用置信度调整的意外度，让材料发现更省时省钱

Accelerating the discovery and manufacturing of advanced materials with specific properties is a critical yet formidable challenge due to vast search space, high costs of experiments, and time-intensive nature of material characterization. In recent years, active learning, where a surrogate machine learning (ML) model mimics the scientific discovery process of a human scientist, has emerged as a promising approach to address these challenges by guiding experimentation toward high-value outcomes with a limited budget. Among the diverse active learning philosophies, the concept of surprise (capturing the divergence between expected and observed outcomes) has demonstrated significant potential to drive experimental trials and refine predictive models. Scientific discovery often stems from surprise thereby making it a natural driver to guide the search process. Despite its promise, prior studies leveraging surprise metrics such as Shannon and Bayesian surprise lack mechanisms to account for prior confidence, leading to excessive exploration of uncertain regions that may not yield useful information. To address this, we propose the Confidence-Adjusted Surprise Measure for Active Resourceful Trials (CA-SMART), a novel Bayesian active learning framework tailored for optimizing data-driven experimentation. On a high level, CA-SMART incorporates Confidence-Adjusted Surprise (CAS) to dynamically balance exploration and exploitation by amplifying surprises in regions where the model is more certain while discounting them in highly uncertain areas. We evaluated CA-SMART on two benchmark functions (Six-Hump Camelback and Griewank) and in predicting the fatigue strength of steel. The results demonstrate superior accuracy and efficiency compared to traditional surprise metrics, standard Bayesian Optimization (BO) acquisition functions and conventional ML methods.