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DOE OSTI2022

Exploiting Machine Learning in Multiscale Modelling of Materials

Recent developments in efficient machine learning algorithms have spurred significant interest in the materials community. The inherently complex and multiscale problems in Materials Science and Engineering pose a formidable challenge. The present scenario of machine learning research in Materials Science has a clear lacunae, where efficient algorithms are being developed as a separate endeavour, while such methods are being applied as ‘black-box’ models by others. The present article aims to discuss pertinent issues related to the development and application of machine learning algorithms for various aspects of multiscale materials modelling. The authors present an overview of machine learning of equivariant properties, machine learning-aided statistical mechanics, the incorporation of ab initio approaches in multiscale models of materials processing and application of machine learning in uncertainty quantification. In addition to the above, the applicability of Bayesian approach for multiscale modelling will be discussed. Critical issues related to the multiscale materials modelling are also discussed.

42 ENGINEERING↗

DOE OSTI2019

Designing Multiscale Porous Metal by Simple Dealloying with 3D Morphological Evolution Mechanism Revealed via X-ray Nano-tomography

Designing materials with multiscale, hierarchical structure is critical to drive the advancement of new technology. Specifically, porous metals with multiscale porosity from nanometer to micrometer sizes would lead to enhanced physical and chemical properties—the micron-sized pores can increase the effective diffusivity of ion transport within the porous media, and the nano-sized pores provide high specific surface area, enabling functionalities that are unique to nanoporous metals. A new ternary precursor alloy selection concept utilizing the different mixing enthalpies is demonstrated in this work for the design of multiscale, bimodal porous copper from a simple, one-step dealloying of Cu–Fe–Al ternary alloy. The nanoporosity in the bimodal porous structure is formed from dealloying of the Cu-rich phase, whereas the microporosity is controlled by dissolving the Fe-rich phase, determined by both the initial Fe particle size and sintering profile. In addition to advancing the materials design method, the multiscale pore formation during dealloying was directly visualized and quantified via an interrupted in situ synchrotron X-ray nano-tomography. The 3D morphological analysis on tortuosity showed that the presence of the microporosity can compensate the increase of the diffusion path length due to nanoporosity, which facilitates diffusion within the porous structure. Altogether the focus of the work is to introduce a new strategy to design multiscale porous metals with enhanced transport properties, and sheds light on the fundamental mechanisms on the 3D morphological evolution of the system using advanced synchrotron X-ray nano-tomography for future materials development and applications.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunityin this regard. However, classical machine learning techniques often ignore the fundamental laws of physics and result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large data sets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We critically review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Nonlinear multiphysics and multiscale modeling of dynamic ferromagnetic–thermal problems

A coupled ferromagnetic–thermal solver is developed for the multiphysics and multiscale modeling and simulation of nonlinear magnetic materials in the time domain. By adopting a temperature-dependent dynamic hysteresis model, the power loss is characterized and calculated from the solution of Maxwell's equations, which serves as the heat source for the thermal problem. By solving the thermal problem, the temperature change is obtained, and its effect on the magnetic material property can be quantified, which is then coupled back to Maxwell's equations. Due to different temporal characteristics of the electromagnetic fields and the thermal response, the resulting coupled ferromagnetic–thermal system has two significantly different time scales. Such a temporal multiscale issue is addressed with a proposed multiscale time integration method to account for the multiscale coupling between the two physics. With the proposed multiphysics and multiscale modeling method, both the electromagnetic fields and the thermal responses can be captured accurately in a dynamic operation.

Yan, Su (ORCID:0000000273763493)↗

DOE OSTI2017

Multiscale Pressure-Balanced Structures in Three-dimensional Magnetohydrodynamic Turbulence

Observations of solar wind turbulence indicate the existence of multiscale pressure-balanced structures (PBSs) in the solar wind. In this work, we conduct a numerical simulation to investigate multiscale PBSs and in particular their formation in compressive magnetohydrodynamic turbulence. By the use of the higher-order Godunov code Athena, a driven compressible turbulence with an imposed uniform guide field is simulated. The simulation results show that both the magnetic pressure and the thermal pressure exhibit a turbulent spectrum with a Kolmogorov-like power law, and that in many regions of the simulation domain they are anticorrelated. The computed wavelet cross-coherence spectra of the magnetic pressure and the thermal pressure, as well as their space series, indicate the existence of multiscale PBSs, with the small PBSs being embedded in the large ones. These multiscale PBSs are likely to be related to the highly oblique-propagating slow-mode waves, as the traced multiscale PBS is found to be traveling in a certain direction at a speed consistent with that predicted theoretically for a slow-mode wave propagating in the same direction.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Multiscale mechanical design of the lightweight, stiff, and damage-tolerant cuttlebone: A computational study

