We present a unified, data-driven framework for quantifying and enhancing offensive momentum and scoring likelihood (expected goals, xG) in professional hockey. Leveraging a Sportlogiq dataset of 541,000 NHL event records, our end-to-end pipeline comprises five stages: (1) interpretable momentum weighting of micro-events via logistic regression; (2) nonlinear xG estimation using gradient-boosted decision trees; (3) temporal sequence modeling with Long Short-Term Memory (LSTM) networks; (4) spatial formation discovery through principal component analysis (PCA) followed by K-Means clustering on standardized player coordinates; and (5) use of an X-Learner causal inference estimator to quantify the average treatment effect (ATE) of adopting the identified "optimal" event sequences and formations. We observe an ATE of 0.12 (95% CI: 0.05-0.17, p < 1e-50), corresponding to a 15% relative gain in scoring potential. These results demonstrate that strategically structured sequences and compact formations causally elevate offensive performance. Our framework delivers real-time, actionable insights for coaches and analysts, advancing hockey analytics toward principled, causally grounded tactical optimization.

We conduct a post hoc analysis of solar flare predictions made by a Long Short Term Memory (LSTM) model employing data in the form of Space-weather HMI Active Region Patches (SHARP) parameters. These data are distinguished in that the parameters are calculated from data in proximity to the magnetic polarity inversion line where the flares originate. We train the the LSTM model for binary classification to provide a prediction score for the probability of M/X class flares to occur in next hour. We then develop a dimension-reduction technique to reduce the dimensions of SHARP parameter (LSTM inputs) and demonstrate the different patterns of SHARP parameters corresponding to the transition from low to high prediction score. Our work shows that a subset of SHARP parameters contain the key signals that strong solar flare eruptions are imminent. The dynamics of these parameters have a highly uniform trajectory for many events whose LSTM prediction scores for M/X class flares transition from very low to very high. The results suggest that there exist a few threshold values of a subset of SHARP parameters when surpassed could indicate a high probability of strong flare eruption. Our method has distilled the knowledge of solar flare eruption learnt by deep learning model and provides a more interpretable approximation where more physics related insights could be derived.