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

  title={Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagation},
  author={Xiao Sun and Bahador Bahmani and Nikolaos N. Vlassis and Waiching Sun and Yanxun Xu},
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… 
Constitutive model characterization and discovery using physics-informed deep learning
It is demonstrated that the proposed framework can efficiently identify the underlying constitutive model describing different datasets from the von Mises family, and leverage foundations of elastoplasticity theory as regularization terms in the total loss function to find parametric constitutive models that are also theoretically sound.
Thermodynamics-based Artificial Neural Networks (TANN) for multiscale modeling of materials with inelastic microstructure
The efficiency and accuracy of TANN in predicting the average and local stress-strain response, the internal energy and the dissipation of both regular and perturbed 2D and 3D lattice microstructures in inelasticity are shown.
Use of machine learning for unraveling hidden correlations between particle size distributions and the mechanical behavior of granular materials
An artificial Neural Network scheme, trained with a few hundred DEM simulations, was able to anticipate the value of the model parameters for all these PSDs, with considerable accuracy, and revealed the existence of hidden correlations between PSD of granular materials and their macroscopic mechanical behavior.
DEM simulations of agglomerates impact breakage using Timoshenko beam bond model
Attrition and breakage of agglomerates are prevalent during production and handling processes in many industries. Therefore, it is highly desirable to be able to model and analyse the agglomerate


Meta-modeling game for deriving theory-consistent , microstructure-based traction – separation laws via deep reinforcement learning
This paper presents a new meta-modeling framework that employs deep reinforcement learning (DRL) to generate mechanical constitutive models for interfaces that is capable of detecting hidden mechanisms among micro-structural features and incorporating them in constitutive model to improve the forward prediction accuracy, both of which are difficult tasks to do manually.
Causal network reconstruction from time series: From theoretical assumptions to practical estimation.
The problem of inferring causal networks including time lags from multivariate time series is recapitulated from the underlying causal assumptions to practical estimation problems and method performance evaluation approaches and criteria are suggested.
A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation
A new concept from graph theory where a modeler agent is tasked with evaluating all the modeling options recast as a directed multigraph and find the optimal path that links the source of the directed graph to the target measured by an objective function is introduced.
Causal Discovery from Heterogeneous/Nonstationary Data
A framework for causal discovery from heterogeneous/NOnstationary Data to find causal skeleton and directions and estimate the properties of mechanism changes, and finds that data heterogeneity benefits causal structure identification even with particular types of confounders.
Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models
This paper treats forecasting as a problem in Bayesian inference in the causal model, which exploits the timevarying property of the data and adapts to new observations in a principled manner.
Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
A new theoretical framework is developed casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes, which mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy.
Multi-domain Causal Structure Learning in Linear Systems
This work introduces the approach for finding causal direction in a system comprising two variables and proposes efficient methods for identifying causal direction, and generalizes to the case that there is no such invariance across domains.
Challenges and Opportunities with Causal Discovery Algorithms: Application to Alzheimer’s Pathophysiology
Two CSD methods were evaluated in their ability to discover this structure from data collected by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) and managed to discover graphs that nearly coincided with the gold standard.
Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning