skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Uncertainty Quantification of Microstructures: A Perspective on Forward and Inverse Problems for Mechanical Properties of Aerospace Materials
In this review, state‐of‐the‐art studies on the uncertainty quantification (UQ) of microstructures in aerospace materials is examined, addressing both forward and inverse problems. Initially, it introduces the types of uncertainties and UQ algorithms. In the review, the forward problem of uncertainty propagation in process–structure and structure–property relationships is then explored. Subsequently, the inverse UQ problem, also known as the design under uncertainty problem, is discussed focusing on structure–process and property–structure linkages. Herein, the review concludes by identifying gaps in the current literature and suggesting key areas for future research, including multiscale topology optimization under uncertainty, implementing physics‐informed neural networks to UQ problems, investigating the effects of uncertainty on extreme mechanical behavior, reliability‐based design, and UQ in additive manufacturing.  more » « less
Award ID(s):
2053840 2236947
PAR ID:
10640383
Author(s) / Creator(s):
 ;  ;  ;  ;  ;  ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Advanced Engineering Materials
Volume:
27
Issue:
2
ISSN:
1438-1656
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Joan Bruna, Jan S (Ed.)
    In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-constrained framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty. Numerical results for an elliptic PDE-constrained Bayesian inverse problem are provided to verify the proposed framework. 
    more » « less
  2. Abstract There are two broad modeling paradigms in scientific applications: forward and inverse. While forward modeling estimates the observations based on known causes, inverse modeling attempts to infer the causes given the observations. Inverse problems are usually more critical as well as difficult in scientific applications as they seek to explore the causes that cannot be directly observed. Inverse problems are used extensively in various scientific fields, such as geophysics, health care and materials science. Exploring the relationships from properties to microstructures is one of the inverse problems in material science. It is challenging to solve the microstructure discovery inverse problem, because it usually needs to learn a one-to-many nonlinear mapping. Given a target property, there are multiple different microstructures that exhibit the target property, and their discovery also requires significant computing time. Further, microstructure discovery becomes even more difficult because the dimension of properties (input) is much lower than that of microstructures (output). In this work, we propose a framework consisting of generative adversarial networks and mixture density networks for inverse modeling of structure–property linkages in materials, i.e., microstructure discovery for a given property. The results demonstrate that compared to baseline methods, the proposed framework can overcome the above-mentioned challenges and discover multiple promising solutions in an efficient manner. 
    more » « less
  3. Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave‐based responses or deformation‐induced property variation). This work addresses rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and nonunique solutions. Unlike data‐intensive and noninterpretable deep‐learning‐based methods, this work proposes the random‐forest‐based interpretable generative inverse design (RIGID), a single‐shot inverse design method for fast generation of metamaterials with on‐demand functional behaviors. RIGID leverages the interpretability of a random forest‐based “design → response” forward model, eliminating the need for a more complex “response → design” inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. RIGID is validated on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm‐based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on‐demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints. 
    more » « less
  4. In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-informed framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty. 
    more » « less
  5. Hybrid rocket motors with paraffin-based fuels are of interest due to higher regression rates compared to other polymers. During paraffin combustion, a liquid layer forms on the fuel surface that, together with shearing forces from the oxidizer flow, results in the formation of instabilities at the fuel-oxidizer interface. These instabilities lead to the formation and entrainment of heterogeneous sized liquid droplets into the main flow and the combusting droplets result in higher motor output. The atomization process begins with droplet formation and ends with droplet pinch-off. The goal of this paper is to conduct an uncertainty quantification (UQ) analysis of the pinch-off process characterized by a pinch-off volume ($$V_{po}$$) and time ($$t_{po}$$). We study these quantities of interest (QoIs) in the context of a slab burner setup. We have developed a computationally expensive mathematical model that describes droplet formation under external forcing and trained an inexpensive Gaussian Process surrogate of the model to facilitate UQ. We use the pinch-off surrogate to forward propagate uncertainty of the model inputs to the QoIs and conduct two studies: one with gravity present and one without gravity effects. After forward-propagating the uncertainty of the inputs using the surrogate, we concluded that both QoIs have right-skewed distributions, corresponding to larger probability densities towards smaller pinch-off volumes and times. Specifically, for the pinch-off times, the resulting distributions reflect the effect of gravity acting against droplet formation, resulting in longer pinch-off times compared to the case where there is no gravity. 
    more » « less