We consider parameter estimation in dynamical systems from finite-time, partially observed trajectories. Rather than calibrating parameters within a prescribed model structure, we formulate parameter estimation as an inverse problem for a parameter-to-observation operator and learn its inverse directly from data using deep neural networks. Under appropriate identifiability assumptions, this inverse map is well-defined and continuous, making it amenable to approximation by neural networks. We discuss identifiability, stability, and noise sensitivity of the inverse problem and provide a simple error decomposition that separates approximation error from noise amplification. Numerical experiments on linear, nonlinear, nonautonomous, partially observed, noisy, and chaotic systems demonstrate accurate parameter recovery. For chaotic systems, recovery is validated through agreement of invariant dynamical quantities rather than pointwise trajectories.
Tatsuoka et al. (Thu,) studied this question.