9.2.5 Inverse Modeling

Many models in TCAD applications contain free parameters which depend on properties of the device material and have to be calibrated using measurements. Usually vectors of measured values are fit to characteristic curves of the device in question.

It is not obvious which goal function should be used in an inverse modeling experiment where the distance between two vectors (where one is constant) is to be minimized. To facilitate experimentation and allow users to construct a suitable goal function, we provide the log10, euclidean-norm, p-metric, p-norm, append-vectors and relative-error functions.

Example.

? (mapcar #'log10 (list 1e10 1e20 1e30))

> (10.0 20.0 30.0)

? (p-norm (list 1 2 3))

> 3.7416575

? (mapcar #'(lambda (p)
              (p-norm (vector 1 2 3) p))
          (list 1/4 1/3 1/2 1 2 3 4))

> (150.97025 50.7422 17.19151 6 3.7416575 3.3019273 3.1463463)