Analytical solutions for non-quadratic growth penalties

Determine whether analytical solutions exist for unbalanced dynamic optimal transport with non-quadratic growth penalties.

Background

The paper studies unbalanced dynamic optimal transport (UDOT), in which a growth penalty si] governs proliferation and apoptosis along transport paths. Existing analytical travelling-Dirac solutions and efficient simulation-free solvers are available for the quadratic Wasserstein–Fisher–Rao penalty, but the paper considers more general penalties and replaces unavailable closed forms with learned path models. The existence of analytical solutions for non-quadratic penalties is therefore identified as an unresolved mathematical question.