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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

A Monte Carlo Thermal Radiative Transfer Solver with Nonlinear Elimination

Here in this paper, we present a new Monte Carlo method for solving the thermal radiative transfer (TRT) equations via the method of nonlinear elimination (NLEM). This method is inspired by the previous application of NLEM to thermal radiation diffusion. Our approach, called diffusion accelerated Implicit Monte Carlo (DAIMC), is a hybrid technique which combines a Monte Carlo method for solving a purely-absorbing transport equation and a diffusion solution that accounts for effective scattering, or absorption–reemission. The method aims to improve the implicitness of the traditional implicit Monte Carlo (IMC) method. We derive DAIMC generally for 3D Cartesian geometries, but in this paper, we present results and analysis in 1D slab geometry. These preliminary results indicate that DAIMC implementations may provide more accurate and robust TRT solutions than IMC in certain test problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

On the possibility of footprint compression with one lens in nonlinear accelerator lattice

Electromagnetic interaction of colliding beams along with other nonlinear fields often limits the beams' lifetimes and luminosities. Nonlinearities result in the spread of betatron frequencies (footprint) and, thus, may enhance dynamic diffusion of particles due to high order resonances. One of the possible ways to eliminate nonlinearities and overcome the corresponding difficulties is compensation of nonlinear forces, but, in practice, it is hardly possible to obtain exact linearity of the system. The compensation with a single nonlinear lens cannot cope with distributed nonlinearities, nonlinearities due to parasitic crossings, etc. Here, we present a method to compute parameters of nonlinear element (lens) that eliminates both the footprint and resonance strength without achieving full compensation.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Efficient smoothed particle radiation hydrodynamics I: Thermal radiative transfer

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the number of iterations needed to converge the emission source, and how the radiation diffusion equation is solved, which must be done in each iteration. The coupled material and radiation energy equations are solved using an inexact Newton iteration scheme based on nonlinear elimination, which reduces the number of Newton iterations needed to converge within each time step. During each Newton iteration, the radiation diffusion equation is solved using Krylov iterative methods with a multigrid preconditioner, which abstracts and optimizes much of the communication when running in parallel. The code is verified for an infinite medium problem, a one-dimensional Marshak wave, and a two and three-dimensional manufactured problem, and exhibits first-order convergence in time and second-order convergence in space. For these problems, the number of iterations needed to converge the inexact Newton scheme and the diffusion equation is independent of the number of spatial points and the number of processors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Fully Implicit Monte Carlo (FIMC) (September 2019-September 2020 Progress Report)

This research is focused on applying the NLem method to the full thermal radiative transfer (TRT) equations in the context of a Monte Carlo solution strategy. A framework has been developed for obtaining a solution to the TRT equations using the nonlinear elimination method (NLem) method. Current efforts are focused of the development and verification of the required Monte Carlo algorithm, diffusion algorithm, and material energy solver. Once all three pieces have been verified, the algorithms will then be coupled into a fully functioning method for applying NLem to the TRT equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A Causal Inference Model Based on Random Forests to Identify the Effect of Soil Moisture on Precipitation

Soil moisture influences precipitation mainly through its impact on land–atmosphere interactions. Understanding and correctly modeling soil moisture–precipitation (SM–P) coupling is crucial for improving weather forecasting and subseasonal to seasonal climate predictions, especially when predicting the persistence and magnitude of drought. However, the sign and spatial structure of SM–P feedback are still being debated in the climate research community, mainly due to the difficulty in establishing causal relationships and the high degree of nonlinearity in land–atmosphere processes. To this end, we developed a causal inference model based on the Granger causality analysis and a nonlinear machine learning model. This model includes three steps: nonlinear anomaly decomposition, nonlinear Granger causality analysis, and evaluation of the quality of SM–P feedback, which eliminates the nonlinear response of interannual and seasonal variability and the memory effects of climatic factors and isolates the causal relationship of local SM–P feedback. We applied this model by using National Climate Assessment–Land Data Assimilation System (NCA-LDAS) datasets over the United States. Here, the results highlight the importance of nonlinear atmosphere responses in land–atmosphere interactions. In addition, the strong feedback over the southwestern United States and the Great Plains both highlight the impacts of topographic factors rather than only the sensitivity of evapotranspiration to soil moisture. Furthermore, the SM–P index defined by our framework is used to benchmark Earth system models (ESMs), which provides a new metric for efficiently identifying potential model biases in modeling local land–atmosphere interactions and may help the development of ESMs in improving simulations of water cycle variability and extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Automated and efficient local adaptive regression for principal component-based reduced-order modeling of turbulent reacting flows

