Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “multiscale problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

Predicting mechanical responses of heterogeneous materials across scales remains a significant challenge. Traditional computational methods often struggle with complex and multiscale nature of these materials, limiting their effectiveness in real-world applications. Here, in this paper, we introduce Micrometer, a vision transformer based deep learning model designed to predict full field mechanical responses of heterogeneous materials, bridging the gap between computer vision and solid mechanics problems. We show that Micrometer, trained on a large-scale high-resolution dataset of 2D fiber-reinforced composites, can achieve state-of-the-art performance in predicting microscale strain fields across a wide range of material properties and loading conditions. Our model demonstrates accuracy and computational efficiency in applications such as computational homogenization and multiscale modeling, reducing computational time by up to two orders of magnitude compared to conventional numerical solvers while maintaining less than 1 % errors in predicting macroscale stress fields. Furthermore, we showcase Micrometer’s adaptability through transfer learning experiments on new materials with limited data, highlighting its potential to tackle diverse scenarios in computational solid mechanics. These results represent a significant step towards AI-driven innovation in materials science, addressing the limitations of traditional numerical methods and paving the way for more efficient simulations of heterogeneous materials across various industrial applications.

Composite materials↗
DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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

Primal interface debonding formulation for finite strain isotropic plasticity

In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.

42 ENGINEERING↗
DOE OSTI2025

A Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet‐Neumann Schwarz Alternating Method

Contact phenomena are crucial for understanding the behavior of mechanical systems. However, existing computational approaches for simulating mechanical contact often face numerical challenges, such as inaccurate physical predictions, energy conservation errors, and unwanted oscillations. Here, we introduce an alternative technique for simulating dynamic contact based on the non‐overlapping Schwarz alternating method, originally developed for domain decomposition. In multibody contact scenarios, this method treats each body as a separate, non‐overlapping domain and prevents interpenetration using an alternating Dirichlet–Neumann iterative process. This approach has a strong theoretical foundation, eliminates the need for contact constraints, and offers flexibility, making it ideal for multiscale and multiphysics applications. We conducted a numerical comparison between the Schwarz method and traditional methods, such as the Lagrange multiplier and penalty methods, focusing on a benchmark impact problem. Our results indicate that the Schwarz alternating method outperforms traditional methods in several key areas: it provides more accurate predictions for various measurable quantities and demonstrates exceptional energy conservation capabilities. To address unwanted oscillations in contact velocities and forces, we explored various algorithms and stabilization techniques, ultimately opting for the naïve‐stabilized Newmark scheme for its simplicity and effectiveness. Additionally, we validated the efficiency of the Schwarz method in a three‐dimensional impact problem, highlighting its inherent capacity to accommodate different mesh topologies, time‐integration schemes, and time steps for each interacting body.

Schwarz alternating method↗
DOE OSTI2021

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as O(Ne4) where Ne is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to O(Ne 3 ) in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the O(Ne 3 ) complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. In this work, we demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Enhanced multiscale restriction-smoothed basis (MsRSB) preconditioning with applications to porous media flow and geomechanics

A novel method to enable application of the Multiscale Restricted Smoothed Basis (MsRSB) method to non M-matrices is presented. The original MsRSB method is enhanced with a filtering strategy enforcing M-matrix properties to enable the robust application of MsRSB as a preconditioner. Through applications to porous media flow and linear elastic geomechanics, the method is proven to be effective for scalar and vector problems with multipoint finite volume (FV) and finite element (FE) discretization schemes, respectively. Realistic complex (un)structured two- and three-dimensional test cases are considered to illustrate the method's performance.

58 GEOSCIENCES↗
DOE OSTI2020

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

In this paper, an extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.

multiscale↗
DOE OSTI2020

Use of Remote Sensing and In-situ Observations to Develop and Evaluate Improved Representations of Convection and Clouds for the Accelerated Climate Model for Energy. Final report

Representation of unresolved cloud processes has been one of the most challenging problems in numerical modeling of the atmosphere. During the last decades, considerable efforts have been spent to better represent the collective effects of those processes in terms of resolved scales (see Arakawa 2004 for a review). Still, the progress on this problem has been unacceptably slow as pointed out by Randall et al. (2003). The large part of the difficulty is inherent in the artificial separation of atmospheric processes into the explicitly simulated resolved scales and the highly parameterized subgrid scales. Arakawa (2004) and Arakawa et al. (2011) suggested two plausible approaches to eliminate the problem of artificial separation of atmospheric processes: “parameterize everything” and “resolve everything”.

