Neural ordinary differential equations (NODEs) (Chen, 2018) naturally bring hybrid machine learning (ML) approaches into the modeling of spring–mass–damper (SMD) systems, which are ubiquitous in practical engineering simulations. However, retaining the underlying SMD structure within NODE frameworks offers several advantages. Prior work (Marlantes et al., 2024) shows that incorporating known linear forces while learning a data-driven force-correction term improves model generalizability, numerical stability, and the preservation of small-amplitude dynamics such as fixed points, when applied to industry-focused datasets. However, when the learned force-correction term becomes large relative to the linear physics, interpretability deteriorates. To address this, the correction term can be modeled probabilistically—for example, using Gaussian Process Regression (GPR)—so that at each time step the correction is represented as a normal distribution with known mean and variance. During the numerical integration of the system, Monte Carlo sampling of this distribution yields a collection of trajectories, from which confidence intervals can be computed. Yet obtaining accurate confidence bounds typically requires hundreds or thousands of trajectories, making this approach computationally expensive and impractical for real-time prediction. Marlantes (2025) proposed a first-order uncertainty propagation method to approximate these confidence bounds analytically, but the approach was limited to a single degree-of-freedom (DOF) and performed poorly for strongly coupled multi-DOF SMD systems. In this work, we generalize the uncertainty propagation framework to arbitrarily coupled multi-DOF SMD systems and derive closed-form expressions for the propagated variance and associated 95% confidence intervals. The method is demonstrated on two datasets: nonlinear ship rolling motion modeled as a Duffing oscillator with random forcing, and the coupled heave–pitch response of a Fast Displacement Ship (FDS) in irregular head seas. For both cases, the analytical confidence bounds are validated against Monte Carlo simulations. The results show that the proposed expressions provide practical, low-cost, and real-time uncertainty estimates for hybrid SMD-based time-series prediction models.