Randomized neural network for solving PDE-constrained optimization problems

doi:10.1016/j.camwa.2026.07.011

Randomized neural network for solving PDE-constrained optimization problems

2026-07-01

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DOI：10.1016/j.camwa.2026.07.011

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The state and adjoint state variables are approximated within a unified neural network framework, avoiding conventional mesh-based discretization. The control variable is then obtained from the adjoint state via the optimality condition. Numerical results show that the RaNN-based approach can achieve satisfactory accuracy with a relatively small number of degrees of freedom and is capable of handling pointwise control constraints. Moreover, for problems defined on non-smooth domains, such as the circular sector domain with a reentrant corner, suitable singular treatments are incorporated to enhance the approximation quality near corner singularities. Several two-and three-dimensional numerical examples are presented to demonstrate the effectiveness and robustness of the RaNN method.

Keywords:

Randomized neural networks

PDE-constrained optimal control

Pointwise control constraints

Non-smooth domains

Randomized neural network for solving PDE-constrained optimization problems

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