论文标题
通过针对PINN的数据调节的损失景观工程
Loss Landscape Engineering via Data Regulation on PINNs
论文作者
论文摘要
物理知识的神经网络在使用自动分化和残留损失的情况下参数定义明确的部分微分方程的解决方案进行了独特的实用性。尽管它们提供了融合的理论保证，但实际上，所需的培训制度往往是严格和要求的。在本文的过程中，我们深入研究了与Pinn相关的损失景观，以及如何提供有关为什么很难优化Pinns的一些见解。我们证明了如何通过以稀疏或粗数据作为调节器来喂食PINN可以更好地融入溶液。数据调节和变形了与PINN相关的损失景观的拓扑，以使其容易为最小化器遍历。 PINN的数据调控有助于通过调用混合无监督的监督训练方法来简化收敛所需的优化，在这种方法中，标记的数据将网络推向了解决方案附近，而未标记的微调将其转向解决方案。
Physics-Informed Neural Networks have shown unique utility in parameterising the solution of a well-defined partial differential equation using automatic differentiation and residual losses. Though they provide theoretical guarantees of convergence, in practice the required training regimes tend to be exacting and demanding. Through the course of this paper, we take a deep dive into understanding the loss landscapes associated with a PINN and how that offers some insight as to why PINNs are fundamentally hard to optimise for. We demonstrate how PINNs can be forced to converge better towards the solution, by way of feeding in sparse or coarse data as a regulator. The data regulates and morphs the topology of the loss landscape associated with the PINN to make it easily traversable for the minimiser. Data regulation of PINNs helps ease the optimisation required for convergence by invoking a hybrid unsupervised-supervised training approach, where the labelled data pushes the network towards the vicinity of the solution, and the unlabelled regime fine-tunes it to the solution.
