Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagation

TL;DR

This paper introduces a data-driven framework that uncovers interpretable causal relations in material laws, enabling uncertainty quantification and robust predictions for complex material behaviors using deep learning and causal discovery algorithms.

Contribution

It develops a novel causal discovery algorithm combined with deep neural networks to infer and propagate causal relations in material law modeling with uncertainty quantification.

Findings

Accurately infers causal relations from RVE simulation data.

Provides robust predictions with quantified uncertainty.

Demonstrates effectiveness on traction-separation and elastoplasticity models.

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.