Principal Component Analysis can be used to reduce the cost of Computational Fluid Dynamics simulations of turbulent reacting flows by reducing the dimensionality of the transported variables through projection of the thermochemical state onto a lower-dimensional manifold. However, because of the nonlinearity of the principal component source terms, nonlinear regression techniques must be utilized for the source terms in terms of the principal components. Unfortunately, widely available and utilized nonlinear regression techniques can have prohibitive computational requirements and/or accuracy that is highly dependent on user experience in ad hoc tuning of model architecture and hyperparameters. Here, in this work, a new nonlinear regression approach is proposed that is both computationally efficient and automated so does not require any user input. The approach is evaluated through a priori prediction of principal component source terms using data from a Direct Numerical Simulation of a turbulent nonpremixed n-heptane/air jet flame. In particular, the proposed framework consists of local regressions whose complexity is adapted according to the local nonlinearity of the data: local linear regression when accurate enough and local Artificial Neural Networks when nonlinear regression is required. The number of local clusters for local regression is determined automatically using the Davies-Bouldin index. In addition, Bayesian optimization is utilized for model training (i.e., to select the best architectures and hyperparameters of the nonlinear regressions in an unsupervised fashion), eliminating ad hoc hand-tuning and/or expensive grid searches. Overall, compared to a single, global neural network, the new local adaptive regression approach is shown to have comparable accuracy but 69% less training time due to the utilization of local linear regression and faster training of local neural networks.

42 ENGINEERING↗
DOE OSTI2025

Thermal modulation of nonlinear ultrasonic waves for nondestructive evaluation of elastic materials

Temperature variation is often considered an undesirable factor in ultrasonic testing, as wave velocity is highly sensitive to thermal fluctuations. However, completely eliminating the temperature effect is difficult, particularly in tests requiring precise velocity measurements. Recently, a method called Thermal Modulation of Nonlinear Ultrasonics (TMNL) has been developed. Instead of eliminating the thermal effect, the TMNL method leverages the temperature variation as a driving force to stimulate the nonlinear response of the medium and modulate the ultrasonic waves propagating in it. These modulated waves can then be used to evaluate the nonlinear behaviours of the test medium. This paper presents a focused review of the TMNL technique, including its theoretical foundations, particularly the conceptual challenges in integrating thermal effects into classical acoustoelastic theory, and recent applications in non-destructive evaluation (NDE). Three case studies are presented to demonstrate TMNL’s application in detecting microcracking in concrete, assessing ageing in polymer materials, and enabling temperature compensation in acoustoelastic tests. In conclusion, the review also summarises related studies, including photothermal crack modulation, and discusses current limitations and future directions of TMNL in elastic media.

