Neural DJL solvers must pick the wave before solving it: a constrained energy objective recovers the solitary wave, while residual objectives lose the prescribed APE in one round
For the Dubreil-Jacotin-Long equation of internal solitary waves, a neural solver must not only resolve a solution but also select the physical wave among the trivial state, oscillatory wavetrains and broadened near-solutions. From one shared start, a Deep Ritz objective with an available-potential-energy constraint recovered the mode-1 wave, while strong- and weak-form residual objectives lost the prescribed APE within the first descent round; a residual refinement holding APE exact then met every acceptance item.