Our collaborative paper (with Johns Hopkins) on causal discovery of interpretable deep learning material laws with uncertainty propagation has been accepted by Granular Matter

Author: Xiao Sun, Bahador Bahmani, Nikolaos N. Vlassis, WaiChing Sun, Yanxun Xu

Abstract: 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.

The preprint is available at [URL]. The key ideas are to explore if causal discovery algorithm can deduce the plausible causal relations and whether the discovered causal relations match with our current state-of-the-art knowledge discovered by human. One interesting aspect I found quite interesting is that, while incorporating the causal relation into the deep learning constitutive laws might improve the interpretability, it does not always improve the accuracy (for instance, when prediction the properties of the immediate vertices is harder than that of the leaves of the causal graph).