NDE↗
DOE OSTI2020

Two-epoch Orbit Estimation for Wide Binaries Resolved in Hipparcos and Gaia

The Hipparcos catalog and its Double and Multiple System Annex (DMSA) lists 4099 components with individual proper motions and coordinates on the epoch 1991.25. Many of these long-period binary stars are also present in Gaia Data Release 2 (DR2). Using the available relative positions and proper motions separated by 24.25 yr, the equations of relative orbital motion can be solved for the two epoch eccentric anomalies, orbital period, and eccentricity. This method employs elimination of the linear Thiele–Innes unknowns and nonlinear optimization of the remaining condition equations. The quality of these solutions is compromised by the insufficient condition and modest precision of the Hipparcos astrometric data, as revealed by Monte Carlo simulations with artificially perturbed data points. The presence of multiple systems and optical pairs can also perturb the results. Limited experiments with artificial data indicate that useful estimates can be obtained with a 25 yr epoch difference for wide binaries with orbital periods up to ~500 yr. The prospects of this method dramatically improve with the proposed next-generation space astrometry missions such as Gaia-NIR and Theia, especially when additional conditions are included from astrometric or spectroscopic measurements. An ancillary catalog of cross-identification and astrometric information for 1295 double-star pairs cross-matched in Gaia DR2 and Hipparcos is also published.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The competing effects of wave amplitude and collisions on multi-ion species suppression of stimulated Brillouin scattering in inertial confinement fusion Hohlraums

Reduction in stimulated Brillouin scattering (SBS) from National Ignition Facility Hohlraums has been predicted through the use of multi-ion species materials on Hohlraum walls. This approach to controlling SBS is based upon introducing a lighter ion species to the heavier ion species Hohlraum wall in order to greatly increase the ion Landau damping of ion acoustic waves (IAWs). In a collisionless plasma, if the IAWs driven by SBS reach sufficient amplitudes, this increased damping is reduced or even eliminated by ion trapping in the IAWs. Here, the nonlinear behavior of IAWs is simulated with a multi-ion species Vlasov code, including interspecies ion–ion collisions, self-collisions, and electron–ion pitch-angle collisions. The effect of collisions on the trapping of ions and electrons in a large-amplitude IAW is studied in a regime of relevance to current Inertial Confinement Fusion experiments. Our simulations show that collisions can scatter trapped particles out of resonance with the IAW, suppressing trapping and helping to maintain an effective Landau damping of the IAW. The IAW amplitude required to trap particles in the presence of strong collisions is estimated analytically. These estimates are tested for strongly damped IAWs in tantalum oxide and pure helium plasmas. Here our simulations show that, above a threshold amplitude, the damping is reduced by an amount inversely proportional to the wave amplitude. Thus, the success of controlling SBS using a multispecies plasma may depend sensitively on laser power and pulse length.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

InAs Terahertz Metalens Emitter for Focused Terahertz Beam Generation

Metasurfaces have opened doors to combining multiple photonic functionalities in a single compact device. In particular, the ability to generate short terahertz (THz) pulses with precise wavefront engineering in a single THz metasurface redefined the role metasurfaces can play in THz systems. Here, an InAs metalens emitter which generates and focuses a THz pulse beam is demonstrated using a 130 nm thick InAs metasurface designed as a binary‐phase Fresnel zone plate. The THz beam is focused to a spot of ≈430 μm at 1 THz with a short focal length of 5 mm and large numerical aperture of 0.5. Nanoscale InAs Mie resonators comprising the metasurface enable THz generation with an amplitude as high as 20 times compared to plasmonic THz emitters and several times compared to a 1 mm thick ZnTe crystal. This InAs metasurface emitter provides a new paradigm for designing THz imaging, spectroscopy, and communication systems, where THz beam generation and shaping are performed with a single device without compromising the generation efficiency, while eliminating losses and avoiding limitations of phase matching of conventional nonlinear optics approaches.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Efficient bidirectional quantum frequency conversion between telecom and visible bands using adaptively phase-matched III-V nanophotonic waveguides

