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DOE OSTI2022

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for their technologically promising properties remain mostly elusive. Computational approaches have played a major role in efforts to fill this void. In particular, dynamical mean field theory and its cluster extension, the dynamical cluster approximation have allowed significant progress. However, despite all the insightful results of these embedding schemes, computational constraints, such as the minus sign problem in quantum Monte Carlo (QMC), and the exponential growth of the Hilbert space in exact diagonalization (ED) methods, still limit the length scale within which correlations can be treated exactly in the formalism. A recent advance aiming to overcome these difficulties is the development of multiscale many body approaches whereby this challenge is addressed by introducing an intermediate length scale between the short length scale where correlations are treated exactly using a cluster solver such QMC or ED, and the long length scale where correlations are treated in a mean field manner. At this intermediate length scale correlations can be treated perturbatively. This is the essence of multiscale many-body methods. Furthermore, we will review various implementations of these multiscale many-body approaches, the results they have produced, and the outstanding challenges that should be addressed for further advances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Vector Field Decompositions Using Multiscale Poisson Kernel

Extraction of multiscale features using scale-space is one of the fundamental approaches to analyze scalar fields. However, similar techniques for vector fields are much less common, even though it is well known that, for example, turbulent flows contain cascades of nested vortices at different scales. The challenge is that the ideas related to scale-space are based upon iteratively smoothing the data to extract features at progressively larger scale, making it difficult to extract overlapping features. Instead, we consider spatial regions of influence in vector fields as scale, and introduce a new approach for the multiscale analysis of vector fields. Rather than smoothing the flow, we use the natural Helmholtz-Hodge decomposition to split it into small-scale and large-scale components using progressively larger neighborhoods. Our approach creates a natural separation of features by extracting local flow behavior, for example, a small vortex, from large-scale effects, for example, a background flow. We demonstrate our technique on large-scale, turbulent flows, and show multiscale features that cannot be extracted using state-of-the-art techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Polynomial Chaos Characterization of Uncertainty in Multiscale Models and Behavior of Carbon Reinforced Composites

Design of non-crimp fabric (NCF) composites entails major challenges pertaining to (1) the complex fine-scale morphology of the constituents, (2) the manufacturing-produced inconsistency of this morphology spatially, and thus (3) the ability to build reliable, robust, and efficient computational surrogate models to account for this complex nature. Traditional approaches to construct computational surrogate models have been to average over the fluctuations of the material properties at different scale lengths. This fails to account for the fine-scale features and fluctuations in morphology, material properties of the constituents, as well as fine-scale phenomena such as damage and cracks. In addition, it fails to accurately predict the scatter in macroscopic properties, which is vital to the design process and behavior prediction. In this work, funded in part by the Department of Energy, we present an approach for addressing these challenges by relying on polynomial chaos representations of both input parameters and material properties at different scales. Moreover, we emphasize the efficiency and robustness of integrating the polynomial chaos expansion with multiscale tools to perform multiscale assimilation, characterization, propagation, and prediction, all of which are necessary to construct the data-driven surrogate models required to design under the uncertainty of composites. These data-driven constructions provide an accurate map from parameters (and their uncertainties) at all scales and the system-level behavior relevant for design. While this perspective is quite general and applicable to all multiscale systems, NCF composites present a particular hierarchy of scales that permits the efficient implementation of these concepts.

42 ENGINEERING↗

DOE OSTI2025

Machine-Learning-Based Multiscale Methods for 3D Modelling of Granular Materials by Incorporating History-Dependent State Variables

Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.

granular materials↗

DOE OSTI2012

Multiscale framework for predicting the coupling between deformation and fluid diffusion in porous rocks

In this project, a predictive multiscale framework will be developed to simulate the strong coupling between solid deformations and fluid diffusion in porous rocks. We intend to improve macroscale modeling by incorporating fundamental physical modeling at the microscale in a computationally efficient way. This is an essential step toward further developments in multiphysics modeling, linking hydraulic, thermal, chemical, and geomechanical processes. This research will focus on areas where severe deformations are observed, such as deformation bands, where classical phenomenology breaks down. Multiscale geometric complexities and key geomechanical and hydraulic attributes of deformation bands (e.g., grain sliding and crushing, and pore collapse, causing interstitial fluid expulsion under saturated conditions), can significantly affect the constitutive response of the skeleton and the intrinsic permeability. Discrete mechanics (DEM) and the lattice Boltzmann method (LBM) will be used to probe the microstructure---under the current state---to extract the evolution of macroscopic constitutive parameters and the permeability tensor. These evolving macroscopic constitutive parameters are then directly used in continuum scale predictions using the finite element method (FEM) accounting for the coupled solid deformation and fluid diffusion. A particularly valuable aspect of this research is the thorough quantitative verification and validation program at different scales. The multiscale homogenization framework will be validated using X-ray computed tomography and 3D digital image correlation in situ at the Advanced Photon Source in Argonne National Laboratories. Also, the hierarchical computations at the specimen level will be validated using the aforementioned techniques in samples of sandstone undergoing deformation bands.

