Large disparity between sensitivity of model parameters


I am trying to estimate the values of a number parameters. The sensitivity of the parameters with respect to the model output varies by several orders of magnitude. By sensitivity I am referring to the partial derivate of my cost function SE with respect to each parameter. See below image for parameter sensitivity magnitudes.

Analytical Gradients_1D_FE_FV

Notice that, for example, the sensitivity of parameter \beta is 1.8e5 while parameter \rho C_{pF} has a sensitivity of only 8.6e-1.

My questions are the following:

  • Can the NUTS sampler handle this level of disparity between parameter sensitivities?
  • If not, are there any tricks to help the sampler for this kind of model?

Re-parameterising is difficult as each parameter has a very specific and individual purpose (they are material coefficients in the heat equation which is solved using the Forward Euler Finite Difference method).