Quantum frequency conversion (QFC) is essential for interfacing quantum systems operating at different wavelengths and for realizing scalable quantum networks. Despite extensive progress, achieving QFC with simultaneous high efficiency, low pump power, minimal noise, broad bandwidth, and pump-wavelength flexibility remains challenging. Here, we demonstrate efficient, low-noise, and bidirectional QFC between the telecom (1550-nm) and visible (780-nm) bands using unpoled indium gallium phosphide (InGaP) χ (2) nanophotonic waveguides, eliminating the need for a long-wavelength pump. Leveraging the large nonlinear susceptibility of InGaP together with adaptive phase-matching control, we obtain 27% (55%) internal efficiency in a 6-mm (2.5-mm)-long waveguide with a low pump power of 20 mW (50 mW) and a noise flux spectral density of 10 −4 counts per second per hertz at signal–pump detuning of 20 nm. These results mark a significant advance in integrated nonlinear photonics for high-performance QFC, facilitating the development of versatile and scalable quantum networks.

Hu, Jierui [Univ. of Illinois at Urbana-Champaign,↗
DOE OSTI2021

High yield polar direct drive fusion neutron sources at the National Ignition Facility

Polar direct drive neutron source experiments were performed at the National Ignition Facility showing substantial improvement in total neutron yield and efficiency of conversion of laser energy to fusion output. Plastic capsules 3–4 mm in diameter were filled with 1.5 mg/cc of deuterium–tritium (DT) fuel and imploded with laser beam pointing and defocus designed to compensate for polar asymmetry introduced by the facility beam entrance angles. Radiation-hydrodynamics simulations were employed to optimize the multi-dimensional laser and target parameter space, within facility and target fabrication constraints. Ensembles of 1D simulations tuned to match the outputs of early shots in the series were used to design subsequent shots in the series. This allowed the later shots to be designed based on empirically motivated sensitivities to laser and target input parameters, while eliminating the need to explicitly model phenomena such as hydrodynamic instabilities and nonlinear laser–plasma interactions. Additionally, one experiment with a 3.0 mm diameter CH capsule produced 13.6 kJ (4.81 × 10 15 DT neutrons) from a laser input below the NIF optics damage threshold at 585 kJ, 328 TW. Two experiments with 4.0 mm capsules produced 31.3 and 33.6 kJ of fusion output (1.11 × 10 16 and 1.19 × 10 16 DT neutrons) with 1.10 MJ, 390 TW and 1.26 MJ, 425 TW of laser input, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Improving Deep Neural Networks’ Training for Image Classification With Nonlinear Conjugate Gradient-Style Adaptive Momentum

Momentum is crucial in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated constant. However, tuning the hyperparameter for momentum can be a significant computational burden. In this article, we propose a novel adaptive momentum for improving DNNs training; this adaptive momentum, with no momentum-related hyperparame- ter required, is motivated by the nonlinear conjugate gradient (NCG) method. Stochastic gradient descent (SGD) with this new adaptive momentum eliminates the need for the momentum hyperparameter calibration, allows using a significantly larger learning rate, accelerates DNN training, and improves the final accuracy and robustness of the trained DNNs. For example, SGD with this adaptive momentum reduces classification errors for training ResNet110 for CIFAR10 and CIFAR100 from 5.25% to 4.64% and 23.75% to 20.03%, respectively. Furthermore, SGD, with the new adaptive momentum, also benefits adversarial training and, hence, improves the adversarial robustness of the trained DNNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Elimination of MHD current sheets by modifications to the plasma wall in a fixed boundary model

Models of magnetohydrodynamic (MHD) equilibia that for computational convenience assume the existence of a system of nested magnetic flux surfaces tend to exhibit singular current sheets. These sheets are located on resonant flux surfaces that are associated with rational values of the rotational transform. We study the possibility of eliminating these singularities by suitable modifications of the plasma boundary, which we prescribe in a fixed boundary setting. We find that relatively straightforward iterative procedures can be used to eliminate weak current sheets that are generated at resonant flux surfaces by the nonlinear interactions of resonating wall harmonics. These types of procedures may prove useful in the design of fusion devices with configurations that enjoy improved stability and transport properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