Identifiable inverse optimal transport for single-cell state transitions

Signed effects of target-state programmes are unidentifiable in balanced optimal transport because fixed endpoint distributions make their contributions constant across feasible plans. We introduce UOT-IOT, a semi-relaxed inverse transport framework that restores measurable targetmass responses and provides a rank condition for local identifiability. It recovers coefficients inground-truth benchmarks (correlation 0.997 versus 0.081 for balanced transport), transfers frozen directions to six unseen samples with specificity controls, and achieves the lowest transition error against seven methods under matched evaluation conditions. GH-IOT separates shared directions from context and lineage-history offsets, revealing opposing history-associated effects. IFN/HLA is associated with patient treatment response, whereas EMT relates to drug sensitivity and perturbation-induced state changes. PERSIST-IOT improves future population-composition prediction in an independent experiment. Together, these modules distinguish current state,transition propensity and future population outcomes while supporting testable biological interpretations.