PDE Family Reunion: When Symbolic AI Learns the Skeleton, Not Just the Skin
Simulation teams know the ritual. Change the material coefficient, rerun the solver. Change the viscosity, rerun the solver. Change the flow velocity, rerun the solver. The physical system is still recognizably the same, but the computation behaves like a forgetful intern: every parameter setting is treated as a fresh assignment. This is not because finite element, finite volume, or spectral methods are bad. Quite the opposite. Their reliability is precisely why serious engineering organizations still use them. The problem is that parameterized simulation often asks the same mathematical family of questions again and again. The expensive part is not always solving one equation. It is solving a family of related equations while pretending they are strangers. ...