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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Toward real-time optimization through model reduction and model discrepancy sensitivities

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs—those that do not require access to the full-order model at evaluation time—is popular because they facilitate the computation of optimization solutions within the wall-clock time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, a limited number of full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. In conclusion, the HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data.

PDE-constrained optimization↗
DOE OSTI2024

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗
DOE OSTI2025

Exploring urban typologies using comprehensive analysis of transportation dynamics

Abstract As urban areas continue to expand and develop, categorizing cities into typologies offers a valuable framework for understanding metropolitan dynamics and fostering inter-city collaboration. However, existing typologies related to urban mobility have limitations, failing to consider cities within a single large urban region and often overlooking crucial dimensions such as trip demand and traffic flow. In this paper, we introduce a transportation-focused characterization for cities within a large urban region, specifically the San Francisco Bay Area, California. We incorporate over 40 metrics across five transportation dimensions: trip demand, road network, multi-modal network, traffic flow, and land use. Specifically, for the trip demand dimension, we include metrics capturing residents’ trip characteristics, such as mode share, intra-city trips, and inter-city trips. Additionally, we analyze the purpose of trips entering the city to gain a deeper understanding of incoming trip patterns. In the traffic flow dimension, we examine metrics like vehicle miles traveled, delay, and congestion to assess the traffic conditions on the street network. These, combined with other dimensions, provide a comprehensive view of a city’s transportation dynamics. Using unsupervised machine learning clustering methods, we identified eight distinct typologies for the Bay Area: Live Work Cities; Job and Activity Magnet Cities; Anchor Cities; Multi-modal Cities; Hyper-connected Cities; Low-density Residential Cities; Medium-density Residential Cities; and Mixed-use Residential Cities. Our findings show that many clusters are strongly influenced by trip demand and traffic flow metrics. Finally, we examine the practicality of this typology and its potential to guide collaborative transportation management strategies. The typologies provide a foundation for dialogue among Bay Area cities, focusing on evaluating shared characteristics and leveraging successes or challenges to develop unified strategies for transportation management.

Kuncheria, Anu↗
DOE OSTI2021

DeepShadows: Separating low surface brightness galaxies from artifacts using deep learning

Searches for low-surface-brightness galaxies (LSBGs) in galaxy surveys are plagued by the presence of a large number of artifacts (e.g., objects blended in the diffuse light from stars and galaxies, Galactic cirrus, star-forming regions in the arms of spiral galaxies, etc.) that have to be rejected through time consuming visual inspection. In future surveys, which are expected to collect hundreds of petabytes of data and detect billions of objects, such an approach will not be feasible. We investigate the use of convolutional neural networks (CNNs) for the problem of separating LSBGs from artifacts in survey images. We take advantage of the fact that we have available a large number of labeled LSBGs and artifacts from the Dark Energy Survey, that we use to train, validate, and test a CNN model. That model, which we call DeepShadows , achieves a test accuracy of 92.0%, a significant improvement relative to feature-based machine learning models. We also study the ability to use transfer learning to adapt this model to classify objects from the deeper Hyper-Suprime-Cam survey, and we show that after the model is retrained on a very small sample from the new survey, it can reach an accuracy of 87.6%. Finally, these results demonstrate that CNNs offer a very promising path in the quest to study the low-surface-brightness universe.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Evaluation of dual-weighted residual and machine learning error estimation for projection-based reduced-order models of steady partial differential equations

Projection-based reduced-order models (pROMs) show great promise as a means to accelerate many-query applications such as forward error propagation, solving inverse problems, and design optimization. In order to deploy pROMs in the context of high-consequence decision making, accurate error estimates are required to determine the region(s) of applicability in the parameter space. The following paper considers the dual-weighted residual (DWR) error estimate for pROMs and compares it to another promising pROM error estimate, machine learned error models (MLEM). Here, we show how DWR can be applied to ROMs and then evaluate DWR on two partial differential equations (PDEs): a two-dimensional linear convection–reaction–diffusion equation, and a three-dimensional static hyper-elastic beam. It is shown that DWR is able to estimate errors for pROMs extrapolating outside of their training set while MLEM is best suited for pROMs used to interpolate within the pROM training set.

42 ENGINEERING↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

SpectrumSDT: A program for parallel calculation of coupled rotational-vibrational energies and lifetimes of bound states and scattering resonances in triatomic systems

In this work, we present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗
DOE OSTI2022

Unconventional desalination: The use of cyclone separators in HDH desalination to achieve zero liquid discharge

Research in water desalination technologies is constantly growing to meet global demands for freshwater. Though acting to meet these demands, the rapid growth and spread of desalination technologies poses environmental issues due to the increasing brine concentrates that are ultimately discharged back to nature. This article presents a cyclone separator to transform a humidification-dehumidification (HDH) cycle to a dual-product cycle to produce freshwater and solid salt crystals for highly saline streams. A desalination cycle equipped with a cyclone separator is used to treat water with 3.5%–81% salinity. The separation efficiency is well above 99% and can produce potable water from hyper saline feed in a once-through process. Further, the cyclone separator performance was tested under different conditions including humidity ratios, relative humidities, and feed stream's salinities. The cyclone separator is self-cleaning and overcomes salt scaling. This behavior is a direct function of the walls' temperature and the carrier air dew point. Self-cleaning capability allows the cyclone separator to treat feed water of extreme salinities (up to 810,000ppm) down to freshwater salinity with zero liquid discharge. The cyclone separator was utilized in a novel HDH desalination technology to treat different salinities. The product was freshwater of salinity <500ppm.

