Model-Form Uncertainty
Model-form uncertainty is the error from choosing the wrong equations, distinct from uncertain parameters or numerical error.
The hardest uncertainty
Parametric uncertainty concerns the values in a model; numerical uncertainty concerns how well it is solved. Model-form (structural) uncertainty concerns whether the model equations themselves are right, for example an omitted physical mechanism or an inadequate closure. It is the hardest to quantify because it lives outside the model's own parameter space.
Why parameters cannot absorb it
Tuning parameters to compensate for a missing mechanism produces a model that fits calibration data but fails to extrapolate, because the compensation is specific to the calibration conditions. Separating model-form error explicitly (see Model Discrepancy Function) prevents this false confidence.
Approaches to quantify it
- Discrepancy functions added to the model output, learned from data
- Model averaging across a set of plausible model forms, weighted by evidence
- Comparing alternative closures or physics and treating the spread as uncertainty
- Embedded stochastic terms inside the governing equations
Bayesian model averaging
When several candidate models exist, Bayesian model averaging weights each by its posterior probability given the data and mixes their predictions. The resulting uncertainty includes disagreement between model forms, which a single model cannot express. Its weakness is that it assumes the true model is among the candidates.
Honest reporting
Model-form uncertainty is often the dominant term in extrapolation yet the most frequently ignored. For fusion design where machines are simulated rather than built, distinguishing 'the parameters might be off' from 'the physics model might be incomplete' is essential to honest gates: predictions carry both, and structured discrepancy is reported as a signal to investigate missing physics rather than retuned away.