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

\textbf{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. \textbf{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. \textbf{Results and Conclusion:} Using Monte Carlo simulations of $J/\psi\to\gamma \pi^+\pi^-\pi^0\pi^0$ 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.