Veronica Saz Ulibarrena

Veronica Saz Ulibarrena, Philipp Horn, Simon Portegies Zwart et al.

Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural Networks (ANNs) to replace expensive parts of the integration of planetary systems. Neural networks that include physical knowledge have grown in popularity in the last few years, although few attempts have been made to use them to speed up the simulation of the motion of celestial bodies. We study the advantages and limitations of using Hamiltonian Neural Networks to replace computationally expensive parts of the numerical simulation. We compare the results of the numerical integration of a planetary system with asteroids with those obtained by a Hamiltonian Neural Network and a conventional Deep Neural Network, with special attention to understanding the challenges of this problem. Due to the non-linear nature of the gravitational equations of motion, errors in the integration propagate. To increase the robustness of a method that uses neural networks, we propose a hybrid integrator that evaluates the prediction of the network and replaces it with the numerical solution if considered inaccurate. Hamiltonian Neural Networks can make predictions that resemble the behavior of symplectic integrators but are challenging to train and in our case fail when the inputs differ ~7 orders of magnitude. In contrast, Deep Neural Networks are easy to train but fail to conserve energy, leading to fast divergence from the reference solution. The hybrid integrator designed to include the neural networks increases the reliability of the method and prevents large energy errors without increasing the computing cost significantly. For this problem, the use of neural networks results in faster simulations when the number of asteroids is >70.

Veronica Saz Ulibarrena, Simon Portegies Zwart

Astrophysical simulations frequently address multi-scale, multi-physics problems through subsystem decomposition, problem-tailored integration schemes, and coupling on fixed manually set timescales. Here we introduce ReLaTS, a reinforcement learning framework that dynamically selects the coupling time step to optimize the trade-off between accuracy and computational cost. We validate ReLaTS on star clusters containing a planetary system, and test the method by varying the number of stars $N_\star$ in the cluster and the number of planets ($N_{\rm planet}$) orbiting one of them. The method finds the optimal coupling time step that balances speed and accuracy without requiring expert knowledge. In addition, the trained network operates independently of the coupled \textit{N}-body algorithms, displaying stable performance across a range of setups. We observe that the method is less reliable for cases with infinitesimal masses, as their contribution to the total energy is negligible compared to that of the massive bodies, and the network is not capable of recognizing potential errors generated while integrating them. For long-time integration of large $N$ systems, the error accumulates. The reinforcement learning algorithm, however, manages to keep the energy error below a pre-set threshold. This approach substantially reduces energy errors relative to fixed-time step baselines without substantial additional computational overhead. Once trained, ReLaTS requires no expert tuning and generalizes across diverse astrophysical domains, enabling adaptive multi-scale simulations.