论文标题
PSO-PINN：用粒子群优化训练的物理信息的神经网络
PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimization
论文作者
论文摘要
物理知识的神经网络（PINN）最近已成为基于部分微分方程（PDE）模型在广泛的工程和科学问题中深入学习的有希望的应用。然而，有证据表明，梯度下降的PINN训练显示出在用不规则溶液求解PDE时通常可以阻止收敛的病理。在本文中，我们建议使用粒子群优化（PSO）方法来训练PINN。所得的PSO-PINN算法不仅减轻了经过标准梯度下降训练的PINN的不希望的行为，而且还为Pinn提供了合奏方法，可以提供具有量化不确定性的稳健预测的可能性。我们还提出了PSO-BP-CD（带有后传播和系数衰减的PSO），这是一种混合PSO变体，将群体优化与梯度下降结合在一起，随着训练的进展，后者增加了重量，并且在良好的局部最佳最佳中加入了群。全面的实验结果表明，提出的PSO-BP-CD算法的PSO-PINN优于使用其他PSO变体或纯梯度下降训练的PINN合奏。
Physics-informed neural networks (PINN) have recently emerged as a promising application of deep learning in a wide range of engineering and scientific problems based on partial differential equation (PDE) models. However, evidence shows that PINN training by gradient descent displays pathologies that often prevent convergence when solving PDEs with irregular solutions. In this paper, we propose the use of a particle swarm optimization (PSO) approach to train PINNs. The resulting PSO-PINN algorithm not only mitigates the undesired behaviors of PINNs trained with standard gradient descent but also presents an ensemble approach to PINN that affords the possibility of robust predictions with quantified uncertainty. We also propose PSO-BP-CD (PSO with Back-Propagation and Coefficient Decay), a hybrid PSO variant that combines swarm optimization with gradient descent, putting more weight on the latter as training progresses and the swarm zeros in on a good local optimum. Comprehensive experimental results show that PSO-PINN with the proposed PSO-BP-CD algorithm outperforms PINN ensembles trained with other PSO variants or with pure gradient descent.
