The authors interpret neural networks as PDEs, propose a dual formulation for parabolic coefficient control with an existence proof for minimizers, and establish existence for an approximated hyperbolic control problem.
Pozzoli, Small-time global approximate controllability of bilinear wave equations , Journal of Differ- ential Equations 388 (2024), 421–438
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Control and optimization for Neural Partial Differential Equations in Supervised Learning
The authors interpret neural networks as PDEs, propose a dual formulation for parabolic coefficient control with an existence proof for minimizers, and establish existence for an approximated hyperbolic control problem.