可靠性成为关键问题。本文以Pix2Pix网络预测高弹性对比复合材料的应力场为例，实现多种强制应力平衡的损失函数，发现它们在多次训练中表现出显著的收敛性、准确性和应力平衡维持方面的差异。该研究强调报告模型变异的重要性，有助于更公平地比较不同方法，并提出相关实践建议。
原文摘要 · Abstract (English)
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.
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