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

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.

Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks

Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.