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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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28 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The contribution of Humboldt Glacier, northern Greenland, to sea-level rise through 2100 constrained by recent observations of speedup and retreat

Abstract. Humboldt Glacier, northern Greenland, has retreated and accelerated through the 21st century, raising concerns that it could be a significant contributor to future sea-level rise. We use a data-constrained ensemble of three-dimensional higher-order ice sheet model simulations to estimate the likely range of sea-level rise from the continued retreat of Humboldt Glacier. We first solve for basal traction using observed ice thickness, bed topography, and ice surface velocity from the year 2007 in a PDE-constrained (partial differential equation) optimization. Next, we impose calving rates to match mean observed retreat rates from winter 2007–2008 to winter 2017–2018 in a transient calibration of the exponent in the power-law basal friction relationship. We find that power-law exponents in the range of 1/7–1/5 – rather than the commonly used 1/3–1 – are necessary to reproduce the observed speedup over this period. We then tune an iceberg calving parameterization based on the von Mises stress yield criterion in another transient-calibration step to approximate both observed ice velocities and terminus position in 2017–2018. Finally, we use the range of basal friction relationship exponents and calving parameter values to generate the ensemble of model simulations from 2007–2100 under three climate forcing scenarios from CMIP5 (two RCP8.5 forcings, Representative Concentration Pathway) and CMIP6 (one SSP5-8.5 forcing, Shared Socioeconomic Pathway). Our simulations predict 5.2–8.7 mm of sea-level rise from Humboldt Glacier, significantly higher than a previous estimate (∼ 3.5 mm) and equivalent to a substantial fraction of the 40–140 mm predicted by ISMIP6 from the whole Greenland Ice Sheet. Our larger future sea-level rise prediction results from the transient calibration of our basal friction law to match the observed speedup, which requires a semi-plastic bed rheology. In many simulations, our model predicts the growth of a sizable ice shelf in the middle of the 21st century. Thus, atmospheric warming could lead to more retreat than predicted here if increased surface melt promotes hydrofracture of the ice shelf. Our data-constrained simulations of Humboldt Glacier underscore the sensitivity of model predictions of Greenland outlet glacier response to warming to choices of basal shear stress and iceberg calving parameterizations. Further, transient calibration of these parameterizations, which has not typically been performed, is necessary to reproduce observed behavior. Current estimates of future sea-level rise from the Greenland Ice Sheet could, therefore, contain significant biases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Synergistic learning with multi-task DeepONet for efficient PDE problem solving

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Finally, our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

42 ENGINEERING↗
DOE OSTI2024

Grad–Shafranov equilibria via data-free physics informed neural networks

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad–Shafranov equation by using physics-informed neural networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the partial differential equation as a loss function. We show that PINNs can accurately and effectively solve the Grad–Shafranov equation with several different boundary conditions, making it more flexible than traditional solvers. This method is flexible as it does not require any mesh and basis choice, thereby streamlining the computational process. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various tradeoffs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parameterized PINNs could be used in future work to solve inverse problems such as shape optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Diskoseismology: Probing accretion disks. II - G-modes, gravitational radiation reaction, and viscosity

A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.

Nowak, Michael A.↗
NASA NTRS2007

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗
NASA NTRS1994

A simple hyperbolic model for communication in parallel processing environments

We introduce a model for communication costs in parallel processing environments called the 'hyperbolic model,' which generalizes two-parameter dedicated-link models in an analytically simple way. Dedicated interprocessor links parameterized by a latency and a transfer rate that are independent of load are assumed by many existing communication models; such models are unrealistic for workstation networks. The communication system is modeled as a directed communication graph in which terminal nodes represent the application processes that initiate the sending and receiving of the information and in which internal nodes, called communication blocks (CBs), reflect the layered structure of the underlying communication architecture. The direction of graph edges specifies the flow of the information carried through messages. Each CB is characterized by a two-parameter hyperbolic function of the message size that represents the service time needed for processing the message. The parameters are evaluated in the limits of very large and very small messages. Rules are given for reducing a communication graph consisting of many to an equivalent two-parameter form, while maintaining an approximation for the service time that is exact in both large and small limits. The model is validated on a dedicated Ethernet network of workstations by experiments with communication subprograms arising in scientific applications, for which a tight fit of the model predictions with actual measurements of the communication and synchronization time between end processes is demonstrated. The model is then used to evaluate the performance of two simple parallel scientific applications from partial differential equations: domain decomposition and time-parallel multigrid. In an appropriate limit, we also show the compatibility of the hyperbolic model with the recently proposed LogP model.

Stoica, Ion↗
NASA NTRS1992

Chemical differentiation of a convecting planetary interior: Consequences for a one-plate planet such as Venus

Chemically depleted mantle forming a buoyant, refractory layer at the top of the mantle can have important implications for the evolution of the interior and surface. On Venus, the large apparent depths of compensation for surface topographic features might be explained if surface topography were supported by variations in the thickness of a 100-200 km thick chemically buoyant mantle layer or by partial melting in the mantle at the base of such a layer. Long volcanic flows seen on the surface may be explained by deep melting that generates low-viscosity MgO-rich magmas. The presence of a shallow refractory mantle layer may also explain the lack of volcanism associated with rifting. As the depleted layer thickens and cools, it becomes denser than the convecting interior and the portion of it that is hot enough to flow can mix with the convecting mantle. Time dependence of the thickness of a depleted layer may create episodic resurfacing events as needed to explain the observed distribution of impact craters on the venusian surface. We consider a planetary structure consisting of a crust, depleted mantle layer, and a thermally and chemically well-mixed convecting mantle. The thermal evolution of the convecting spherical planetary interior is calculated using energy conservation: the time rate of change of thermal energy in the interior is equated to the difference in the rate of radioactive heat production and the rate of heat transfer across the thermal boundary layer. Heat transfer across the thermal boundary layer is parameterized using a standard Nusselt number-Rayleigh number relationship. The radioactive heat production decreases with time corresponding to decay times for the U, Th, and K. The planetary interior cools by the advection of hot mantle at temperature T interior into the thermal boundary layer where it cools conductively. The crust and depleted mantle layers do not convect in our model so that a linear conductive equilibrium temperature distribution is assumed. The rate of melt production is calculated as the product of the volume flux of mantle into the thermal boundary layer and the degree of melting that this mantle undergoes. The volume flux of mantle into the thermal boundary layer is simply the heat flux divided by amount of heat lost in cooling mantle to the average temperature in the thermal boundary layer. The degree of melting is calculated as the temperature difference above the solidus, divided by the latent heat of melting. A maximum degree of melting is prescribed corresponding to the maximum amount of basaltic melt that the mantle can initially generate. As the crust thickens, the pressure at the base of the crust becomes high enough and the temperature remains low enough for basalt to transform to dense eclogite.

Parmentier, E. M.↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