Machine-Learning-Based Method for Goodness-of-Fit Test in Amplitude Analysis

$\mathbf{\text{Purpose:}}$ Amplitude analysis is a pivotal tool in hadron spectroscopy, fundamentally involving a series of likelihood fits to multi-dimensional experimental distributions. While robust goodness-of-fit tests exist for low-dimensional scenarios, evaluating goodness-of-fit in amplitude analysis remains challenging. $\mathbf{\text{Methods:}}$ We propose a machine-learning approach using anomaly detection for goodness-of-fit assessment in amplitude analysis. Our method employs a classifier to identify discrepancies between data and fit results in multi-dimensional phase space. $\mathbf{\text{Results}}\mathbf{\text{and}}\mathbf{\text{Conclusion:}}$ Using Monte Carlo simulations of $J\mathrm{/}\psi \to \gamma {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ decays, we demonstrate that this method detects contributions from an additional resonance with a signal strength of 1%. The detection power is sufficient for practical amplitude analyses, where contributions with fit fractions larger than 1% are typically included in the nominal fit. This approach shows promise for amplitude analyses of multi-body processes.