High-throughput characterization (HTC) of composition-process-structure-property relations is essential for accelerating molecular and material discovery and manufacturing paradigms. Here, we present a rapid, autonomous method for HTC of hydrogel rheological properties in well plate formats via automated sensing and physics-guided supervised machine learning. The novel HTC method facilitates rapid, autonomous characterization of hydrogel rheological properties and percolation processes associated with gelation and network interpenetration in 96-well plate formats at a rate of 24 s/sample (70 times faster than the state-of-the-art). Viscoelastic properties and phase behavior obtained by the method were benchmarked against traditional rheology studies. The speed and utility of the method were demonstrated by high-resolution characterization of the gel point of Pluronic F127, collagen, and alginate-PNIPAM hydrogels in 96-well plate formats at resolutions of 0.31 wt% (Pluronic F127), 0.031 mg/ml (collagen), and 0.069 wt% (NIPAM), respectively. Experimental composition-property relation data generated from sensor multivariate time-series data, calibration data, and fluid-structure interaction models enabled accurate classification of sample phase using supervised machine learning. Feature augmentation using sensor physics, here, a fluid-structure interaction model, improved material (i.e., sample) phase classification accuracy relative to that obtained in the absence of physics-based feature augmentation. Ultimately, creating rapid, autonomous HTC methods that synergize with common high-throughput experimentation formats, such as well plates, can accelerate the pace of research across several disciplines as well as generate new tools for quality assurance and control across emerging industries.