Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagation
This work addresses the need for interpretable and uncertain-aware predictive models in civil engineering material science, representing an incremental advancement by combining existing causal discovery and Bayesian deep learning techniques.
The paper tackles the problem of predicting material laws in civil engineering by developing a framework that uses causal discovery from simulation data and deep neural networks with dropout for uncertainty quantification, achieving accurate and robust predictions in two numerical examples.
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.