  The traditional method of identifying symmetry-breaking phase transitions
through the emergence of a single-particle gap encounters significant
challenges in quantum materials with strong fluctuations. To address this, we
have developed a data-driven approach using a domain-adversarial neural network
trained on simulated spectra of cuprates. This model compensates for the
scarcity of experimental data -- a significant barrier to the wide deployment
of machine learning in physical research -- by leveraging the abundance of
theoretically simulated data. When applied to unlabeled experimental spectra,
our model successfully distinguishes the true superconducting states from
gapped fluctuating states, without the need for fine temperature sampling
across the transition. Further, the explanation of our machine learning model
reveals the crucial role of the Fermi-surface spectral intensity even in gapped
states. It paves the way for robust and direct spectroscopic identification of
fluctuating orders, particularly in low-dimensional, strongly correlated
materials.
