A zero-one law for one-shot system identification
Can a model be identified from one experiment? We study analytic systems that are linearly parameterized by a combination of prescribed dictionary terms, such as partial differential operators and dynamical systems. For a single input-response pair, recovery is possible exactly when the evaluated dictionary terms are linearly independent. We prove a sharp zero-one law: either no input uniquely determines the coefficients, or almost every random input sampled from a nondegenerate Gaussian measure does. This dichotomy reduces one-shot system identification to a question about degenerate inputs and provides an a posteriori certificate for any recovered model. Numerical examples recover dynam...
| Authors | Nicolas Boullé, Diana Halikias, Samuel E. Otto et al. |
|---|---|
| Primary category | math.NA |
| Published | 17 July 2026 |
| Last updated at source | 17 July 2026 |
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