MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning
For researchers learning dynamical systems from data, MPINeuralODE offers a method that improves long-horizon stability and generalization to unseen initial conditions.
MPINeuralODE combines a soft physics-informed residual with a multiple-initial-condition curriculum to improve generalization of Neural ODEs for dynamical systems. It achieves a 26% reduction in out-of-sample and long-horizon MSE over baseline Neural ODE on Lotka-Volterra, while matching PINN on Hamiltonian drift.
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.