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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A priori error analysis of high-order LL* (FOSLL*) finite element methods

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are LL* methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. Here, we show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow for obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. Here, in this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^0$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a priori but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, using synthetic and experimental data. This work aims to set a new paradigm for interpretable machine learning models in the broad area of solid mechanics where low and limited data is available along with prior knowledge of physical constraints that the learned maps need to obey. This paradigm can potentially be extended to a broader spectrum of scientific exploration.

Data-driven constitutive models↗
DOE OSTI2024

Surrogate construction via weight parameterization of residual neural networks

Surrogate model development is a critical step for uncertainty quantification or other sample-intensive tasks for complex computational models. Here, in this work, we develop a multi-output surrogate form using a class of neural networks (NNs) that employ shortcut connections, namely Residual NNs (ResNets). ResNets are known to regularize the surrogate learning problem and improve the efficiency and accuracy of the resulting surrogate. Inspired by the continuous, Neural ODE analogy, we augment ResNets with weight parameterization strategy with respect to ResNet depth. Weight-parameterized ResNets regularize the NN surrogate learning problem and allow better generalization with a drastically reduced number of learnable parameters. We demonstrate that weight-parameterized ResNets are more accurate and efficient than conventional feed-forward multi-layer perceptron networks. We also compare various options for parameterization of the weights as functions of ResNet depth. We demonstrate the results on both synthetic examples and a large scale earth system model of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗
DOE OSTI2012

Gyroaverage effects on nontwist Hamiltonians: separatrix reconnection and chaos suppression

A study of nite Larmor radius (FLR) eects on E B test particle chaotic transport in non- monotonic zonal ows with drift waves in magnetized plasmas is presented. Due to the non- monotonicity of the zonal ow, the Hamiltonian does not satisfy the twist condition. The electro- static potential is modeled as a linear superposition of a zonal ow and regular neutral modes of the Hasegawa-Mima equation. FLR eects are incorporated by gyro-averaging the EB Hamiltonian. It is shown that there is a critical value the Larmor radius for which the zonal ow transitions from a prole with one maximum to a prole with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor ra- dius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal ow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections shows that, for large enough Larmor radius, chaos can be practically suppressed. In particular, small changes on the Larmor radius can restore the shearless curve.

Del-Castillo-Negrete, Diego B↗
DOE OSTI2020

Front propagation formulation for large eddy simulation of turbulent premixed flames

The front propagation formulation (FPF) for large eddy simulation (LES) of turbulent premixed flames is presented and discussed. The FPF method adopts a regularized Dirac delta function to minimize the spurious propagation of under-resolved filtered flame fronts in LES, while reproducing the reaction characteristics of premixed flame fronts. Here, the extension of the FPF method to LES and the relation to existing sub-filter combustion models are discussed. An algebraic model for the regularized Dirac delta function is presented and validated using direct numerical simulation (DNS) data for statistically planar premixed flames propagating in homogeneous isotropic turbulence. A posteriori validation for a filtered 1-D planar laminar flame is performed to demonstrate the characteristics of FPF in reproducing the propagation speed and the thickness of the under-resolved flame front. LES of a turbulent Bunsen flame is also performed to demonstrate the performance of the proposed method.

42 ENGINEERING↗
DOE OSTI2018

In-plane crashworthiness of bio-inspired hierarchical honeycombs

Biological tissues like bone, wood, and sponge possess hierarchical cellular topologies, which are lightweight and feature an excellent energy absorption capability. Here we present a system of bio-inspired hierarchical honeycomb structures based on hexagonal, Kagome, and triangular tessellations. The hierarchical designs and a reference regular honeycomb configuration are subjected to simulated in-plane impact using the nonlinear finite element code LS-DYNA. The numerical simulation results show that the triangular hierarchical honeycomb provides the best performance compared to the other two hierarchical honeycombs, and features more than twice the energy absorbed by the regular honeycomb under similar loading conditions. We also propose a parametric study correlating the microstructure parameters (hierarchical length ratio r and the number of sub cells N) to the energy absorption capacity of these hierarchical honeycombs. The triangular hierarchical honeycomb with N = 2 and r = 1/8 shows the highest energy absorption capacity among all the investigated cases, and this configuration could be employed as a benchmark for the design of future safety protective systems.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Electrically regenerated ion-exchange technology for desalination of low-salinity water sources

