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.