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DOE OSTI2016

SU-G-BRB-05: Automation of the Photon Dosimetric Quality Assurance Program of a Linear Accelerator

Purpose: To develop an automated method to calculate a linear accelerator (LINAC) photon radiation field size, flatness, symmetry, output and beam quality in a single delivery for flattened (FF) and flattening-filter-free (FFF) beams using an ionization chamber array. Methods: The proposed method consists of three control points that deliver 30×30, 10×10 and 5×5cm{sup 2} fields (FF or FFF) in a step-and-shoot sequence where the number of monitor units is weighted for each field size. The IC Profiler (Sun Nuclear Inc.) with 5mm detector spacing was used for this study. The corrected counts (CCs) were calculated and the locations of the maxima and minima values of the first-order gradient determined data of each sub field. Then, all CCs for each field size are summed in order to obtain the final profiles. For each profile, the radiation field size, symmetry, flatness, output factor and beam quality were calculated. For field size calculation, a parameterized gradient method was used. For method validation, profiles were collected in the detector array both, individually and as part of the step-and-shoot plan, with 9.9cm buildup for FF and FFF beams at 90cm source-to-surface distance. The same data were collected with the device (plus buildup) placed on a movable platform to achieve a 1mm resolution. Results: The differences between the dosimetric quantities calculated from both deliveries, individually and step-and-shoot, were within 0.31±0.20% and 0.04±0.02mm. The differences between the calculated field sizes with 5mm and 1mm resolution were ±0.1mm. Conclusion: The proposed single delivery method proved to be simple and efficient in automating the photon dosimetric monthly and annual quality assurance.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2026

Decadal Spiciness Variability in the Subtropical-Tropical Pacific in the CESM2 Large Ensemble

Tropical Pacific decadal variations impact weather and climate around the world and are also connected to variations in the global warming trend. The mechanisms driving these long-term modulations, particularly the role of subsurface ocean dynamics, are still debated. Here, we investigate the dynamics of spiciness (density-compensated temperature and salinity) anomalies in the tropical and subtropical Pacific, which are hypothesized as a possible driving mechanism of decadal climate variability. Based on the analysis of 100 realizations from the Community Earth System Model Version 2 Large Ensemble (CESM2-LE), we demonstrate a coupling between the subtropics and the equatorial Pacific by propagating spiciness anomalies at decadal time scales. The CESM2-LE simulates spiciness variability along a subduction path from the subtropics to the equator with frequency spectra that show the highest power at low frequencies and a power decay proportional to a −4 slope for frequencies greater than 0.01 cycles per months, corresponding to periods smaller than ∼8.5 years. Signals that originate in the Southern Hemisphere (SH) dominate and arrive with a larger magnitude at the equator compared to spiciness anomalies from the Northern Hemisphere (NH). Spiciness anomalies from the SH have shorter propagation times and are strengthened along their pathway as stochastic wind stress curl forcing generates anomalous baroclinic ocean pressure gradients. These pressure gradients generate spiciness anomalies via anomalous advection across climatological spiciness gradients in the SH. We conclude that the observed spiciness variance at decadal time scales is consistent with a forcing by stochastic wind variations that are low-pass filtered by ocean dynamics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2011

Advanced Engine/Aftertreatment System R&D

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2011

CRADA Final Report for CRADA Number ORNL00-0605: Advanced Engine/Aftertreatment System R&D

