Bondi Iceberg pool 1. Introduction: R² and Its Relation to RSQ The coefficient of determination, denoted as R² (R-squared), is one of the most widely used validation metrics in statistics and machine learning (ML) for assessing how well predicted values $\hat{y}$ agree with observed values $y_{true}$. In spreadsheet software and many engineering reports, R² is…
The Core Principle of PIML: Loss Function $$ { \mathcal{L}_{total} = \mathcal{L}_{data} + \lambda \cdot \mathcal{L}_{phys} } $$ Experience(Observations) + Reason(First Principles) Numeric data-driven AI/ML models are powerful when abundant training data is available, but they suffer from fundamental limitations: poor performance with scarce data, physically implausible predictions, and rapid degradation outside the training distribution…
Introduction to Center Alignment Index (CAI) as a Regression Metric 1. Mathematical Definition and Components The Center Alignment Index (CAI) is a bounded metric designed to quantify how closely the central tendency of paired observations aligns with the 1:1 identity line (y = x). In many scientific and engineering domains, comparing two measurement systems or…
Introduction to Lin’s Concordance Correlation Coefficient (CCC) In the fields of Artificial Intelligence (AI) and Machine Learning (ML), evaluating model performance typically revolves around accuracy, precision, or error metrics. However, when the goal is to assess agreement between two continuous variables—specifically, how well a model’s predicted values ($Y$) match the gold-standard observed values ($X$)—standard correlation…
1. Executive Summary The Coefficient of Determination, denoted as $R^2$, is one of the most widely used metrics for assessing the goodness-of-fit in linear regression models. However, its interpretation is often fraught with misunderstanding, particularly regarding how it fluctuates not just with the “correctness” of a model, but with the underlying distribution of the data….
1. Executive Summary In advanced engineering domains—such as semiconductor manufacturing, virtual metrology, and multi-sensor time-series analysis—the validation of predictive models requires more than a single performance score. We must distinguish between how well a model tracks a trend (Precision) versus how close the prediction is to the physical truth (Accuracy). This report establishes a rigorous…