58 GEOSCIENCES↗

DOE OSTI2015

The center for multiscale plasma dynamics

This final report describes research performed in Princeton University, led by Professor Yannis G. Kevrekidis, over a period of six years (August 1, 2014 to July 31, 2010, including a one-year, no-cost extension) as part of the Center for Multiscale Plasma Dynamics led by the University of Maryland. The work resulted in the development and implementation of several multiscale algorithms based on the equation-free approach pioneered by the PI, including its applications in plasma dynamics problems. These algoriithms include coarse projective integration and coarse stability/bifurcation computations. In the later stages of the work, new links were made between this multiscale, coarse-graining approach and advances in data mining/machine learning algorithms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Finite Dimensional Approximations for Continuum Multiscale Problems

The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed research was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge of computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Addressing Critical Problems in Materials Science Through Multiscale and Multimode Characterization (Project 1); Characterization and Optimization of Novel Triple-Conducting Oxide Materials for Energy Applications (Project 2) (CRADA Final Report)

PROJECT 1: Address critical problems in materials science and simultaneously advance the state-of-the-art in multiscale and multimode characterization using the combined advanced analytical capabilities and expertise of Colorado School of Mines (CSM) and the National Renewable Energy Laboratory (NREL). The primary effort of the Phase I of this CRADA is to establish the International Center for Multiscale Characterization using shared resources at both NREL and CSM. Phase II will focus on capability development and marketing, choosing candidate materials science issues in the areas of structure imaging, chemical composition mapping, and correlating properties and performance of materials for impact in energy-related, environmental and critical materials areas. The CRADA will be modified to include specific topics of concern in materials science to industry member partners. Advanced analytical capabilities and expertise at CSM and NREL will be used to advance materials understanding and performance through characterization of multiscale phenomena including structural imaging, chemical composition mapping, and other techniques correlating properties and performance of materials. PROJECT 2: As part of the International Center for Materials Characterization, work under Modification #1 will be led by Colorado School of Mines (CSM), working in collaboration with NREL staff to mentor and advise CSM postdoctoral researchers on set up of diffusion annealing experiments. The purpose of the modification is to provide for NREL staff to mentor and advise CSM postdoctoral researchers on set up of diffusion annealing experiments, including mentoring and advising the CSM-NREL team on proper Secondary Ion Mass Spectrometry (SIMS) data analysis as needed. SIMS measurements of 10-20 samples will be performed at NREL during the project duration.

08 HYDROGEN↗

DOE OSTI2023

Assessing turbulence and mixing parameterizations in the gray-zone of multiscale simulations over mountainous terrain during the METEX21 field experiment

Multiscale numerical weather prediction models transition from mesoscale, where turbulence is fully parameterized, to microscale, where the majority of highly energetic scales of turbulence are resolved. The turbulence gray-zone is situated between these two regimes and multiscale models must downscale through these resolutions. Here, we compare three multiscale simulations which vary by the parameterization used for turbulence and mixing within the gray-zone. The three parameterizations analyzed are the Mellor-Yamada Nakanishi and Niino (MYNN) Level 2.5 planetary boundary layer scheme, the TKE-1.5 large eddy simulation (LES) closure scheme, and a recently developed three-dimensional planetary boundary layer scheme based on the Mellor-Yamada model. The simulation domain includes complex (i.e., mountainous) terrain in Nevada that was instrumented with meteorological towers, profiling and scanning lidars, a tethered balloon, and a surface flux tower. Simulations are compared to each other and to observations, with assessment of model skill at predicting wind speed, wind direction and TKE, and qualitative evaluations of transport and dispersion of smoke from controlled releases. This analysis demonstrates that microscale predictions of transport and dispersion can be significantly influenced by the choice of turbulence and mixing parameterization in the terra incognita , particularly over regions of complex terrain and with strong local forcing. This influence may not be apparent in the analysis of model skill, and motivates future field campaigns involving controlled tracer releases and corresponding modeling studies of the turbulence gray-zone.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

ezAlign: A Tool for Converting Coarse-Grained Molecular Dynamics Structures to Atomistic Resolution for Multiscale Modeling

