Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations
Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations
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DOI：
10.1109/ijcnn52387.2021.9533606
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Pongpisit Thanasutives;Ken-ichi Fukui;M. Numao
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文献类型：
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作者：
Pongpisit Thanasutives;Ken-ichi Fukui;M. Numao
最近，研究人员利用神经网络精确求解偏微分方程（PDE），使无网格方法能够用于科学计算。不幸的是，当遇到高非线性域时，网络性能下降。为了提高泛化能力，我们引入了新的方法，采用多任务学习技术，不确定性加权损失和梯度手术，在学习PDE解决方案的背景下。多任务方案利用了学习共享表示的好处，由十字绣模块控制，多个相关PDE之间，这是通过改变PDE参数化系数，以更好地概括原始PDE。为了鼓励网络更加关注学习更具挑战性的高非线性域区域，我们还提出了对抗性训练来生成补充的高损失样本，这些样本与原始训练分布类似。在实验中，我们提出的方法被发现是有效的，并减少了错误的看不见的数据点相比，以前的方法在各种PDE的例子，包括高维随机PDE。
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high nonlinearity domain. To improve the generalizability, we introduce the novel approach of employing multi-task learning techniques, the uncertainty-weighting loss and the gradients surgery, in the context of learning PDE solutions. The multi-task scheme exploits the benefits of learning shared representations, controlled by cross-stitch modules, between multiple related PDEs, which are obtainable by varying the PDE parameterization coefficients, to generalize better on the original PDE. Encouraging the network pay closer attention to the high nonlinearity domain regions that are more challenging to learn, we also propose adversarial training for generating supplementary high-loss samples, similarly distributed to the original training distribution. In the experiments, our proposed methods are found to be effective and reduce the error on the unseen data points as compared to the previous approaches in various PDE examples, including high-dimensional stochastic PDEs.