  ICME approaches provide decision support for materials design by establishing
quantitative process-structure-property relations. Confidence in the decision
support, however, must be achieved by establishing uncertainty bounds in ICME
model chains. The quantification and propagation of uncertainty in
computational materials science, however, remains a rather unexplored aspect of
computational materials science approaches. Moreover, traditional uncertainty
propagation frameworks tend to be limited in cases with computationally
expensive simulations. A rather common and important model chain is that of
CALPHAD-based thermodynamic models of phase stability coupled to phase field
models for microstructure evolution. Propagation of uncertainty in these cases
is challenging not only due to the sheer computational cost of the simulations
but also because of the high dimensionality of the input space. In this work,
we present a framework for the quantification and propagation of uncertainty in
a CALPHAD-based elasto-chemical phase field model. We motivate our work by
investigating the microstructure evolution in Mg$_2$(Si$_x$Sn$_{1-x}$)
thermoelectric materials. We first carry out a Markov Chain Monte Carlo-based
inference of the CALPHAD model parameters for this pseudobinary system and then
use advanced sampling schemes to propagate uncertainties across a
high-dimensional simulation input space. Through high-throughput phase field
simulations we generate 200,000 time series of synthetic microstructures and
use machine learning approaches to understand the effects of propagated
uncertainties on the microstructure landscape of the system under study. The
microstructure dataset has been curated in the Open Phase-field Microstructure
Database (OPMD), available at
\href{http://microstructures.net}{http://microstructures.net}.
