The parameter-recovery inverse problem. A population spreads by the Fisher–KPP equation ∂_tu = D∇²u + ρu(1−u) — the canonical model for biological invasion, tumor growth, and epidemic fronts. The diffusion D and growth rate ρ are unknown; we observe only a few noisy snapshots. The inverse problem recovers D and ρ by matching simulated fronts to the observations. More snapshots and less noise yield sharper estimates; the invasion front travels at speed c = 2√(Dρ), which the data must pin down. Related to reaction–diffusion modeling in mathematical biology.