Effects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamics
This addresses the problem of boundary condition sensitivity in neural network surrogates for physics simulations, which is incremental but important for computational physics applications.
The paper investigated how different boundary condition implementations affect the accuracy and stability of fully convolutional networks when modeling spatio-temporal dynamics like acoustic waves and heat diffusion, finding that optimal padding depends on data semantics and that adding spatial context or physics-based rules improves robustness for many recurrences.
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.