42 ENGINEERING↗
DOE OSTI2022

Rapid Load Transition for Integrated Solid Oxide Fuel Cell - Gas Turbine (SOFC-GT) Energy Systems: A Demonstration of the Potential for Grid Response

Rapid load transition is an essential requirement for integrated energy systems to maintain grid resilience as more renewable resources are added to the grid. Integrated solid oxide fuel cell - gas turbine (SOFC-GT) systems can provide high efficiency and low carbon emissions over a broad range of turndown. These hybrids also have the potential to enable rapid grid response. The challenge has been to demonstrate effective control strategies to manage load transitions. In the present study, a load transition of ~50% was achieved in 10 s using a novel but simple strategy. Power demand on the SOFC and the GT were ramped down concurrently. During this transition, the SOFC anode fuel was manipulated to maintain SOFC fuel utilization while the cathode inlet air flow and temperature were also manipulated to thermally protect the SOFC. This study was conducted using the Hybrid Performance (Hyper) facility at the National Energy Technology Laboratory (NETL) in a co-simulation environment with the Idaho National Laboratory (INL)'s grid-simulation. The load ramping strategy was tested using a hardware-based cyber-physical simulation methodology. The results demonstrate a high-fidelity representation of SOFC-GT hybrid dynamics and validation of the control strategy. Thermal and electrochemical transients indicated that the SOFC was well protected during rapid load turndown without violating operability constraints. This demonstration revealed the non-linear nature of tightly coupled SOFC-GT system components, especially the non-linear response of SOFC cathode air flow and inlet temperature controls. These results highlight the needs and challenges in developing adaptive automatic controls for autonomous rapid load transitions. This work demonstrates that SOFC-GT hybrids are a viable option to provide the fast-ramping characteristics essential to accommodate high levels of variable renewable power while maintaining grid resilience, reliability, and environmental performance. The results also demonstrate the utility of co-simulation in advancing the tightly-coupled integrated energy systems needed to meet goals for zero-carbon power generation.

DIRECT ENERGY CONVERSION,POWER TRANSMISSION AND DI↗
DOE OSTI2025

Development of a River Dynamical Core for E3SM to simulate compound flooding on Exascale-class heterogeneous supercomputers

Flooding events pose significant risk to human life, property, and infrastructure. Physically-consistent quantification of altered flood risks in global models requires hyper-resolution (~1 km) or fine flood simulations using two-dimensional (2D) physics schemes, both of which are unavailable in the current generation Earth System Models. Here, in this work, we have developed the River Dynamical Core (RDycore), which is an open-source, 2D shallow water equation (SWE) library for the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM). RDycore uses PETSc and libCEED libraries that allows it to run efficiently on CPUs and GPUs, as well as select a time-integration algorithm at runtime without requiring any code modifications. RDycore achieves spatial error convergence rates for problems with analytical and manufactured solutions similar to those reported previously in the literature, or consistent with the implemented first-order spatial discretization scheme. RDycore's accuracy in predicting flooding for a well-studied dam break problem is comparable to existing SWE models. For a problem with 471 million grid cells, RDycore achieves a speedup of 6.6x and 7.6x on GPUs compared to CPUs when using 320 compute nodes on DOE's Perlmutter and Frontier supercomputers, respectively. The one-way coupling of the RDycore library within E3SM is demonstrated by performing multiple 5-day flooding simulations during Hurricane Harvey driven by five precipitation datasets. The E3SM--RDycore simulations at 30 m spatial resolution accurately simulate maximum water height during the hurricane when benchmarked against a previously published study and achieve a speedup of 15x (Perlmutter) and 21x (Frontier) on GPUs relative to CPUs. The work presented here is the foundational step in providing hardware and algorithmic portability framework for simulating kilometer-scale river dynamics within E3SM.

