Appellian Neural Networks

Appellian Neural Networks (ANNet) unify inverse and forward dynamics for a double pendulum by learning Appell’s acceleration energy, enabling accurate real-time simulations for unseen trajectories.

• Why it matters: Inverse and forward dynamics are usually treated as separate mappings, which can hide shared structure despite both following the same equations of motion.
• What they did: ANNet learns a single scalar energy from classical mechanics; inverse dynamics comes from differentiating it to recover joint torques, while forward dynamics uses the same learned energy in an optimization objective satisfying the Gibbs-Appell equation.
• The result: In a double pendulum paradigm, both inverse and forward simulations are accurate and real-time for trajectories not seen in training, propagate input noise similarly, and inverse adaptation to a modified pendulum generalizes to forward simulation without extra forward-specific training.