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.
Pazy, Semigroups of linear operators and applications to partial differential equations , Applied Mathematical Sciences, vol
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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.