58 GEOSCIENCES↗
DOE OSTI2021

Towards developing multiscale-multiphysics models and their surrogates for digital twins of metal additive manufacturing

Artificial intelligence (AI) embedded within digital models of manufacturing processes can be used to improve process productivity and product quality significantly. The application of such advanced capabilities particularly to highly digitalized processes such as metal additive manufacturing (AM) is likely to make those processes commercially more attractive. AI capabilities will reside within Digital Twins (DTs) which are living virtual replicas of the physical processes. DTs will be empowered to operate autonomously in a diagnostic control capacity to supervise processes and can be interrogated by the practitioner to inform the optimal processing route for any given product. The utility of the information gained from the DTs would depend on the quality of the digital models and, more importantly, their faster-solving surrogates which dwell within DTs for consultation during rapid decision-making. In this article, we point out the exceptional value of DTs in AM and focus on the need to create high-fidelity multiscale-multiphysics models for AM processes to feed the AI capabilities. We identify technical hurdles for their development, including those arising from the multiscale and multiphysics characteristics of the models, the difficulties in linking models of the subprocesses across scales and physics, and the scarcity of experimental data. We discuss the need for creating surrogate models using machine learning approaches for real-time problem-solving. We further identify non-technical barriers, such as the need for standardization and difficulties in collaborating across different types of institutions. We offer potential solutions for all these challenges, after reflecting on and researching discussions held at an international symposium on the subject in 2019. Here, we argue that a collaborative approach can not only help accelerate their development compared with disparate efforts, but also enhance the quality of the models by allowing modular development and linkages that account for interactions between the various sub-processes in AM. A high-level roadmap is suggested for starting such a collaboration.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials

This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media

Abstract The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ( $$>512^3$$ > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Scalable algorithms for physics-informed neural and graph networks

Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.

42 ENGINEERING↗
DOE OSTI2024

Anomaly Detection in Materials Digital Twins with Multiscale ICME for Additive Manufacturing

Detecting anomaly in fatigue and fracture experimental materials science is an interesting yet challenging topic. The reasons are threefold. First, the anomalous microstructure feature that gives rise to structural failure is small, sometimes in the order of 10 -7 of the interrogated volume. This, in turn, results in a highly imbalanced classification problem in machine learning (ML). Second, the consequence is high, in the sense that the test specimen is destructed in such case. Third, the convolution between microstructure stochasticity and the small probability of void nucleation, growth, and coalescence makes failure and fracture a hard-to-predict and challenging problem in materials science due to its irreproducibility, even experimentally. In this paper, we developed a materials digital twin and applied anomaly detection methods to detect voids and anomaly in additive manufacturing (AM). The materials digital twin is driven by two integrated computational materials engineering (ICME) models, which are kinetic Monte Carlo (kMC) and crystal plasticity finite element method (CPFEM). In conclusion, we demonstrated that by using anomaly detection, it is possible to detect voids and other defects in materials digital twin, which paves way for future research in integrating materials digital twin with its physical counterpart.

ICME↗
DOE OSTI2020

Non-autoregressive time-series methods for stable parametric reduced-order models

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant interest in the use of techniques borrowed from machine learning to reduce the computational expense and/or improve the accuracy of predictions for these systems. These rely on the identification of a basis that reduces the dimensionality of the problem and the subsequent use of time series and sequential learning methods to forecast the evolution of the reduced state. Often, however, machine-learned predictions after reduced-basis projection are plagued by issues of stability stemming from incomplete capture of multiscale processes as well as due to error growth for long forecast durations. To address these issues, we have developed a non-autoregressive time series approach for predicting linear reduced-basis time histories of forward models. In particular, we demonstrate that non-autoregressive counterparts of sequential learning methods such as long short-term memory (LSTM) considerably improve the stability of machine-learned reduced-order models. Further, we evaluate our approach on the inviscid shallow water equations and show that a non-autoregressive variant of the standard LSTM approach that is bidirectional in the principal component directions obtains the best accuracy for recreating the nonlinear dynamics of partial observations. Moreover-and critical for many applications of these surrogates-inference times are reduced by three orders of magnitude using our approach, compared with both the equation-based Galerkin projection method and the standard LSTM approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. Further, the core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

42 ENGINEERING↗
DOE OSTI2022

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

Abstract Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Yang, Hyung Jun↗