Inverse problems in computational mechanics often involve sparse and noisy data, nonlinear dynamics, and significant uncertainty, making reliable inference challenging for both data-driven and mechanistic approaches. Physics-enhanced machine learning provides a principled framework for combining physical constraints with data-driven representations to enable robust inference. In this work, we propose a physics-informed smoothing and data assimilation approach based on Physics-Informed Neural Networks (PINNs) for joint state and parameter inference in nonlinear dynamical systems. PINNs are utilized as latent trajectory representations, constrained by governing equations, which enable the reconstruction of system states and the calibration of model parameters from limited time-series data. The method relies on an alternating optimization strategy inspired by generalized smoothing to balance data fidelity and dynamical consistency. To evaluate the reliability of the inferred dynamics, we introduce a sliding prediction error criterion that assesses short-horizon predictive consistency with the underlying model, providing a practical tool for hyperparameter selection and monitoring under uncertainty. The approach is illustrated using microbial community dynamics modeled by the Generalized Lotka–Volterra system, which exhibits stationary, oscillatory, and mixed regimes, posing a challenging high-dimensional inverse problem. Overall, the proposed framework demonstrates how PINN-based smoothing strategies can support uncertainty-aware data assimilation and monitoring and can be extended to a broad class of inverse problems in nonlinear dynamical systems.