Physical-intuition-driven nonlinear ignition-threshold scaling and shell-aspect-ratio regime separation for 1D ICF via TreeSHAP explainable AI

Laser-driven inertial-confinement-fusion achieves thermonuclear ignition via spherical capsule compression, yet high-fidelity multi-dimensional radiation-hydrodynamic simulations demand prohibitive computational resources. The ignition-threshold-factor (ITF) quantifies ignition margins to constrain target-design parameter spaces. Conventional log-linear ITF scaling-laws exhibit systematic prediction bias at extreme shell aspect ratios, while black-box machine-learning models achieve high accuracy but lack interpretable hydrodynamic mechanisms. Guided by physical-intuition-informed priors, we apply TreeSHAP explainable artificial intelligence for quantitative nonlinear feature-coupling analysis and leverage large-language models to boost script development and paper organization, avoiding unrestricted blind data fitting. Using the MULTI-IFE one-dimensional uniform-deceleration-shell setup with spatially uniform hotspot-shell flow initialized at peak implosion velocity, together with a neutron-gain-amplification ignition criterion Mα = 6.5, we construct a dataset of 60 000 critical-ignition capsule snapshots governed by seven key peak-implosion hydrodynamic quantities. The strong second-order nonlinear coupling between in-flight adiabat αif and shell aspect ratio Ar is inferred from residual-topology features and supported by SHAP-based decomposition analysis. We derive two closed-form analytical scaling-laws: nonlinear-SL, equipped with quadratic Ar and αif ⊗ Ar cross-coupling correction terms, reaches a test-set R2 = 0.922 and a piecewise bifurcation-SL at Ar = 2.32, where the Ar exponent flips from −2.14 (thin-shell) to +2.37 (thick-shell) to signal the switch between two dominant energy-loss channels. This regime boundary marks an inferred trade-off between thin-shell radiative-conductive losses and thick-shell inertial-drag dissipation. Both formulas deliver competitive interpolation performance against the random-forest baseline while retaining full analytical interpretability. All derived scaling relations are strictly valid only for perturbation-free one-dimensional MULTI-IFE simulations and cannot be generalized to multi-dimensional or experimental implosions.