Flood Simulation↗
DOE OSTI2021

Origin of the isotopic composition of natural perchlorate: Experimental results for the impact of reaction pathway and initial ClO x reactant

Natural perchlorate (ClO 4 - ) exists in many places on Earth, in lunar regolith, meteorites, and on the surface of Mars. Terrestrial natural ClO 4 - has widely variable Cl and O stable isotopic compositions (δ 37 Cl, δ 18 O, Δ 17 O). The δ 18 O and Δ 17 O values of ClO 4 - from the most hyper-arid locations co-vary. ClO 4 - from less arid areas has relatively little 17 O excess and poor Δ 17 O-δ 18 O correlation. ClO 4 - from the Atacama Desert has unusually low δ 37 Cl (<-10‰) and exhibits a positive correlation between δ 37 Cl and δ 18 O, while the δ 37 Cl of ClO 4 - from all other locations varies between -5 and +7‰ with no δ 37 Cl-δ 18 O covariation. To evaluate the impact of different precursors (ClO x ) and reaction pathways on the isotopic composition of ClO 4 - , we measured the isotopic composition of ClO 4 - produced in the laboratory by UV or O 3 mediated aqueous oxidation of Cl-, OCl-, ClO2-, and ClO2° as well as O 3 mediated oxidation of dry NaCl. ClO x oxidation in aqueous or dry systems enriched in O 3 produced ClO 4 - with Δ 17 O values that generally increased with the number of O atoms required and included evidence that the site-specific 17 O anomaly in O 3 was preferentially transferred to ClO 4 - . Based on the inferred number of O atoms sourced from O 3 , and known Cl and O reaction pathways, it appears that ClO 2 ° and ClO 3 * were required intermediates in the production of ClO 4 - in the O 3 experiments. ClO x aqueous oxidation by UV irradiation produced ClO 4 - with a large range of δ 18 O values and little or no 17 O anomaly. ClO 3 - was produced to a much greater extent than ClO 4 - in all experiments except dry oxidation of NaCl by O 3 . The isotopic composition of ClO 3 - was distinct from that of ClO 4 - produced from the same initial reactants. Combined results of O 3 and UV mediated reactions largely bracketed the range of natural ClO 4 - δ 18 O and Δ 17 O values as well as δ 37 Cl values of non-Atacama natural samples, but no conditions produced the low δ 37 Cl values of Atacama ClO 4 - . Finally, our results indicate that variation in production mechanisms, possibly combined with isotopically variable precursors, could be responsible for much of the observed isotopic variation in natural ClO 4 - and ClO 3 - .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

KRAS4a and KRAS4b show distinct lipid-dependent regulation of RAS-RAF membrane dynamics

KRAS4a and KRAS4b are important regulators of signaling, and their interactions with the plasma membrane are dynamic and influenced by lipid composition. KRAS 4a and 4b have nearly identical globular domains but differ in their membrane-associated hyper variable region (HVR). The functional distinctions between these isoforms remain unclear, particularly with regards to their dependence on specific lipids and the membrane environment. Previous work showed that the membrane orientation of KRAS4b affects its ability to bind to RAF kinase RBDCRD and that the KRAS–RBDCRD complex adopts different poses on the membrane as well as influences the size and composition of the lipid environment. To model differences between KRAS 4a and 4b protein–lipid interactions, we extended the Multiscale Machine-Learned Modeling Infrastructure (MuMMI) to incorporate continuum simulations in the grand canonical ensemble, enabling sampling across macroscopic, coarse-grained, and all-atom resolutions. Using this framework, we systematically altered PIP2 concentrations, KRAS 4a versus 4b, and RAF RBDCRD complexation to assess impacts on membrane–protein interactions and dynamics. Our results reveal that reducing PIP2 shifts and broadens the membrane orientational preference of both KRAS 4b and 4a, with stronger effects on 4b HVR localization versus 4a. We demonstrate that with depletion of the strong negatively charged PIP2 lipid, the less charged phosphatidylserine replaces PIP2. Our findings highlight similarities and distinctions in the dynamics and lipid dependency of KRAS isoforms and suggest that ordering of the local lipid composition by HVRs is a shared property and key modulator of RAS-mediated signaling at the plasma membrane.

Biological and medical sciences↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A hybrid deep neural operator/finite element method for ice-sheet modeling

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level projections is due to uncertainty in ice sheet dynamics. At the moment, accurate quantification of the uncertainty is hindered by the cost of ice sheet computational models. In this work we develop a hybrid approach to approximate existing ice sheet models at a fraction of their cost. Our approach consists of replacing the finite element model for the momentum equations for the ice velocity, the most expensive part of an ice sheet model, with a Deep Operator Network, while we retain a classic finite element discretization for the evolution of the ice thickness. We show that the resulting hybrid model is very accurate and it is an order of magnitude faster than the traditional finite element model. Further, a distinctive feature of the proposed model, compared to other neural network approaches, is that it can handle high-dimensional parameter spaces (parameter fields) such as the basal friction at the bed of the glacier and can therefore be used for generating samples for uncertainty quantification. Further, we study the impact of hyper-parameters, number of unknowns and correlation length of the parameter distribution on the training and accuracy of the Deep Operator Network on a synthetic ice sheet model. We then target the evolution of the Humboldt glacier in Greenland and show that our hybrid model can provide accurate statistics of the glacier mass loss and can be effectively used to accelerate the quantification of uncertainty.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