Cuttlebone, the endoskeleton of cuttlefish, offers an intriguing biological structural model for designing low-density cellular ceramics with high stiffness and damage tolerance. Cuttlebone is highly porous (porosity ~93%) and lightweight (density less than 20% of seawater), constructed mainly by brittle aragonite (95 wt%), but capable of sustaining hydrostatic water pressures over 20 atmospheres and exhibits energy absorption capability under compression comparable to many metallic foams (~4.4 kJ/kg). Here, in this work, we computationally investigate how such remarkable mechanical efficiency is enabled by the multiscale structure of cuttlebone. Using the common cuttlefish, Sepia Officinalis, as a model system, we first conducted high-resolution synchrotron micro-computed tomography (µ-CT) and quantified the cuttlebone's multiscale geometry, including the 3D asymmetric shape of individual walls, the wall assembly patterns, and the long-range structural gradient of walls across the entire cuttlebone (ca. 38 chambers). The acquired 3D structural information enables systematic finite-element simulations, which further reveal the multiscale mechanical design of cuttlebone: at the wall level, wall asymmetry provides optimized energy absorption while maintaining high structural stiffness; at the chamber level, variation of walls (number, pattern, and waviness amplitude) contributes to progressive damage; at the entire skeletal level, the gradient of chamber heights tailors the local mechanical anisotropy of the cuttlebone for reduced stress concentration. Our results provide integrated insights into understanding the cuttlebone's multiscale mechanical design and provide useful knowledge for the designs of lightweight cellular ceramics.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A multiscale recurrent neural network model for predicting energy production from geothermal reservoirs

Optimization of energy production from geothermal reservoirs requires reliable prediction of energy production performance under alternative operation and development scenarios. Traditionally, reservoir simulation models are used for the evaluation and screening of alternative production and development plans. However, simulation models require extensive data collection and modeling efforts and are time-consuming to build, run, and update. Data-driven predictive models, on the other hand, can serve as efficient prediction tools that can be used for decision support and management of daily operations and surveillance activities. Data-driven models become particularly attractive when a reservoir simulation model for a field does not exist and/or is difficult to build. Machine learning (ML)-based data-driven models that have recently become popular in several fields exploit statistical patterns and relations in training data to generate predictions. As such, they tend to perform better in interpolation problems (that is, prediction within the training data range) than when they are used to extrapolate beyond the training data. Production data from geothermal reservoirs tend to exhibit short-term variabilities as well as long-term trends, such as monotonically declining production temperatures. Capturing both short-term features and long-term trends with ML-based models is not trivial. We evaluate the use of recurrent neural networks (RNN) for the prediction of energy production from geothermal reservoirs. RNN is a class of ML architectures that are used to represent and predict sequential/dynamic data. Thus, it can be challenging to apply RNN to problems where long-term trends must be captured and extrapolation beyond the training data range is needed. We introduce the multiscale RNN architecture to extend the application of RNN to detect and predict both short-term variabilities and long-term trends in geothermal data. The developed architecture consists of a long-term component to only capture low-frequency data patterns, and a short-term component to detect features with higher frequency and more nonlinearity. The final prediction is obtained by combining the long-term and short-term predictions. Both synthetic and field data are used to evaluate the presented multiscale RNN model. The prediction performance of the multiscale RNN is compared against those obtained from the regular RNN and the autoregressive (AR) model. The results suggest that the multiscale architecture improves the long-term prediction performance of the regular RNN and enhances its robustness against noise.

15 GEOTHERMAL ENERGY↗

DOE OSTI2019

Stochastic multiscale flux basis for Stokes-Darcy flows

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Physics-informed neural network (PINN) is a data-driven approach to solving equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization approximates a multiscale equation by a homogenized equation without multiscale property; it includes solving cell problems and the homogenized equation. The cell problems are periodic, and we propose an oversampling strategy that significantly improves the PINN accuracy on periodic problems. The homogenized equation has a constant or slow dependency coefficient and can also be solved by PINN accurately. We hence proposed a 3-step method, neural homogenization based PINN (NH-PINN), to improve the PINN accuracy for solving multiscale problems with the help of homogenization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

