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A block-coordinate approach of multi-level optimization with an application to physics-informed neural networks

Author

Listed:
  • Serge Gratton

    (Université de Toulouse)

  • Valentin Mercier

    (Université de Toulouse
    Ingénierie)

  • Elisa Riccietti

    (Université de Lyon)

  • Philippe L. Toint

    (University of Namur)

Abstract

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level methods from a block-coordinate point of view, we propose a multi-level algorithm for the solution of nonlinear optimization problems and analyze its evaluation complexity. We apply it to the solution of partial differential equations using physics-informed neural networks (PINNs) and consider two different types of neural architectures, a generic feedforward network and a frequency-aware network. We show that our approach is particularly effective if coupled with these specialized architectures and that this coupling results in better solutions and significant computational savings.

Suggested Citation

  • Serge Gratton & Valentin Mercier & Elisa Riccietti & Philippe L. Toint, 2024. "A block-coordinate approach of multi-level optimization with an application to physics-informed neural networks," Computational Optimization and Applications, Springer, vol. 89(2), pages 385-417, November.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:2:d:10.1007_s10589-024-00597-1
    DOI: 10.1007/s10589-024-00597-1
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    References listed on IDEAS

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    1. V. S. Amaral & R. Andreani & E. G. Birgin & D. S. Marcondes & J. M. Martínez, 2022. "On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization," Journal of Global Optimization, Springer, vol. 84(3), pages 527-561, November.
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