Probing optimisation in physics-informed neural networks
Probing optimisation in physics-informed neural networks
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DOI：
10.48550/arxiv.2303.15196
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
Nayara Fonseca;V. Guidetti;Will Trojak
中科院分区：
文献类型：
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作者：
Nayara Fonseca;V. Guidetti;Will Trojak
提出了一种新的比较优化器选择对物理信息神经网络(PINN)精度影响的方法。为了深入了解为什么某些优化器更好，提出了一种新的方法，该方法跟踪训练轨迹的曲率，并且可以以较低的计算成本进行动态评估。对几种平流速度下的线性平流方程进行了研究，结果表明，优化器的选择对PINNS模型的性能和精度有很大影响。此外，利用曲率度量，我们发现在优化器局部参考系中，收敛误差与曲率之间存在负相关。得出的结论是，在这种情况下，局部曲率值越大，得到的解越好。因此，PINN的优化变得更加困难，因为极小值位于高度弯曲的区域。
A novel comparison is presented of the effect of optimiser choice on the accuracy of physics-informed neural networks (PINNs). To give insight into why some optimisers are better, a new approach is proposed that tracks the training trajectory curvature and can be evaluated on the fly at a low computational cost. The linear advection equation is studied for several advective velocities, and we show that the optimiser choice substantially impacts PINNs model performance and accuracy. Furthermore, using the curvature measure, we found a negative correlation between the convergence error and the curvature in the optimiser local reference frame. It is concluded that, in this case, larger local curvature values result in better solutions. Consequently, optimisation of PINNs is made more difficult as minima are in highly curved regions.