A promising approach to increasing freshwater availability is the effective desalination of widely available and abundant low-salinity water sources. Here we report a new approach to desalinate low-salinity water sources using inexpensive ion exchange resins (IER) which are commonly used for water softening and require regular chemical regeneration. We incorporate IER into a functional composite material that enables electrical regeneration of IER, eliminating the need for regular use of corrosive chemicals. These proof-of-concept results demonstrate reliable regeneration of IER-composite electrodes using a lab-scale prototype device. With further characterization and development, this new approach offers a path to sustainable use of conventional IER for desalination of low-salinity water sources.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Reducing impacts of artificial ponding in modeling salt marshes using a conductivity-formulated subgrid model

The landforms of salt marsh systems are rather complex, with meandering channel networks cutting through low-lying, extensive marsh platforms. Some small-scale topographic details are critical to flooding and draining processes but cannot be reflected in the Digital Elevation Model (DEM) due to limited measurement resolution and vegetation bias. Numerical models need a grid with high enough resolution to capture the small-scale connectivity to correctly model the small-scale flow processes, making the model computationally unaffordable. Here, in this study, we derived a subgrid model, which couples two flow components, one is the regular subgrid model for simulating the subgrid-resolved flows, and the other is a conductivity-formulated porous flow model for modeling small-scale gut flows unresolved at the subgrid level. The model validation was performed using an idealized case with a narrow slot that was unresolved in the coupled flow model. Model results were compared with a slot-resolved regular subgrid model where only surface flows are solved and suggested that, with a proper model parameterization, the coupled flow model is capable of reproducing flooding and draining processes similar to the slot-resolved subgrid model of surface flow. The model was applied to simulating flooding and draining processes in a meso-tidal salt marsh. The model results demonstrate that the coupled subgrid model can be used to reduce the impacts of artificial ponding that usually occur in numerical simulations of salt marshes with numerous narrow gullies and creeks.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Determination and modeling of the thermodynamic properties of liquid calcium-antimony alloys

The thermodynamic properties of Ca-Sb alloys were determined by emf measurements in a cell configured as Ca(s)vertical bar CaF2 vertical bar Ca-Sb over the temperature range 550-830 degrees C. Activity coefficients of Ca and Sb, enthalpy, Gibbs free energy, and entropy of mixing of Ca-Sb alloys were calculated for xc(a) < 0.55. To explain the connection between short-range order of liquid Ca-Sb alloys and the strong deviation from ideality in the thermodynamic properties, two thermodynamic models were invoked and reconciled: the regular associated solution model, assuming the presence of a CaSb2 associate, and the molecular interaction volume model (MIVM). For the first time, the MIVM was used successfully to model the activity coefficients of a system with high-melting intermetallics, reducing the number of fitting parameters necessary from 5 (regular associated model) to 2 (MIVM). From the interaction parameters optimized by fitting at 800 degrees C, the with an average error of less than value. (C) 2012 Elsevier Ltd. All rights reserved,

Poizeau, S↗
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 OSTI2015

DNS and LES of turbulent flow in a closed channel featuring a pattern of hemispherical roughness elements

Three mesh adaptivity algorithms were developed to facilitate and expedite the use of the CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques in accurate full-scale neutronics simulations of fusion energy systems with immense sizes and complicated geometries. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility and resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation. Additionally, because of the significant increase in the efficiency of FW-CADIS simulations, the three algorithms enabled this difficult calculation to be accurately solved on a regular computer cluster, eliminating the need for a world-class super computer.

