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Effects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamics

Alguacil, Antonio and Pinto, Wagner Gonçalves and Bauerheim, Michaël and Jacob, Marc C. and Moreau, Stéphane Effects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamics. (2021) In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, 13 September 2021 - 17 September 2021 (Virtual event, France).

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Official URL: https://doi.org/10.1007/978-3-030-86517-7_7

Abstract

Accurate modeling of boundary conditions is crucial in com- putational physics. The ever increasing use of neural networks as surro- gates for physics-related problems calls for an improved understanding of boundary condition treatment, and its influence on the network ac- curacy. In this paper, several strategies to impose boundary conditions (namely padding, improved spatial context, and explicit encoding of phys- ical 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.

Item Type:Conference or Workshop Item (Paper)
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Institut National des Sciences Appliquées - INSA (FRANCE)
Other partners > Université de Lyon - UDL (FRANCE)
Other partners > Université de Sherbrooke (CANADA)
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Deposited On:08 Oct 2021 09:18

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