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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks. We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. Furthermore, the DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a “plug-and-play” mode.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Rosen, I. G.↗
NASA NTRS1988

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Rosen, I. G.↗
DOE OSTI2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

In-medium similarity renormalization group with flowing 3-body operators, and approximations thereof

Here, we explore the impact of retaining three-body operators within the in-medium similarity renormalization group (IMSRG), as well as various approximations schemes. After studying two toy problems, identical fermions with a contact interaction and the Lipkin-Meshkov-Glick model, we employ the valence-space formulation of the IMSRG to investigate the even- A carbon isotopes with a chiral two-body potential. We find that retaining only those commutators expressions that scale as N 7 provides an excellent approximation of the full three-body treatment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2006

Life Test Approach for Refractory Metal/Sodium Heat Pipes

Heat pipe life tests described in the literature have seldom been conducted on a systematic basis. Typically one or more heat pipes are built and tested for an extended period at a single temperature with simple condenser loading. This paper describes an approach to generate carefully controlled data that can conclusively establish heat pipe operating life with material-fluid combinations capable of extended operation. Approximately 10 years of operational life might be compressed into 3 years of laboratory testing through a combination of increased temperature and mass fluence. Two specific test series have been identified and include: investigation of long term corrosion rates based on the guidelines contained in ASTM G-68-80 (using 7 heat pipes); and investigation of corrosion trends in a cross correlation sequence at various temperatures and mass fluences based on a central composite test design (using 9 heat pipes). The heat pipes selected for demonstration purposes are fabricated from a Mo-44.5%Re alloy with a length of 0.3 meters and a diameter of 1.59 cm(to conserve material) with a condenser to evaporator length ratio of approximately 3. The wick is a crescent annular design formed from 400-mesh Mo-Re alloy material hot isostatically pressed to produce a final wick core of 20 microns or less.

Martin, James J.↗
NASA NTRS1991

Thermographic detection of cracks in thin sheets

A thermographic inspection technique for crack detection based on a 2D filter convolved with the thermal temperature images is presented. The filter is designed to approximate operating on the temperature images with a Laplacian operator. This operation yields an image which approximates changes in the heat flux in a thin plate. This filtering method results in an enhanced contrast due to the presence of cracks. Measurements have been performed on samples with fabricated electrical discharge machining (EDM) notches (both through-the-thickness and surface notches) and closed fatigue cracks around rivets. It is shown that the technique is effective for the detection of various crack lengths down to the resolution limits of the imager used.

Cramer, K. E.↗
NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗
NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. II.

Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.

Baxley, J. V.↗
DOE OSTI2022

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

Here, the Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Short-range correlation physics at low renormalization group resolution

Recent experiments have succeeded in isolating processes for which short-range correlation (SRC) physics is dominant and well accounted for by SRC phenomenology. But an alternative and compelling picture emerges from renormalization group (RG) evolution to low RG resolution. At high RG resolution, SRCs are identified as components in the nuclear wave function with relative pair momenta greater than the Fermi momentum. Scale separation results in wave-function factorization that can be exploited with phenomenologies such as the generalized contact formalism or the low-order correlation operator approximation. Evolution to lower resolution shifts SRC physics from nuclear structure to the reaction operators without changing the measured observables. We show how the features of SRC phenomenology manifested at high RG resolution are cleanly identified at low RG resolution using simple two-body operators and local-density approximations with uncorrelated wave functions, all of which can be systematically generalized. We verify that the experimental consequences to date follow directly at low resolution from well-established properties of nucleon-nucleon interactions such as the tensor force. Thus the RG reconciles the contrasting pictures of the same experiment and shows how to get correct results using wave functions without SRC components. Finally, our demonstration has implications for the analysis of knockout reactions for which SRC physics is not cleanly isolated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1948

Simulated Altitude Performance of Combustor of Westinghouse 19XB-1 Jet-Propulsion Engine

A 19XB-1 combustor was operated under conditions simulating zero-ram operation of the 19XB-1 turbojet engine at various altitudes and engine speeds. The combustion efficiencies and the altitude operational limits were determined; data were also obtained on the character of the combustion, the pressure drop through the combustor, and the combustor-outlet temperature and velocity profiles. At altitudes about 10,000 feet below the operational limits, the flames were yellow and steady and the temperature rise through the combustor increased with fuel-air ratio throughout the range of fuel-air ratios investigated. At altitudes near the operational limits, the flames were blue and flickering and the combustor was sluggish in its response to changes in fuel flow. At these high altitudes, the temperature rise through the combustor increased very slowly as the fuel flow was increased and attained a maximum at a fuel-air ratio much leaner than the over-all stoichiometric; further increases in fuel flow resulted in decreased values of combustor temperature rise and increased resonance until a rich-limit blow-out occurred. The approximate operational ceiling of the engine as determined by the combustor, using AN-F-28, Amendment-3, fuel, was 30,400 feet at a simulated engine speed of 7500 rpm and increased as the engine speed was increased. At an engine speed of 16,000 rpm, the operational ceiling was approximately 48,000 feet. Throughout the range of simulated altitudes and engine speeds investigated, the combustion efficiency increased with increasing engine speed and with decreasing altitude. The combustion efficiency varied from over 99 percent at operating conditions simulating high engine speed and low altitude operation to less than 50 percent at conditions simulating operation at altitudes near the operational limits. The isothermal total pressure drop through the combustor was 1.82 times as great as the inlet dynamic pressure. As expected from theoretical considerations, a straight-line correlation was obtained when the ratio of the combustor total pressure drop to the combustor-inlet dynamic pressure was plotted as a function of the ratio of the combustor-inlet air density to the combustor-outlet gas density. The combustor-outlet temperature profiles were, in general, more uniform for runs in which the temperature rise was low and the combustion efficiency was high. Inspection of the combustor basket after 36 hours of operation showed very little deterioration and no appreciable carbon deposits.