Soft condensed matter is challenging to study due to the vast time and length scales that are necessary to accurately represent complex systems and capture their underlying physics. Multiscale simulations are necessary to study processes that have disparate time and/or length scales, which abound throughout biology and other complex systems. Herein we present ezAlign, an open-source software for converting coarse-grained molecular dynamics structures to atomistic representation, allowing multiscale modeling of biomolecular systems. The ezAlign v1.1 software package is publicly available for download at github.com/LLNL/ezAlign. Its underlying methodology is based on a simple alignment of an atomistic template molecule, followed by position-restraint energy minimization, which forces the atomistic molecule to adopt a conformation consistent with the coarse-grained molecule. The molecules are then combined, solvated, minimized, and equilibrated with position restraints. Validation of the process was conducted on a pure POPC membrane and compared with other popular methods to construct atomistic membranes. Additional examples, including surfactant self-assembly, membrane proteins, and more complex bacterial and human plasma membrane models, are also presented. By providing these examples, parameter files, code, and an easy-to-follow recipe to add new molecules, this work will aid future multiscale modeling efforts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRSDate not supplied

Software Architecture and Hierarchy of the Nasa Multiscale Analysis Tool

The NASA Multiscale Analysis Tool (NASMAT) serves as a state-of-the-art, “plug and play,” software package which utilizes multiscale recursive micromechanics as a platform for massively multiscale modeling for hierarchical materials and structures subjected to thermomechanical loads on high performance computing systems. This paper is intended to give an overview of the design of NASMAT and how the design supports modularity, upgradability and maintainability, interoperability, and utility. First, the software architecture and hierarchy will be explored. Details on each of the 11 NASMAT procedures and the arrangement of NASMAT data will be presented. Finally, application program interfaces (APIs) that were developed to facilitate the communication of NASMAT with other programs will be described.

multiscale modeling↗

NASA NTRSDate not supplied

A Partitioned -Task Parallel Implementation of the NASA Multiscale Analysis Tool for High Performance Computing

The NASA Multiscale Analysis Tool (NASMAT) is a “plug and play” software package that allows users to conduct massively multiscale modeling of hierarchical and nonlinear materials. This work extends the scalability and improves the High Performance Computing friendliness of NASMAT by adopting a Partitioned Task-Parallel approach. Interoperability of NASMAT with external software is enhanced through preCICE, a open source library for multiphysics coupling in a partitioned manner. Enhancement through preCICE allows for easy integration of NASMAT to other macro solvers and dissociates the parallelization strategy adopted within NASMAT from the macro solver. The task-parallel framework based on Master-Worker approach is implemented as the parallelization scheme. The scheme accounts for hierarchy of multiple scales (task-dependence) and heterogeneous nature (dynamic load balancing) of computations. The applicability and scalability of the framework will be evaluated by analyzing large scale engineering problems through massively multiscale methods.

NASMAT↗

NASA NTRSDate not supplied

Multiscale and Multifidelity Modeling of a 3D Woven Composite Thermal Protection System

Complex three-dimensional (3D) woven composites have been considered by multiple NASA projects in recent years as a means of offering improved mechanical and thermal performance over traditional laminated composite systems. Parallel efforts have focused on developing simulation capabilities for these systems, which have traditionally and heavily relied on experimental testing to evaluate composite performance. One system is the Heatshield for Extreme Entry Environment Technology (HEEET), which is being considered for the thermal protection system on reentry spacecraft. Optical microscopy was used to characterize the blended carbon and phenolic fiber tows. A section of HEEET insulation layer was imaged with high-resolution micro-computed tomography (microCT) and segmented to separate individual tows, porous matrix, and voids. These data were used to develop multiscale thermomechanical computational models within the NASA Multiscale Analysis Tool (NASMAT). Two NASMAT modeling approaches were considered to capture the details of the 3D woven architecture: a coarse model appropriate for inclusion in multiscale structural analyses and a high-fidelity model created by downsampling the microCT data. Both elastic and thermal properties were computed and compared. The feasibility and challenges associated with modeling complex, hybrid 3D woven composites were also addressed.

