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Uncertainty propagates through calculations, down to molecular scales toinfer microstructural features, and up to macroscopic scales with predictiveflow simulations. Here we study uncertainty quantification for sequential(two-step) versus simultaneous (all at once) fitting methods with linear andweakly-nonlinear rheological data. Using an example of a combined dataset onsmall-amplitude oscillatory shear (SAOS) and medium-amplitude oscillatory shear(MAOS) for a linear entangled polymer melt (cis-1,4-polyisoprene), wedemonstrate with a multi-mode Giesekus model how the fit parameteruncertainties are significantly under-estimated with the sequential fit becauseof the neglect of model parameter correlations. These results are surprisingbecause weakly-nonlinear data is only an asymptotic step away from the lineardata, yet it has significant impact on calibrating the linear model parameters.Similarly, the nonlinear parameter estimates and uncertainties are impacted byconsidering the linear data in a simultaneous fit. To compare multi-modespectra of nonlinear parameters (mobility parameters {\alpha_i} from theGiesekus model), we derive new average measures based on moments of the spectrarelated to the high-frequency MAOS limit. The spectral averages are alsosensitive to sequential versus simultaneous fitting. Our results reveal theimportance of using simultaneous fitting for honest uncertainty quantification,even with weakly-nonlinear data.

On simultaneous fitting of nonlinear and linear rheology data: Preventing a false sense of certainty