MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

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Main Authors: Yang, Lake, Malpica-Morales, Antonio, Wood, Frank Ioannis Papadakis, Kalliadasis, Serafim
Format: Preprint
Published: 2026
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author Yang, Lake
Malpica-Morales, Antonio
Wood, Frank Ioannis Papadakis
Kalliadasis, Serafim
author_facet Yang, Lake
Malpica-Morales, Antonio
Wood, Frank Ioannis Papadakis
Kalliadasis, Serafim
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_13305
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning
Yang, Lake
Malpica-Morales, Antonio
Wood, Frank Ioannis Papadakis
Kalliadasis, Serafim
Machine Learning
Dynamical Systems
Chemical Physics
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.
title MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning
topic Machine Learning
Dynamical Systems
Chemical Physics
url https://arxiv.org/abs/2605.13305