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.

研究了在完全卷积神经网络中引入空间上下文和物理边界的几种策略，并在两个时空演化问题上进行了评估，揭示了边界实现对于精度和稳定性的高度敏感性。

全卷积网络中边界条件对时空动态学习的影响