A neural operator is trained once including a PDE residual penalty and then reused inside gradient-based optimization to solve multiple PDE-constrained tracking control problems.
The admm-pinns algorithmic framework for nonsmooth pde-constrained optimization: A deep learning approach
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Employing Deep Neural Operators for PDE control by decoupling training and optimization
A neural operator is trained once including a PDE residual penalty and then reused inside gradient-based optimization to solve multiple PDE-constrained tracking control problems.