<![CDATA[Objective: Inverter-dominated microgrids exhibit low rotational inertia and fast electro-magnetic dynamics, making transient stability assessment significantly more challenging than in synchronous-machine-dominated systems. This paper pro-poses a Physics-Informed Neural ODE (PI-NODE) framework that models post-disturbance inverter dynamics in continuous time, embedding the governing ODE as a hybrid of known droop-controlled inverter physics and a learned neural correction solved forward by an adaptive-step Dormand-Prince integrator. Gradients are propagated through the solver via the continuous adjoint method, keeping memory cost constant with respect to integration depth. A total of 1200 disturbance scenarios were generated from reduced-order time-domain simulations of droop-controlled grid-forming inverter microgrids with randomized virtual inertia, droop damping, fault severity, clearing time, and stochastic renewable fluctuations. On the held-out test set (180 scenarios), PI-NODE achieved 95.56% accuracy, 98.67% precision, 96.10% recall, and 97.37% F1-score for transient stability classification, with CCT MAE of 55.72 ms and RMSE of 140.48 ms. Compared with the discrete-time physics-informed deep learning (PIDL) baseline, PI-NODE yields higher precision (+1.27 percentage points) at the cost of lower recall (−1.30 percentage points), while CCT regression error is substantially larger, attributable to insufficient trajectory-fitting convergence under the 40-epoch Adam training configuration. Inference latency of 2.78 ms per sample (CPU-only) represents a 3.2× speedup over direct RK4 numerical simulation (8.98 ms per sample). Robustness testing under ±20% virtual inertia and droop scaling yielded 82.22% and 92.78% accuracy respectively, revealing that the current PI-NODE training configuration does not yet achieve the parametric robustness of the PIDL baseline. These findings identify the conditions under which continuous-time ODE formulation requires additional training strategies extended optimization, trajectory regularization, and boundary-aware sampling to realize its theoretical advantage over discrete-time physics penalization for microgrid transient stability assessment.]]>
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