Physical‑Intuition‑Driven Nonlinear Ignition‑Threshold Scaling and Shell‑Aspect‑Ratio Regime Separation for 1D ICF via TreeSHAP Explainable AI

Abstract

Laser-driven inertial-confinement-fusion (ICF) 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 manuscript 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 $M_\alpha=6.5$, 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 $\alpha_{if}$ and shell aspect ratio $A_r$ 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 $A_r$ and $\alpha_{if} \otimes A_r$ cross-coupling correction terms, reaches a test-set $R^2=0.922$, and a piecewise Bifurcation-SL at $A_r=2.32$, where the $A_r$ 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.