How Long Can We Predict a Double Pendulum? Physics-Based Models Versus Neural Networks

Chaotic systems are deterministic, yet small errors in initial conditions or parameters grow quickly. This limits how long predictions stay useful. We compared two models of a physical double pendulum. The first was a physics-based model built from the pendulum's measured properties and Lagrangian equations. The second was a neural network trained directly on observed trajectories, without those equations. Both models started from matching experimental states. We scored them on nine held-out trajectories (36 were used for training) by prediction horizon, the time until the predicted lower-arm angle diverged from the experimental value by more than 35°. To characterize the network's variability, we trained it with ten random seeds. The physics model outperformed the mean network result on seven of nine trajectories. The network showed substantial run-to-run variability, although 6 of 90 seeds tracked the full recorded duration without diverging. Horizons were mostly under one second for both models. Explicit physical knowledge therefore gave a modest edge for this system and data size. Reliability is also a separate consideration from average accuracy when forecasting chaotic dynamics.