2024/08/26 by Marian Petrica, Marian Petrică, Ionel Popescu +2
Mathematics · #Numerical methods in inverse problems #Statistical and numerical algorithms #math.CA
paper · pdf · doi:10.48550/arxiv.2408.14616
openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We study local identifiability of parameters in ordinary differential equation models from finitely many observations. The central object is the parameter-to-observation map obtained by sampling the solution at prescribed times. We first prove a quantitative injectivity estimate for general C2 observation maps: a lower bound on the smallest singular value of the parameter Jacobian, together with an upper bound on the second derivative, gives an explicit neighborhood on which the inverse problem has a unique and stable local solution. We then treat analytic ODE models. For analytic vector fields the observation map is analytic in observation times, initial states, and parameters; consequently, the loss of full parameter rank is contained in the zero set of a real analytic function. Under a single non-degeneracy condition this gives generic local identifiability, including for randomly chosen observation times with a density. Finally, for homogeneous linear systems X=AX, we separate the recovery of ehA from the recovery of A: cyclic initial states identify the discrete propagator from one trajectory, while the remaining ambiguity is precisely the ambiguity of the real matrix logarithm.