Regression Methods for Fusion Data
Fitting continuous relationships from data, from linear models to flexible learners, with fusion examples.
The regression task
Regression predicts a continuous quantity from inputs: confinement time from engineering parameters, a flux from gradients, a profile value from settings. The choice of method trades flexibility against data efficiency and interpretability.
A spectrum of models
- Linear and log-linear regression: interpretable, data-efficient, limited flexibility
- Regularized linear models (ridge, lasso): stable with many correlated inputs
- Gaussian processes: flexible with calibrated uncertainty, costly at scale
- Gradient-boosted trees: strong on tabular data, limited extrapolation
- Neural networks: flexible for high-dimensional inputs, data-hungry
Regularization
Fusion datasets are often small and their inputs correlated. Regularization, penalizing model complexity, prevents overfitting and stabilizes estimates. Lasso can also select the few inputs that matter, aiding interpretation.
Interpretability versus flexibility
A log-linear scaling law is transparent and extrapolates in a known way; a deep network fits complex structure but is opaque and extrapolates unpredictably. For safety-relevant or design-critical use, the simpler interpretable model is often preferred unless the added flexibility is clearly needed and validated.
Honest evaluation
Cross-validate, report error distributions rather than a single score, and test at the edges of the input domain. Distinguish interpolation performance from extrapolation performance, since fusion often needs the latter and it is always weaker. A good average error can hide large errors exactly where a design pushes into new territory.