AI RESEARCH
PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods
arXiv CS.LG
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ArXi:2604.04920v1 Announce Type: cross We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and indirect viewpoints for optimal control of PDEs, and then present two PINN formulations: a direct formulation based on minimizing the objective under the state constraint, and an indirect formulation based on the first-order optimality system.