Neural ODE Pocket learns a continuous vector field for the Van der Pol oscillator and integrates it with fourth-order Runge–Kutta. An exactly 1,218-parameter black-box transition network is trained on the same one-step examples.

Both models train only at timestep 0.05. Evaluation measures 20 units of closed-loop physical time at both the trained timestep and an unseen timestep of 0.20, separating continuous-time structure from discrete transition fitting.

At exactly 1,218 parameters per model, RK4 neural dynamics reached 0.227 trajectory RMSE at both trained and four-times-larger unseen timesteps. The discrete model rose from 0.607 to 2.212 RMSE. Mean unseen-timestep horizon before state error exceeded 0.5 was 48.46 steps for the neural ODE versus 1.88.

This free static Space preserves the complete original Gradio source, trained artifacts, evaluation files, and local launch requirements. Hugging Face now requires PRO for CPU-backed Gradio hosting, so the public landing page is static while the checked-in app.py remains the authoritative runnable demo.