NASMAT↗

DOE OSTI2014

A Many-Task Parallel Approach for Multiscale Simulations of Subsurface Flow and Reactive Transport

Continuum-scale models have long been used to study subsurface flow, transport, and reactions but lack the ability to resolve processes that are governed by pore-scale mixing. Recently, pore-scale models, which explicitly resolve individual pores and soil grains, have been developed to more accurately model pore-scale phenomena, particularly reaction processes that are controlled by local mixing. However, pore-scale models are prohibitively expensive for modeling application-scale domains. This motivates the use of a hybrid multiscale approach in which continuum- and pore-scale codes are coupled either hierarchically or concurrently within an overall simulation domain (time and space). This approach is naturally suited to an adaptive, loosely-coupled many-task methodology with three potential levels of concurrency. Each individual code (pore- and continuum-scale) can be implemented in parallel; multiple semi-independent instances of the pore-scale code are required at each time step providing a second level of concurrency; and Monte Carlo simulations of the overall system to represent uncertainty in material property distributions provide a third level of concurrency. We have developed a hybrid multiscale model of a mixing-controlled reaction in a porous medium wherein the reaction occurs only over a limited portion of the domain. Loose, minimally-invasive coupling of pre-existing parallel continuum- and pore-scale codes has been accomplished by an adaptive script-based workflow implemented in the Swift workflow system. We describe here the methods used to create the model system, adaptively control multiple coupled instances of pore- and continuum-scale simulations, and maximize the scalability of the overall system. We present results of numerical experiments conducted on NERSC supercomputing systems; our results demonstrate that loose many-task coupling provides a scalable solution for multiscale subsurface simulations with minimal overhead.

high performance computing↗

DOE OSTI2020

Unveiling 3D Morphology of Multiscale Micro-Nanosilver Sintering for Advanced Electronics Manufacturing by Ptychographic X-ray Nanotomography

The sintering processing–structure–property relationship of a multiscale silver materials is investigated: microparticles with nanofeatures, particularly on their three-dimensional (3D) morphology. The target application is to replace conventional lead-based solders in advanced electronic manufacturing. Unlike lead-based solders, silver powders are suited to satisfy increasingly demanding mechanical, electrical, and thermal requirements, meanwhile being free of health effect. Sintering the material at a low temperature and without applied pressure are desirable conditions, which results in a preferred use of silver nanoparticles, as nanofeatures have higher driving force to sinter with the decrease in particle size. However, nanosized powders present potential health/environmental effects. To address the trade-off between the benefits and shortcomings of nano-versus microparticles, this work studies a novel multiscale silver paste, namely micron-sized powders with nanosized features. To get quantitative 3D visualization of micro- and nanoscale features, ptychographic X-ray computed nanotomography is applied. The correlations between conditions (thermal aging, pressure, and substrate metallization), mechanical properties, and morphological parameters are established. Finally, using novel 3D X-ray nanoimaging technique, it is demonstrated that one can design multiscale materials while balancing complex demands required in advanced electronics manufacturing and research directions in materials design and characterization.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Dynamics and lipid membrane coupling of the RAS-RAF complex revealed via multiscale simulations

To gain molecular and mechanistic insights into initiation of the RAS-RAF signaling cascade, we developed and used a combination of multiscale simulation and experimental approaches. The influence and impact of the membrane on RAS and RAF proteins is a factor we are just beginning to understand and appreciate in more detail. Molecular simulation is an ideal methodology to further study this complicated relationship between the membrane and associated proteins. Our previous work using Multiscale Machine-learned Modeling Infrastructure investigated different lipid compositions solely around the KRAS4b protein and the interplay between protein behavior and these membrane environments. Multiscale Machine-learned Modeling Infrastructure uses machine learning to couple adjacent simulation scales and has been efficiently scaled across some of the world’s largest high-performance computers. Recently, we have expanded this multiresolution framework to include the all-atom simulation scale and to incorporate the RAF RBDCRD domains. Here, we present the overall analysis results from this new simulation campaign comprising a mixture of RAS and RAF RBDCRD proteins. Approximately 35,000 coarse-grained and 10,000 all-atom molecular dynamics simulations were completed, sampled from a variety of protein/lipid composition configurations that were generated from a micron-scale continuum simulation containing hundreds of copies of the proteins. Our studies suggest that orientations of the RAS-RBDCRD complex on the membrane occupy distinct configurational states, and the spatial patterns of lipid arrangements around these different protein states are unique to each state. The extent and size of lipid “fingerprints” imposed on the membrane by the RAS-RBDCRD protein complex are significantly larger than observed for just the RAS protein on its own. These protein complexes strongly associate, but we do not observe statistically significant preferred protein-protein orientations. These observations indicate that spatial colocalization of RAS-RBDCRD proteins in the same vicinity may be assisted by specific membrane environments, acting to increase the probability of signaling complex formation.

Carpenter, Timothy S. [Lawrence Livermore National↗