Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its influence on the network accuracy. In this paper, several strategies to impose boundary conditions (namely padding, improved spatial context, and explicit encoding of physical boundaries) are investigated in the context of fully convolutional networks applied to recurrent tasks. These strategies are evaluated on two spatio-temporal evolving problems modeled by partial differential equations: the 2D propagation of acoustic waves (hyperbolic PDE) and the heat equation (parabolic PDE). Results reveal a high sensitivity of both accuracy and stability on the boundary implementation in such recurrent tasks. It is then demonstrated that the choice of the optimal padding strategy is directly linked to the data semantics. Furthermore, the inclusion of additional input spatial context or explicit physics-based rules allows a better handling of boundaries in particular for large number of recurrences, resulting in more robust and stable neural networks, while facilitating the design and versatility of such networks.
翻译:精确的边界条件模型在计算物理学中至关重要。神经网络作为物理相关问题的代孕者越来越多地使用神经网络,这要求人们更好地了解边界状况处理及其对网络准确性的影响。在本文件中,在对经常性任务应用的全面演变网络的背景下,对强制实施边界条件的若干战略(即铺设、改进空间背景和明确将物理边界编码)进行了调查。这些战略根据两个片面时演变的问题进行了评价,这些变化问题是以部分差异方程式为模型的:2D声波(双向PDE)和热方程式(parablic PDE)的传播。结果显示,在这类经常性任务中,边界执行的准确性和稳定性都非常敏感。然后表明,最佳定位战略的选择与数据语义直接相关。此外,增加输入空间空间环境背景或明确的物理规则可以更好地处理边界,特别是大量重现的边界,从而形成更坚固和稳定的神经网络,同时便利这类网络的设计和非常态。