  In engineering, accurately modeling nonlinear dynamic systems from data
contaminated by noise is both essential and complex. Established Sequential
Monte Carlo (SMC) methods, used for the Bayesian identification of these
systems, facilitate the quantification of uncertainty in the parameter
identification process. A significant challenge in this context is the
numerical integration of continuous-time ordinary differential equations
(ODEs), crucial for aligning theoretical models with discretely sampled data.
This integration introduces additional numerical uncertainty, a factor that is
often over looked. To address this issue, the field of probabilistic numerics
combines numerical methods, such as numerical integration, with probabilistic
modeling to offer a more comprehensive analysis of total uncertainty. By
retaining the accuracy of classical deterministic methods, these probabilistic
approaches offer a deeper understanding of the uncertainty inherent in the
inference process. This paper demonstrates the application of a probabilistic
numerical method for solving ODEs in the joint parameter-state identification
of nonlinear dynamic systems. The presented approach efficiently identifies
latent states and system parameters from noisy measurements. Simultaneously
incorporating probabilistic solutions to the ODE in the identification
challenge. The methodology's primary advantage lies in its capability to
produce posterior distributions over system parameters, thereby representing
the inherent uncertainties in both the data and the identification process.
