论文标题
用于解决非线性Biot方程的逆问题的物理信息的神经网络：批次培训
Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training
论文作者
论文摘要
在生物医学工程，地震预测和地下能量收集中，至关重要的是间接估计多孔培养基的物理特性，因为这些直接测量通常是不切实际的/过度的。在这里，我们应用物理知识的神经网络来解决非线性生物方程的逆问题。具体来说，我们考虑批处理培训并探索不同批次大小的效果。结果表明，与使用大批次或完整批处理相比，使用小批量大小的训练提供了物理参数的近似值（百分比误差较低）。物理参数的准确性提高，其成本为更长的训练时间。具体来说，我们发现尺寸不应该太小，因为批次尺寸很小，需要很长的训练时间，而无需相应的估计精度提高。我们发现，批次大小为8或32是一个很好的折衷，这对于数据中的加性噪声也很强。学习率也起着重要作用，应用作超参数。
In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive. Here we apply the physics-informed neural networks to solve the inverse problem with regard to the nonlinear Biot's equations. Specifically, we consider batch training and explore the effect of different batch sizes. The results show that training with small batch sizes, i.e., a few examples per batch, provides better approximations (lower percentage error) of the physical parameters than using large batches or the full batch. The increased accuracy of the physical parameters, comes at the cost of longer training time. Specifically, we find the size should not be too small since a very small batch size requires a very long training time without a corresponding improvement in estimation accuracy. We find that a batch size of 8 or 32 is a good compromise, which is also robust to additive noise in the data. The learning rate also plays an important role and should be used as a hyperparameter.
