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Using simulations at multiple imaginary chemical potentials for$(2+1)$-flavor QCD, we construct multi-point Pad\'e approximants. We determinethe singularties of the Pad\'e approximants and demonstrate that they areconsistent with the expected universal scaling behaviour of the Lee-Yang edgesingularities. We also use a machine learning model, Masked AutoregressiveDensity Estimator (MADE), to estimate the density of the Lee-Yang edgesingularities at each temperature. This ML model allows us to interpolatebetween the temperatures. Finally, we extrapolate to the QCD critical pointusing an appropriate scaling ansatz.

Exploring the Critical Points in QCD with Multi-Point Pad\'e and Machine Learning Techniques in (2+1)-flavor QCD