Uniform controllability for the wave equation with large potential

What the math gives to ML

The paper gives a geometric control principle for wave dynamics with a large positive spatial potential. Its transferable asset is the Hamiltonian symbol q(x,\xi)=\sqrt{|\xi|_g^2+V(x)}, which changes propagation rays through both the local wave speed and the force -\nabla V. The paper's potential-dependent geometric control condition says that uniform observability is possible when all relevant rays reach the observation region. This suggests a neural feature-propagation layer with a learnable positive potential and an observability regularizer that suppresses feature modes remaining hidden from a designated readout or sensor mask.