Surrogate Modeling with Gaussian Processes for an Inverse Problem in Polymer Dynamics

Chouhan, Pankaj; Shanbhag, Sachin

doi:10.1142/S0219876221430039

When rheological models of polymer blends are used for inverse modeling, they can characterize polymer mixtures from rheological observations. This requires repeated evaluation of potentially expensive rheological models. We explored surrogate models based on Gaussian processes (GP-SM) as a cheaper alternative for describing the rheology of polydisperse binary blends. We used the time-dependent diffusion double reptation (TDD-DR) model as the true model; it takes a 5-dimensional input vector specifying the binary blend as input and yields a function called the relaxation spectrum as output. We used the TDD-DR model to generate training data of different sizes [Formula: see text], via Latin hypercube sampling. The optimal values of the GP-SM hyper-parameters, assuming a separable covariance kernel, were obtained by maximum likelihood estimation. The GP-SM interpolates the training data by design and offers reasonable predictions of relaxation spectra with uncertainty estimates. In general, the accuracy of GP-SMs improves as the size of the training data [Formula: see text] increases, as does the cost for training and prediction. The optimal hyper-parameters were found to be relatively insensitive to [Formula: see text]. Finally, we considered the inverse problem of inferring the structure of the polymer blend from a synthetic dataset generated using the true model. Surprisingly, the solution to the inverse problem obtained using GP-SMs and TDD-DR was qualitatively similar. GP-SMs can be several orders of magnitude cheaper than expensive rheological models, which provides a proof-of-concept validation for using GP-SMs for inverse problems in polymer rheology.

More Like this