Deep neural networks and adaptive quadrature for solving variational problems

DOI10.1007/978-3-030-97549-4_42zbMath1490.65038OpenAlexW4225846756MaRDI QIDQ2128466

O. P. Iliev, Daria Fokina, Ivan V. Oseledets

Publication date: 22 April 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-97549-4_42

zbMATH Keywords

variational problemadaptive quadraturephysics-informed neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical quadrature and cubature formulas (65D32)

Uses Software

• GitHub
• JAX
• quadpy

Cites Work

• Data driven approximation of parametrized PDEs by reduced basis and neural networks
• Inferring solutions of differential equations using noisy multi-fidelity data
• High degree efficient symmetrical Gaussian quadrature rules for the triangle

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