Hierarchical multiscale materials modeling: Calibration, uncertainty quantification, and decision support

Computational material models help establish structure-property relationships by simulating properties, and are most effective when physically-based. The length and time scales of each simulation are constrained both by model type and computing power. Significant uncertainty can arise when models attempt to bridge across length and time scales, especially when using different model constructs. Hierarchical multiscale modeling (HMM) links models at different scales by informing parameters and form of higher scale models based on lower scale simulations, which can reduce uncertainty. The combination of diverse information sources in HMMs requires rigorous approaches to evaluate uncertainty propagation. In the pursuit of improved methods for empirical testing and development of model hierarchies, four approaches in which information is coordinated amongst multiple models are presented. (1) In a reconciled top-down and bottom-up approach, a likelihood-based model calibration method is proposed, and bcc Fe crystal plasticity (CP) is used to demonstrate the compatibility of information pathways. (2) A statistical volume element (SVE) ensemble-based homogenization scheme of two models of cartridge brass polycrystal plasticity is used to inform a Bammann-Chiesa-Johnson macroplasticity model with a local variation in parameters. The effects of SVE size and model form on the performance of the homogenization in bridging microstructure variability to macroscale uncertainty are explored. (3) A multiscale model development framework is outlined for the reduced order modeling of mesoscale variability in cartridge brass. The variability in SVE simulations is included with the results of a series of spherical microindentation experiments in a multiscale data collection. An initial study of the modeling involved in connecting the two length scales is performed. (4) In a CP-finite element method (FEM) based Materials Knowledge System model of -Ti, the influence of texture is considered. Texture is parameterized using generalized spherical harmonics. The CP-FEM model is used with polycrystalline SVE-ensembles to calibrate the MKS model across different textures, sampled according to an uncertainty reduction criterion. Results of the work suggest that data collection is an especially critical step in the formulation and deployment of hierarchical multiscale models. The use of bottom-up information in calibrating a multiscale model is shown to be susceptible to bias. A multiscale approach to coarse-grained simulations of polycrystals at the mesoscale is proposed. An approach to automating the data collection for a reduced-order model of microstructure sensitive response is shown to be competitive with manual data selection, prior to full optimization of the automated approach.Ph.D

Uncertainty-aware predictions of molecular X-ray absorption spectra using neural network ensembles

As machine learning (ML) methods continue to be applied to a broad scope of problems in the physical sciences, uncertainty quantification is becoming correspondingly more important for their robust application. Uncertainty aware machine learning methods have been used in select applications, but largely for scalar properties. In this work, we showcase an exemplary study in which neural network ensembles are used to predict the X-ray absorption spectra of small molecules, as well as their point-wise uncertainty, from local atomic environments. The performance of the resulting surrogate clearly demonstrates quantitative correlation between errors relative to ground truth and the predicted uncertainty estimates. Significantly, the model provides an upper bound on the expected error. Specifically, an important quality of this uncertainty-aware model is that it can indicate when the model is predicting on out-of-sample data. This allows for its integration with large scale sampling of structures together with active learning or other techniques for structure refinement. Additionally, our models can be generalized to larger molecules than those used for training, and also successfully track uncertainty due to random distortions in test molecules. While we demonstrate this workflow on a specific example, ensemble learning is completely general. We believe it could have significant impact on ML-enabled forward modeling of a broad array of molecular and materials properties.Comment: 24 pages, 16 figure

Vision 2040: A Roadmap for Integrated, Multiscale Modeling and Simulation of Materials and Systems

Over the last few decades, advances in high-performance computing, new materials characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) and additive manufacturing have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. While these advances have driven significant progress in the development of aerospace components and systems, that progress has been limited by persistent technology and infrastructure challenges that must be overcome to realize the full potential of integrated materials and systems design and simulation modeling throughout the supply chain. As a result, NASA's Transformational Tools and Technology (TTT) Project sponsored a study (performed by a diverse team led by Pratt & Whitney) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. This report describes the findings of this 2040 Vision study (e.g., the 2040 vision state; the required interdependent core technical work areas, Key Element (KE); identified gaps and actions to close those gaps; and major recommendations) which constitutes a community consensus document as it is a result of over 450 professionals input obtain via: 1) four society workshops (AIAA, NAFEMS, and two TMS), 2) community-wide survey, and 3) the establishment of 9 expert panels (one per KE) consisting on average of 10 non-team members from academia, government and industry to review, update content, and prioritize gaps and actions. The study envisions the development of a cyber-physical-social ecosystem comprised of experimentally verified and validated computational models, tools, and techniques, along with the associated digital tapestry, that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of fit-for-purpose materials, components, and systems. Although the vision focused on aeronautics and space applications, it is believed that other engineering communities (e.g., automotive, biomedical, etc.) can benefit as well from the proposed framework with only minor modifications. Finally, it is TTT's hope and desire that this vision provides the strategic guidance to both public and private research and development decision makers to make the proposed 2040 vision state a reality and thereby provide a significant advancement in the United States global competitiveness