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Title: Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling

Journal Article · · Journal of Computational Physics

Scale bridging is a critical need in computational sciences, where the modeling community has developed accurate physics models from first principles, of processes at lower length and time scales that influence the behavior at the higher scales of interest. However, it is not computationally feasible to incorporate all of the lower length scale physics directly into upscaled models. This is an area where machine learning has shown promise in building emulators of the lower length scale models, which incur a mere fraction of the computational cost of the original higher fidelity models. We demonstrate the use of machine learning using an example in materials science estimating continuum scale parameters by emulating, with uncertainties, complicated mesoscale physics. Additionally, we describe a new framework to emulate the fine scale physics, especially in the presence of microstructures, using machine learning, and showcase its usefulness by providing an example from modeling fracture propagation. Our approach can be thought of as a data-driven dimension reduction technique that yields probabilistic emulators. Our results show well-calibrated predictions for the quantities of interests in a low-strain simulation of fracture propagation at the mesoscale level. Furthermore, on average, we achieve ~10% relative errors on time-varying quantities like total damage and maximum stresses. Successfully replicating mesoscale scale physics within the continuum models is a crucial step towards predictive capability in multi-scale problems.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
89233218CNA000001; 20170103DR
OSTI ID:
1645087
Alternate ID(s):
OSTI ID: 1809281
Report Number(s):
LA-UR-19-30618; TRN: US2203081
Journal Information:
Journal of Computational Physics, Vol. 420; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (15)

Reduced-order modeling of time-varying systems journal January 1999
Compressive sensing as a paradigm for building physics models journal January 2013
Microcracks in rocks: A review journal December 1983
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization journal January 2018
Model selection for dynamical systems via sparse regression and information criteria journal August 2017
Machine learning of linear differential equations using Gaussian processes journal November 2017
Hidden physics models: Machine learning of nonlinear partial differential equations journal March 2018
Machine learning in bioinformatics journal March 2006
A kernel-based method for data-driven koopman spectral analysis journal December 2015
Microfractures: A review journal December 2014
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems journal January 2015
Materials informatics journal October 2005
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data journal March 2017
Reduced-order modeling: new approaches for computational physics journal February 2004
Reduced-order modeling through machine learning and graph-theoretic approaches for brittle fracture applications journal February 2019