Symplectic neural networks in Taylor series form for Hamiltonian systems

We propose an effective and light-weight learning algorithm, Symplectic Taylor Neural Networks (Taylor-nets), to conduct continuous, long-term predictions of a complex Hamiltonian dynamic system based on sparse, short-term observations. At the heart our algorithm is novel neural network architecture consisting two sub-networks. Both are embedded with terms in form series expansion designed symmetric structure. The key mechanism underpinning infrastructure strong expressiveness special property expansion, which naturally accommodate numerical fitting process gradients respect generalized coordinates as well preserve its symplectic further incorporate fourth-order integrator conjunction ODEs' framework into Taylor-net learn continuous-time evolution target systems while simultaneously preserving their structures. demonstrated efficacy predicting broad spectrum systems, including pendulum, Lotka–Volterra, Kepler, Hénon–Heiles systems. Our model exhibits unique computational merits by outperforming previous methods great extent regarding prediction accuracy, convergence rate, robustness despite using extremely small training data short period (6000 times shorter than period), sample sizes, no intermediate train networks.