Approximate Feedback Linearization for a Nonlinear Hyperbolic PDE Class -- Part II: Neural Operator

What the math gives to ML

The paper provides a useful recipe for replacing an expensive structured operator with a learned operator while retaining explicit robustness guarantees. Its transferable asset is not merely neural-operator approximation, but the joint Lipschitz bound in both the plant description and the state, together with a small-gain condition that converts uniform approximation error into a linear practical-stability radius. A strong ML adaptation is a plant-conditioned controller or simulator whose coefficient encoder and state encoder are trained and regularized to preserve these sensitivities, rather than treating the operator as an unconstrained black box. The most credible experiments are on families of low-dimensional nonlinear dynamical systems or PDE surrogates, measuring both interpolation and generalization across plant coefficients and closed-loop degradation under approximation error.