Navistar and ORNL established this CRADA to develop diesel engine aftertreatment configurations and control strategies that could meet emissions regulations while maintaining or improving vehicle efficiency. The early years of the project focused on reducing the fuel penalty associated with lean NOx trap (LNT), also known as NOx adsorber catalyst regeneration and desulfation. While Navistar pursued engine-based (in-cylinder) approaches to LNT regeneration, complementary experiments at ORNL focused on in-exhaust fuel injection. ORNL developed a PC-based controller for transient electronic control of EGR valve position, intake throttle position, and actuation of fuel injectors in the exhaust system of a Navistar engine installed at Oak Ridge. Aftertreatment systems consisting of different diesel oxidation catalysts (DOCs) in conjunction with a diesel particle filter and LNT were evaluated under quasi-steady-state conditions. Hydrocarbon (HC) species were measured at multiple locations in the exhaust system with Gas chromatograph mass spectrometry (GC-MS) and Fourier transform infrared (FTIR) spectroscopy. Under full-load, rated speed conditions, injection of fuel upstream of the DOC reduced the fuel penalty for a given level of NOx reduction by 10-20%. GC-MS showed that fuel compounds were 'cracked' into smaller hydrocarbon species over the DOC, particularly light alkenes. GC-MS analysis of HC species entering and exiting the LNT showed high utilization of light alkenes, followed by mono-aromatics; branched alkanes passed through the LNT largely unreacted. Follow-on experiments at a 'road load' condition were conducted, revealing that the NOx reduction was better without the DOC at lower temperatures. The improved performance was attributed to the large swings in the NOx adsorber core temperature. Split-injection experiments were conducted with ultra-low sulfur diesel fuel and three pure HC compounds: 1-pentene, toluene, and iso-octane. The pure compound experiments confirmed the previous results regarding hydrocarbon reactivity: 1-pentene was the most efficient LNT reductant, followed by toluene. Injection location had minimal impact on the reactivity of these two compounds. Iso-octane was an ineffective LNT reductant, requiring high doses (resulting in high HC emissions) to achieve reasonable NOx conversions. Diesel fuel reactivity was sensitive to injection location, with the best performance achieved through fuel injection downstream of the DOC. This configuration generated large LNT temperature excursions, which probably improved the efficiency of the NOx storage/reduction process, but also resulted in very high HC emissions. The ORNL team demonstrated an LNT desulfation under 'road load' conditions using throttling, EGR, and in-pipe injection of diesel fuel. Flow reactor characterization of core samples cut from the front and rear of the engine-aged LNT revealed complex spatially dependent degradation mechanisms. The front of the catalyst contained residual sulfates, which impacted NOx storage and conversion efficiencies at high temperatures. The rear of the catalyst showed significant sintering of the washcoat and precious metal particles, resulting in lower NOx conversion efficiencies at low temperatures. Further flow reactor characterization of engine-aged LNT core samples established that low temperature performance was limited by slow release and reduction of stored NOx during regeneration. Carbon monoxide was only effective at regenerating the LNT at temperatures above 200 C; propene was unreactive even at 250 C. Low temperature operation also resulted in unselective NOx reduction, resulting in high emissions of both N{sub 2}O and NH{sub 3}. During the latter years of the CRADA, the focus was shifted from LNTs to other aftertreatment devices. Two years of the CRADA were spent developing detailed ammonia SCR device models with sufficient accuracy and computational efficiency to be used in development of model-based ammonia injection control algorithms.ORNL, working closely with partners at Navistar and Mi

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2025

Legacy Survey of Space and Time Data Preview 1: visit_table dataset type

The Legacy Survey of Space and Time Data Preview 1 (DP1) is the first release of data from the NSF-DOE Vera C. Rubin Observatory. It consists of raw and calibrated single-epoch images, co-adds, difference images, detection catalogs, and other derived data products. DP1 is based on 1792 science-grade optical/near-infrared exposures acquired over 48 distinct nights by the Rubin Commissioning Camera, LSSTComCam, on the Simonyi Survey Telescope at the Summit Facility on Cerro Pachón, Chile during the first on-sky commissioning campaign in late 2024. DP1 covers a total of approximately 15 sq. deg. over seven roughly equally-sized non-contiguous fields, each independently observed in six broad photometric bands, ugrizy, spanning a range of stellar densities and latitudes and overlapping with external reference datasets. This dataset is a subset of the full data release consisting of the visit_table dataset type. These are metadata, including dates and filters for every visit. This release contains 1 dataset of this type.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

MEASURING THE DARK FLOW WITH PUBLIC X-RAY CLUSTER DATA

We present new results on the 'dark flow' from a measurement of the dipole in the distribution of peculiar velocities of galaxy clusters, applying the methodology proposed and developed by us earlier. Our latest measurement is conducted using new, low-noise 7 yr WMAP data as well as an all-sky sample of X-ray-selected galaxy clusters compiled exclusively from published catalogs. Our analysis of the cosmic microwave background signature of the kinematic Sunyaev-Zel'dovich (SZ) effect finds a statistically significant dipole at the location of galaxy clusters. The residual dipole outside the cluster regions is small, rendering our overall measurement 3{sigma}-4{sigma} significant. The amplitude of the dipole correlates with cluster properties, being larger for the most X-ray luminous clusters, as required if the signal is produced by the SZ effect. Since it is measured at zero monopole, the dipole cannot be due to the thermal SZ effect. Our results are consistent with those obtained earlier by us from 5 yr WMAP data and using a proprietary cluster catalog. In addition, they are robust to quadrupole removal, demonstrating that quadrupole leakage contributes negligibly to the signal. The lower noise of the 7 yr WMAP also allows us, for the first time, to obtain tentative empirical confirmation of our earlier conjecture that the adopted filtering alters the sign of the kinematic SZ (KSZ) effect for realistic clusters and thus of the deduced direction of the flow. The latter is consistent with our earlier measurement in both the amplitude and direction. