Neural operators can approximate control gains for PDE stabilization with high accuracy (~0.1% error), enabling practical implementation of theoretically-grounded feedback designs for systems where traditional single-input methods fail.
This paper develops a feedback control method for stabilizing the Kuramoto-Sivashinsky equation, a complex nonlinear system, using two boundary inputs instead of one. The key innovation is using a neural operator to approximate the control gains, enabling practical implementation while maintaining theoretical stability guarantees.