Deterministic, Finite-Dimensional, Dynamical Systems

When the forward model is a deterministic ODE, the inverse problem becomes a calibration problem for time-dependent trajectories. We observe part of a trajectory and try to infer the parameters, initial conditions, or forcing terms that best explain it.

We formulate this calibration task as a Bayesian inverse problem in which time-series observations constrain the dynamical parameters through the full trajectory. Deterministic ordinary differential equation models already contain the main ingredients of dynamical calibration: nonlinear parameter-to-observable maps, sensitivity to initial conditions, and questions of identifiability from finite data.