Symmetry

Construction-stage surface settlement prediction becomes challenging under changing geological conditions and limited monitoring data in target sections. This study proposes a cross-condition prediction framework integrating key tunneling parameter selection and transfer learning using shield construction data from Chengdu Metro Line 18. The prediction target is the pointwise cumulative surface settlement associated with a specific monitoring point and shield ring state. Ring-level operational records and settlement observations are temporally aligned, while grouped spatial-block splitting is adopted to preserve spatial dependence among samples. Key tunneling parameters are identified by combining Random Forest importance, SHAP or permutation importance, Slime Mould Algorithm optimization, Spearman correlation, and engineering interpretation. A Transfer Multilayer Perceptron is then constructed through source-domain pretraining, parameter transfer, and target-domain fine-tuning. Results show that the proposed T-MLP achieves an MAE of 3.18 mm, an RMSE of 4.08 mm, and an R² of 0.852 in the target domain, reducing MAE by 39.54% relative to direct source-domain prediction. The framework provides an effective data-driven approach for cross-condition settlement prediction under limited target-domain observations.

Symmetry is where understanding begins, and where understanding deepens when ideal assumptions break [...]

Variational Quantum Eigensolvers (VQEs) have become a standard tool for use in preparing eigenstates in quantum simulations of many-body systems. In the case of the nuclear shell model, various adaptations of the VQE have been shown to be able to produce ground and excited states of nuclei. The VQE algorithm works by seeking minima in a cost function, which is often the expectation value of the energy. For a well-formulated problem, symmetries that are respected by the Hamiltonian should appear in the final converged solution provided by the VQE, even if those symmetries are broken by the wave function ansatz. We demonstrate explicit appearance of the particle–hole symmetry, and explicit recovery of angular momentum conservation due to rotational symmetry, during VQE runs in the case of the nuclear shell model. We conduct analyses of how the symmetry convergence appears in different ansatz formulations, and suggest that information obtained could be used in future VQE design.