Childs, J. Howard↗
DOE OSTI2025

Summary of Analytical Services for the Hanford Site Radionuclide NESHAP Program

This document is a summary of the point source analytical requirements used to demonstrate compliance for the Department of Energy (DOE) Hanford Site operations with 40 Code of Federal Regulations (CFR) Part 61, “National Emission Standards for Hazardous Air Pollutants,” (NESHAP) Subpart H, “National Emission Standards for Emissions of Radionuclides Other Than Radon From Department of Energy Facilities,” and the Washington Administrative Code (WAC) 246-247, “Radiation Protection – Air Emissions.” This reference collects information from multiple source documents and is not intended to create, supersede, replace or over-ride any existing contractual, DOE, federal or state statutes, regulations, compliance agreements, orders, permits, licenses or other requirements. The requirement source document governs where any difference may exist. The Hanford Mission Integration Solutions (HMIS) Environmental organization has been contracted by DOE to manage and report data collected from the sampling and monitoring of radioactive air emissions point sources, colloquially called stacks. The Environmental organization coordinates the analyses and reporting of samples collected at various facilities across the Hanford Site. These facilities operate approximately 52 stacks that require sampling, monitoring or estimating radioactive air emissions. The stacks are operated by Bechtel National, Inc. (BNI), Central Plateau Cleanup Company (CPCCo), Hanford Tank Waste Operations & Closure (H2C), Hanford Laboratory Management and Integration (HLMI), and Pacific Northwest National Laboratory (PNNL). Stack samples from CPCCo, HLMI and H2C facilities are collected by the operating contractor staff, delivered to HMIS, and then shipped to an offsite contracted laboratory for analyses. The field and laboratory sample data uploaded into the Sample Management and Analytical Results Tracking (SMART) database are used to calculate sample volumes and concentrations. Sample concentrations are evaluated for compliance with federal and state regulations, permits, and license requirements. The SMART database also calculates total curies released for sampled point sources and stacks. Point source effluent concentrations and releases are published annually in publicly available reports. The BNI and PNNL operate several DOE-Hanford Field Office (HFO) stacks subject to the requirements of 40 CFR 61, Subpart H and WAC 246-247. The concentrations, curies released and dose modeling evaluation for these stacks are included in the DOE-HFO annual radionuclide NESHAP report. The sample collection, analyses and emissions estimates for these stacks are outside the scope of HMIS contracted responsibilities and not addressed further in this document.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2013

Data Compression Algorithm Architecture for Large Depth-of-Field Particle Image Velocimeters

A large depth-of-field particle image velocimeter (PIV) is designed to characterize dynamic dust environments on planetary surfaces. This instrument detects lofted dust particles, and senses the number of particles per unit volume, measuring their sizes, velocities (both speed and direction), and shape factors when the particles are large. To measure these particle characteristics in-flight, the instrument gathers two-dimensional image data at a high frame rate, typically >4,000 Hz, generating large amounts of data for every second of operation, approximately 6 GB/s. To characterize a planetary dust environment that is dynamic, the instrument would have to operate for at least several minutes during an observation period, easily producing more than a terabyte of data per observation. Given current technology, this amount of data would be very difficult to store onboard a spacecraft, and downlink to Earth. Since 2007, innovators have been developing an autonomous image analysis algorithm architecture for the PIV instrument to greatly reduce the amount of data that it has to store and downlink. The algorithm analyzes PIV images and automatically reduces the image information down to only the particle measurement data that is of interest, reducing the amount of data that is handled by more than 10(exp 3). The state of development for this innovation is now fairly mature, with a functional algorithm architecture, along with several key pieces of algorithm logic, that has been proven through field test data acquired with a proof-of-concept PIV instrument.

Bos, Brent↗
DOE OSTI2022

AmeriFlux FLUXNET-1F US-Ne1 Mead - irrigated continuous maize site

This is the AmeriFlux Management Project (AMP) created FLUXNET-1F version of the carbon flux data for the site US-Ne1 Mead - irrigated continuous maize site. This is the FLUXNET version of the carbon flux data for the site US-Ne1 Mead - irrigated continuous maize site produced by applying the standard ONEFlux (1F) software. Site Description - The study site is one of three fields (all located within 1.6 km of each other) at the University of Nebraska Eastern Nebraska Research, Education and Extension Center near Mead, Nebraska. This site is irrigated with a center pivot system. Prior to the initiation of the study, the irrigated site had a 10-yr history of maize-soybean rotation under no-till. A tillage operation (disking) was done just prior to the 2001 planting to homogenize the top 0.1 m of soil, incorporate P and K fertilizers, as well as previously accumulated surface residues. This field was planted with maize every growing season. Since the 2001 tillage operation, the site has been under no-till management until the harvest of 2005. Following harvest, a conservation-plow tillage operation was initiated where a small amount of N fertilizer is sprayed on the residue immediately prior to the plow operation. Approximately 1/3 of the crop residue is left on the surface. The post-harvest conservation-plow operation continued until 2022. Since 2022, the site management has changed such that the field is now a strictly no-till, maize-soybean rotation (maize odd years and soybean even years).

Suyker, Andy↗
DOE OSTI2022

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

97 MATHEMATICS AND COMPUTING↗