ReLaTS: a Reinforcement Learning-based method for dynamically determining the coupling Time Step in multi-scale simulations of self-gravitating systems

2026-06-18

AI Summary

This work addresses the challenge of manually selecting coupling time steps in multi-scale self-gravitating system simulations, which often entails a difficult trade-off between accuracy and computational efficiency. The study introduces, for the first time, a reinforcement learning–based adaptive time-step control framework that is decoupled from any specific coupling algorithm. Integrated with an N-body integrator, the proposed method automatically balances simulation speed against energy conservation accuracy. Without requiring expert intervention, it generalizes across systems of varying scales and significantly reduces energy errors in long-term simulations of star clusters hosting planetary systems. The approach consistently maintains energy errors below a prescribed threshold while introducing negligible additional computational overhead.

Abstract

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.

Problem

• multi-scale simulations
• coupling time step
• self-gravitating systems
• accuracy-computational cost trade-off
• astrophysical simulations

Innovation

• Reinforcement Learning
• Multi-scale Simulation
• Coupling Time Step
• Self-gravitating Systems
• Adaptive Integration