Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons. We propose MPINeuralODE, which combines a soft physics-informed residual with a Multiple-Initial-Condition (MIC) multiple-shooting curriculum whose ingredients are structurally complementary: the physics term anchors the vector-field magnitude on the support that MIC enlarges. We evaluate along three axes: out-of-sample error, long-horizon stability, and Hamiltonian drift, which together expose whether the learned dynamics recover the underlying vector field. On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 26% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.
@article{arxiv.2605.13305,
title = {MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning},
author = {Lake Yang and Antonio Malpica-Morales and Frank Ioannis Papadakis Wood and Serafim Kalliadasis},
journal= {arXiv preprint arXiv:2605.13305},
year = {2026}
}