Abstract
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 types of networks. (Datasets, code and supplementary material are available at https://gitlab.isae-supaero.fr/a.alguacil/boundary_conditions_fcn_dyn).
Supported by the French “Programme d’Investissements d’avenir” ANR-17-EURE- 0005 and the Natural Sciences and Engineering Research Council of Canada (NSERC). W.G.P. and M.B. are supportted by the French Direction Générale de l’Armement (DGA) through the AID POLA3 project.
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Alguacil, A., Pinto, W.G., Bauerheim, M., Jacob, M.C., Moreau, S. (2021). Effects of Boundary Conditions in Fully Convolutional Networks for Learning Spatio-Temporal Dynamics. In: Dong, Y., Kourtellis, N., Hammer, B., Lozano, J.A. (eds) Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track. ECML PKDD 2021. Lecture Notes in Computer Science(), vol 12979. Springer, Cham. https://doi.org/10.1007/978-3-030-86517-7_7
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