The confluence of machine learning and multiscale simulations

Multiscale modeling has a long history of use in structural biology, as computational biologists strive to overcome the time- and length-scale limits of atomistic molecular dynamics. Contemporary machine learning techniques, such as deep learning, have promoted advances in virtually every field of science and engineering and are revitalizing the traditional notions of multiscale modeling. Deep learning has found success in various approaches for distilling information from fine-scale models, such as building surrogate models and guiding the development of coarse-grained potentials. However, perhaps its most powerful use in multiscale modeling is in defining latent spaces that enable efficient exploration of conformational space. In conclusion, this confluence of machine learning and multiscale simulation with modern high-performance computing promises a new era of discovery and innovation in structural biology.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. Here, the decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2016

Revisiting of Multiscale Static Analysis of Notched Laminates Using the Generalized Method of Cells

Composite material systems generally exhibit a range of behavior on different length scales (from constituent level to macro); therefore, a multiscale framework is beneficial for the design and engineering of these material systems. The complex nature of the observed composite failure during experiments suggests the need for a three-dimensional (3D) multiscale model to attain a reliable prediction. However, the size of a multiscale three-dimensional finite element model can become prohibitively large and computationally costly. Two-dimensional (2D) models are preferred due to computational efficiency, especially if many different configurations have to be analyzed for an in-depth damage tolerance and durability design study. In this study, various 2D and 3D multiscale analyses will be employed to conduct a detailed investigation into the tensile failure of a given multidirectional, notched carbon fiber reinforced polymer laminate. Threedimensional finite element analysis is typically considered more accurate than a 2D finite element model, as compared with experiments. Nevertheless, in the absence of adequate mesh refinement, large differences may be observed between a 2D and 3D analysis, especially for a shear-dominated layup. This observed difference has not been widely addressed in previous literature and is the main focus of this paper.

Materials Engineering↗

NASA NTRSDate not supplied

Benchmarking and Performance of the NASA Multiscale Analysis Tool

The NASA Multiscale Analysis Tool (NASMAT) is as a “plug and play,” software package which utilizes multiscale recursive micromechanics as a platform for massively multiscale modeling of hierarchical materials and structures subjected to thermomechanical. 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. Application program interfaces (APIs) that were developed to facilitate the communication of NASMAT with other programs will be described. The intended application for NASMAT is massively multiscale modeling on high performance computing systems. As such, results benchmarking the performance of the integration of NASMAT with the Abaqus commercial finite element method software are also presented.

Multiscale Modeling↗

NASA NTRSDate not supplied

Multiscale Prediction of Yarn Pullout Failure Mode in Unreinforced Textile Fabrics

Unreinforced woven fabrics have been implemented in a variety of high performance applications, including body armor, deployable structures, and as the reinforcement material in composites. Multiscale modeling techniques have significantly improved the capabilities of simulation-based tools to capture fabric mechanics efficiently and accurately, but often lack in their prediction of failure and require pairing with finite element analysis (FEA) software, limiting their application to the design of ‘fit-for-purpose’ materials. NASA’s Multiscale Analysis Tool (NASMAT) is a standalone multiscale program that has been traditionally used in the analysis of reinforced composites materials. More recently, it has been amended to simulate unreinforced fabric behavior by allowing the geometric state of the tows to change with applied loading due to the lack of a reinforcement material, such as the matrix seen in composites. Previous work has shown the ability of NASMAT to capture nonlinear macroscale behavior by predicting geometric changes in the state of each subcell as a function of the applied loading and allowing each subcell in the analysis to rotate according to these predicted changes, as well as predict nonlinear behavior due to the fiber breakage failure mode. In this work, the capability of predicting the onset and propagation of failure in plain woven fabrics in NASMAT is presented for the yarn pullout failure mode, which occurs when a fabric is loaded at an off-axis angle relative to the warp of weft tow direction. Yarn pullout behavior is initiated by determining the applied load in which the shear resistance of the contact area between yarn families is overcome. When failure is initiated, yarn pullout is determined to have occurred when the applied displacement, calculated from global strain, exceeds the deformed position of a given contact points between yarn families, determined from pin-joint kinematics. Contact points where pullout has occurred contribute to a global damage parameter used to modify the homogenized stiffness of the fabric, resulting in nonlinear behavior observed at the macroscale. The off-axis loading behavior and yarn pullout failure theory have been developed and implemented into NASMAT such that users can simulate off-axis tensile behavior of fabrics in a single, standalone multiscale tool. Simulations are compared to uniaxial tensile tests at various off-axis angles to demonstrate the capability of the tool in its prediction of both the onset of failure at each off-axis angles and the stress-strain behavior as failure progresses.

