Improved Training of Physics-Informed Neural Networks with Model Ensembles
Improved Training of Physics-Informed Neural Networks with Model Ensembles
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DOI：
10.1109/ijcnn54540.2023.10191822
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Katsiaryna Haitsiukevich;A. Ilin
中科院分区：
文献类型：
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作者：
Katsiaryna Haitsiukevich;A. Ilin
用神经网络学习偏微分方程（PDE）的解是传统求解器的一个有吸引力的替代方案，因为它的优雅，更大的灵活性和易于合并观测数据。然而，训练这样的物理信息神经网络（PINN）在实践中是非常困难的，因为PINN经常收敛到错误的解决方案。在本文中，我们通过训练PINN的集合来解决这个问题。我们的方法的动机是观察到各个PINN模型在具有目标的点附近找到类似的解决方案（例如，观测数据或初始条件），而它们的解在远离这些点的地方可能有很大的不同。因此，我们建议使用系综一致性作为逐步扩大解区间的标准，即包括新的点来计算微分方程的损失。由于域扩展的灵活性，我们的算法可以很容易地将测量在任意位置。与已有的具有时间自适应策略的PINN算法相比，该算法不需要预定义的区间扩展时间表，并且对时间和空间的处理是平等的。我们的实验表明，该算法可以稳定PINN的训练和产量的性能竞争最近的变种PINN训练时间适应。
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training such physics-informed neural networks (PINNs) is notoriously difficult in practice since PINNs often converge to wrong solutions. In this paper, we address this problem by training an ensemble of PINNs. Our approach is motivated by the observation that individual PINN models find similar solutions in the vicinity of points with targets (e.g., observed data or initial conditions) while their solutions may substantially differ farther away from such points. Therefore, we propose to use the ensemble agreement as the criterion for gradual expansion of the solution interval, that is including new points for computing the loss derived from differential equations. Due to the flexibility of the domain expansion, our algorithm can easily incorporate measurements in arbitrary locations. In contrast to the existing PINN algorithms with time-adaptive strategies, the proposed algorithm does not need a predefined schedule of interval expansion and it treats time and space equally. We experimentally show that the proposed algorithm can stabilize PINN training and yield performance competitive to the recent variants of PINNs trained with time adaptation.