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.
Original language | English |
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Publisher | Arxiv |
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Volume | 2305.14477 |
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Publication status | Published - May 2023 |
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- nonlinear optimization
- deep learning
- physics-informed neural networks (PINNs)
- multi-level methods