Nuclear Science & Technology↗
DOE OSTI2022

A correction procedure for self-induced velocity of a finite-sized particle in two-way coupled Euler–Lagrange simulations

The importance of incorporating a correction to undo the self-induced perturbation velocity of a particle, when its size becomes comparable to the Eulerian grid, in a two-way coupled Euler–Lagrange (EL) simulation is now well appreciated. The present work improves upon the prior correction procedures in a few important ways. First, the past correction procedures have been scalar-based with the assumption that the quasi-steady force is the source of self-induced velocity perturbation. Here we generalize to a vector correction procedure and thereby the directions of feedback force and relative velocity can be different. This allows the correction procedure to be used even in the presence of added-mass, history, and lift forces. Second, the effect of a nearby wall has been systematically included in the correction procedure. The correction procedure depends on fundamental Oseen solutions of streamwise and transverse regularized feedback forces. We present a Fourier transform-based analytical approach to obtaining these regularized Oseen solutions. We also present a step-by-step numerical procedure for obtaining the Oseen solutions in any EL code. With the analytical or numerical Oseen functions, the correction procedure can be easily implemented in any EL code. Iterations are required in solving the implicit correction equations and it is demonstrated that the correction procedure converges rapidly within three or four iterations. In conclusion, a simple empirical approach is also presented to account for unsteady effects in the correction procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Planning 4-Dimensional Computed Tomography (4DCT) Cannot Adequately Represent Daily Intrafractional Motion of Abdominal Tumors

Purpose: To evaluate whether planning 4-dimensional computed tomography (4DCT) can adequately represent daily motion of abdominal tumors in regularly fractionated and stereotactic body radiation therapy (SBRT) patients. Methods and Materials: Intrafractional tumor motion of 10 patients with abdominal tumors (4 pancreas-fractionated and 6 liver-stereotactic patients) with implanted fiducials was measured based on daily orthogonal fluoroscopic movies over 38 treatment fractions. The needed internal margin for at least 90% of tumor coverage was calculated based on a 95th and fifth percentile of daily 3-dimensional tumor motion. The planning internal margin was generated by fusing 4DCT motion from all phase bins. The disagreement between needed and planning internal margin was analyzed fraction by fraction in 3 motion axes (superior-inferior [SI], anterior-posterior [AP], and left-right [LR]). The 4DCT margin was considered as an overestimation/underestimation of daily motion when disagreement exceeded at least 3 mm in the SI axis and/or 1.2 mm in the AP and LR axes (4DCT image resolution). The underlying reasons for this disagreement were evaluated based on interfractional and intrafractional breathing variation. Results: The 4DCT overestimated daily 3-dimensional motion in 39% of the fractions in 7 of 10 patients and underestimated it in 53% of the fractions in 8 of 10 patients. Median underestimation was 3.9 mm, 3.0 mm, and 1.7 mm in the SI axis, AP axis, and LR axis, respectively. The 4DCT was found to capture irregular deep breaths in 3 of 10 patients, with 4DCT motion larger than mean daily amplitude by 18 to 21 mm. The breathing pattern varied from breath to breath and day to day. The intrafractional variation of amplitude was significantly larger than intrafractional variation (2.7 mm vs 1.3 mm) in the primary motion axis (ie, SI axis). The SBRT patients showed significantly larger intrafractional amplitude variation than fractionated patients (3.0 mm vs 2.1 mm, P<.05). Conclusions: It may not be appropriate to use 4DCT without monitoring of patient motion on a regular basis for patients with abdominal tumors, especially SBRT patients.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2023

Tangent functional connectomes uncover more unique phenotypic traits

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projections, resulting into tangent-FCs. Tangent-FCs have led to more accurate models predicting brain conditions or aging. Motivated by the fact that tangent-FCs seem to be better biomarkers than FCs, we hypothesized that tangent-FCs have also a higher fingerprint. We explored the effects of six factors: fMRI condition, scan length, parcellation granularity, reference matrix, main-diagonal regularization, and distance metric. Our results showed that identification rates are systematically higher when using tangent-FCs across the “fingerprint gradient” (here including test-retest, monozygotic and dizygotic twins). Highest identification rates were achieved when minimally (0.01) regularizing FCs while performing tangent space projection using Riemann reference matrix and using correlation distance to compare the resulting tangent-FCs. Such configuration was validated in a second dataset (resting-state).

59 BASIC BIOLOGICAL SCIENCES↗