Materials↗

DOE OSTI2017

Self-consistent clustering analysis: an efficient multiscale scheme for inelastic heterogeneous materials

A predictive computational theory is shown for modeling complex, hierarchical materials ranging from metal alloys to polymer nanocomposites. The theory can capture complex mechanisms such as plasticity and failure that span across multiple length scales. This general multiscale material modeling theory relies on sound principles of mathematics and mechanics, and a cutting-edge reduced order modeling method named self-consistent clustering analysis (SCA) [Zeliang Liu, M.A. Bessa, Wing Kam Liu, “Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials,” Comput. Methods Appl. Mech. Engrg. 306 (2016) 319–341]. SCA reduces by several orders of magnitude the computational cost of micromechanical and concurrent multiscale simulations, while retaining the microstructure information. This remarkable increase in efficiency is achieved with a data-driven clustering method. Computationally expensive operations are performed in the so-called offline stage, where degrees of freedom (DOFs) are agglomerated into clusters. The interaction tensor of these clusters is computed. In the online or predictive stage, the Lippmann-Schwinger integral equation is solved cluster-wise using a self-consistent scheme to ensure solution accuracy and avoid path dependence. To construct a concurrent multiscale model, this scheme is applied at each material point in a macroscale structure, replacing a conventional constitutive model with the average response computed from the microscale model using just the SCA online stage. A regularized damage theory is incorporated in the microscale that avoids the mesh and RVE size dependence that commonly plagues microscale damage calculations. The SCA method is illustrated with two cases: a carbon fiber reinforced polymer (CFRP) structure with the concurrent multiscale model and an application to fatigue prediction for additively manufactured metals. For the CFRP problem, a speed up estimated to be about 43,000 is achieved by using the SCA method, as opposed to FE2, enabling the solution of an otherwise computationally intractable problem. The second example uses a crystal plasticity constitutive law and computes the fatigue potency of extrinsic microscale features such as voids. This shows that local stress and strain are capture sufficiently well by SCA. This model has been incorporated in a process-structure-properties prediction framework for process design in additive manufacturing.

Liu, Z.↗

DOE OSTI2019

A high-order multiscale finite-element method for time-domain elastic wave modeling in strongly heterogeneous media

Efficient and accurate numerical methods for elastic wave modeling in complex media have many important applications. However, it is fairly challenging to model elastic wave propagation in strongly heterogeneous media with high computational efficiency and high-order accuracy simultaneously. We develop a novel high-order multiscale finite-element method to model elastic wave propagation in strongly heterogeneous media in the time domain. The most important feature of our method is a generalization of standard multiscale finite element method by using high-order multiscale finite-element basis functions to capture the fine-scale heterogeneities on the coarse mesh, in contrast to conventional finite-element basis functions that are merely determined by the order of polynomials. These multiscale basis functions leads to a system matrix with significantly reduced dimension, thus enable us to solve the elastic wave equation on the coarse mesh with high-order accuracy and very low computational time cost. In conclusion, we use 2D and 3D numerical examples to demonstrate the superior efficiency and accuracy of our new modeling method compared with the conventional spectral-element method.

58 GEOSCIENCES↗

DOE OSTI2022

Asynchronous Reciprocal Coupling of Martini 2.2 Coarse-Grained and CHARMM36 All-Atom Simulations in an Automated Multiscale Framework

The appeal of multiscale modeling approaches is predicated on the promise of combinatorial synergy. However, this promise can only be realized when distinct scales are combined with reciprocal consistency. Here, we consider multiscale molecular dynamics (MD) simulations that combine the accuracy and macromolecular flexibility accessible to fixed-charge all-atom (AA) representations with the sampling speed accessible to reductive, coarse-grained (CG) representations. AA-to-CG conversions are relatively straightforward because deterministic routines with unique outcomes are achievable. Conversely, CG-to-AA conversions have many solutions due to a surge in the number of degrees of freedom. While automated tools for biomolecular CG-to-AA transformation exist, we find that one popular option, called Backward, is prone to stochastic failure and the AA models that it does generate frequently have compromised protein structure and incorrect stereochemistry. Although these shortcomings can likely be circumvented by human intervention in isolated instances, automated multiscale coupling requires reliable and robust scale conversion. In this work, we detail an extension to Multiscale Machine-learned Modeling Infrastructure (MuMMI), including an improved CG-to-AA conversion tool called sinceCG. This tool is reliable (~98% weakly correlated repeat success rate), automatable (no unrecoverable hangs), and yields AA models that generally preserve protein secondary structure and maintain correct stereochemistry. We describe how the MuMMI framework identifies CG system configurations of interest, converts them to AA representations, and simulates them at the AA scale while on-the-fly analyses provide feedback to update CG parameters. Application to systems containing the peripheral membrane protein RAS and proximal components of RAF kinase on complex eight-component lipid bilayers with ~1.5 million atoms is discussed in the context of MuMMI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