论文标题
vi-pinns：涉及方差的物理信息神经网络，以快速准确预测部分微分方程
VI-PINNs: Variance-involved Physics-informed Neural Networks for Fast and Accurate Prediction of Partial Differential Equations
论文作者
论文摘要
尽管最近在许多实际应用中，物理知识的神经网络（PINN）取得了很多进展，但仍有问题需要进一步研究，例如取得更准确的结果，更少的训练时间并量化了预测结果的不确定性。在许多方面，PINN的最新进展确实显着改善了PINN的性能，但是很少有人认为培训过程中差异的影响。在这项工作中，我们考虑了差异的效果，并提出了我们的VI-Pinns来提供更好的预测。我们在网络的最后一层中输出两个值，分别表示预测的均值和方差，后者用于表示输出的不确定性。引入了修改的负模样损失和辅助任务，以进行快速准确的训练。我们在各种不同的问题上进行了几项实验，以突出我们方法的优势。结果表明，我们的方法不仅给出了更准确的预测，而且可以更快地收敛。
Although physics-informed neural networks(PINNs) have progressed a lot in many real applications recently, there remains problems to be further studied, such as achieving more accurate results, taking less training time, and quantifying the uncertainty of the predicted results. Recent advances in PINNs have indeed significantly improved the performance of PINNs in many aspects, but few have considered the effect of variance in the training process. In this work, we take into consideration the effect of variance and propose our VI-PINNs to give better predictions. We output two values in the final layer of the network to represent the predicted mean and variance respectively, and the latter is used to represent the uncertainty of the output. A modified negative log-likelihood loss and an auxiliary task are introduced for fast and accurate training. We perform several experiments on a wide range of different problems to highlight the advantages of our approach. The results convey that our method not only gives more accurate predictions but also converges faster.
