Abstract
We focus on Isogeometric Analysis (IGA) approximations of Partial Differential Equations (PDEs) solutions. We consider linear combinations of high-order and continuity base functions utilized by IGA. Instead of using the Deep Neural Network (DNN), which is the concatenation of linear operators and activation functions, to approximate the solutions of PDEs, we employ the linear combination of higher-order and continuity base functions, as employed by IGA. In this paper, we compare two methods. The first method trains different DNN for each coefficient of the linear computations. The second method trains one DNN for all coefficients of the linear combination. We show on model L-shape domain problem that training several small DNNs learning how to span B-splines coefficients is more efficient.
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Acknowledgement
The European Union’s Horizon 2020 Research and Innovation Program of the Marie Skłodowska-Curie grant agreement No. 777778.
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Doległo, K., Paszyński, M., Demkowicz, L. (2022). Deep Neural Networks and Smooth Approximation of PDEs. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13351. Springer, Cham. https://doi.org/10.1007/978-3-031-08754-7_41
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DOI: https://doi.org/10.1007/978-3-031-08754-7_41
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