How would you detect that a scaling-law fit is wrong?

Detecting a poor scaling-law fit involves analyzing the residuals (L_hat - L_obs). If the residuals are not zero-mean or show a clear correlation with the input variables, the model is likely misspecified. A monotone sign pattern—where residuals are consistently positive for small models and negative for large ones—suggests that the optimizer has failed to find the global minimum. The standard fix is to use multi-start nonlinear regression, initialized near previous estimates, to ensure convergence to the same parameter values.