  This paper presents a computational framework that generates ensemble
predictive mechanics models with uncertainty quantification (UQ). We first
develop a causal discovery algorithm to infer causal relations among
time-history data measured during each representative volume element (RVE)
simulation through a directed acyclic graph (DAG). With multiple plausible sets
of causal relationships estimated from multiple RVE simulations, the
predictions are propagated in the derived causal graph while using a deep
neural network equipped with dropout layers as a Bayesian approximation for
uncertainty quantification. We select two representative numerical examples
(traction-separation laws for frictional interfaces, elastoplasticity models
for granular assembles) to examine the accuracy and robustness of the proposed
causal discovery method for the common material law predictions in civil
engineering applications.
