Local versus Global Sensitivity
Local sensitivity measures the response to a small nudge at one point; global sensitivity averages influence over the whole uncertain input space.
Two scopes of the same question
Both approaches ask how inputs affect an output, but over different scopes. Local sensitivity examines the neighborhood of a single nominal point. Global sensitivity examines the entire range of plausible inputs. The right choice depends on whether the model is near-linear and whether inputs vary a little or a lot.
Local sensitivity
Local sensitivity is the vector of partial derivatives of the output with respect to each input, evaluated at a reference point. It answers how a small change in each input moves the output there. It is cheap - one gradient, often available by finite differences or automatic differentiation - and it underlies gradient-based optimization and first-order error propagation.
Its blind spots
- Valid only near the reference point; a different point can give different rankings
- Misses nonlinearity - a derivative is a straight-line approximation
- Ignores interactions between inputs
- Depends on input scaling unless the derivatives are normalized
Global sensitivity
Global methods - Sobol indices, Morris effects, regression measures - explore the full input distribution. They capture nonlinear response, interactions, and the effect of large input variation. The price is many model evaluations, which is why they are typically run on surrogates. Their rankings are robust across the input space rather than tied to one location.
Which to use
Use local analysis when uncertainties are small, the model is smooth, and a reference operating point is well defined - for instance, propagating tight tolerances. Use global analysis when uncertainties are large, the model is nonlinear, or interactions are suspected - the usual situation in early design when the operating point itself is uncertain.
In fusion design
Early Kronos design studies favor global sensitivity because operating parameters span wide ranges and the physics is nonlinear. As a design point for the machines settles, local sensitivity becomes useful for propagating manufacturing and control tolerances around that fixed point.