Abstract: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.
| Subjects: | Machine Learning (cs.LG); Dynamical Systems (math.DS); Chemical Physics (physics.chem-ph) |
| Cite as: | arXiv:2605.13305 [cs.LG] |
| (or arXiv:2605.13305v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13305 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Lake Yang [view email]
[v1]
Wed, 13 May 2026 10:18:18 UTC (1,583 KB)