We investigate the capability of TianQin and LISA to reconstruct the model parameters in the Lagrangian of new-physics scenarios that can generate an electroweak strong first-order phase transition. Taking the dimension-six Higgs operator extension of the Standard Model as a representative scenario for a broad class of new-physics models, we establish the mapping between the model parameter $\mathrm{\Lambda }$ and the observable spectral features of the stochastic gravitational-wave background. We begin by generating simulated data incorporating time delay interferometry channel noise, astrophysical foregrounds, and signals from the dimension-six model. The data are then compressed and optimized, followed by geometric parameter inference using both Fisher-matrix analysis and Bayesian nested sampling with polychord, which efficiently handles high-dimensional, multimodal posterior distributions. Finally, machine-learning techniques are employed to achieve precise reconstruction of the model parameter $\mathrm{\Lambda }$. For benchmark points producing strong signals, parameter reconstruction with both TianQin and LISA yields relative uncertainties of approximately 20%–30% in the signal amplitude and sub-percent precision in the model parameter $\mathrm{\Lambda }$. The sub-percent precision reflects the statistical reconstruction capability of the detectors in an idealized setting: it incorporates the machine-learning inference uncertainty and is established at a fixed bubble wall velocity, while theoretical uncertainties in the effective potential calculation are not included.

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• Electroweak phase transition
• Gravitational wave sources