Model predictive control for laser thermal processing: operator learning, closed-loop validation, and out-of-distribution analysis

What the math gives to ML

The paper contains two transferable engineering mechanisms rather than merely a laser-specific controller: a separable branch-trunk operator representation for predicting an entire future trajectory in one forward pass, and a smooth ReLU replacement designed to preserve near-identical outputs while supplying reliable second derivatives to an interior-point optimizer. The first can turn autoregressive neural rollouts into compact, parallel multi-step predictors whose inference cost does not grow through sequential feedback at every horizon step. The second is relevant whenever a neural network is embedded inside constrained optimization, where ReLU kinks can damage Hessian-based solver steps. The most useful validation is to compare one-shot low-rank horizon prediction with autoregressive rollouts, and to compare ReLU, softplus, and the paper's algebraic smoothing under differentiable planning.