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Data Science | Evaluation Metric | Training

Physics-Informed Machine Learning: Integrating Physical Laws and Domain Knowledge into Numeric AI/ML
ByWolf April 18, 2026April 19, 2026

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…

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Data Science | Test | Training

Post-hoc Prediction Correction: Long-Term Bias & Short-Term Drift
ByWolf April 18, 2026April 18, 2026

A trained regressor that performs well on historical data often drifts in production for two distinct reasons: Retraining is the principled fix for both, but it is expensive and sometimes impossible (no fresh labels, frozen model in a regulated pipeline). A cheap, production-friendly alternative is a two-term post-hoc correction: 1. Long-term bias (residual_bias) Definition, computed…

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Data Science | Training

Balancing Model Sensitivity and Explainability (R²)
ByWolf April 16, 2026April 16, 2026

Aerial view of the Great Blue Hole in Belize In the model training process, the responsiveness (sensitivity) of $Y$ to variations in $X$ is a core factor that determines the balance between generalization performance and explainability ($R^2$). $$R^2 = 1 – \frac{SS{res}}{SS_{tot}} = 1- \frac{\sum_{i=1}^{n}{(y_{i} – \hat{y}_{i})^2}}{\sum_{i=1}^{n}{(y_{i} – \bar{y})^2}}$$ Where: 1. Root Causes of Sensitivity…

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Physics-Informed Machine Learning: Integrating Physical Laws and Domain Knowledge into Numeric AI/ML

Post-hoc Prediction Correction: Long-Term Bias & Short-Term Drift

Balancing Model Sensitivity and Explainability (R²)

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