The combination of advanced statistical modeling and informed feature reduction significantly enhances the robustness and reliability of our predictive models for accelerating materials discovery. Our machine learning process is structured into three stages: filtering the noise of intensity curves with a Gaussian process, detecting peaks and extracting crucial curve features, and applying a classification model, such as random forest, bagging, and gradient boosting for material phase prediction. Importantly, we couple this new physicsinformed machine-learning algorithm with a powerful experimental technique recently developed by our groups-automated chromatography-that yields a large set of well-defined and purified block copolymers from a very small number of as-synthesized samples. A notable advantage of this separation process over traditional iterative synthesis is its ability to remove homopolymer impurities and reduce the dispersity of each fraction compared to the as-synthesized parent block copolymer, enhancing the purity and reproducibility of fractionated samples' morphologies. Together, this combined workflow minimizes the synthetic burden of creating comprehensive and systematic sets of training data that were used to evaluate the accuracy and predictive capabilities of the machine-learning framework. Notably, this method achieves approximately 95% predictive accuracy across a variety of block copolymer chemistries, molecular weights, domain spacings, and nanostructures, including both new and existing materials in the training dataset, which is much higher than other alternative approaches. Furthermore, this method can further identify and correct data that was initially mislabeled as a result of human error based on quantified uncertainty of the prediction. After scrutinizing about 15% of the data with the highest uncertainty in predictive labels, the accuracy of our method approaches nearly 100%, marking a crucial advancement towards automated, high-throughput laboratories integrated with SAXS systems. The data and code used in this paper are publicly available ().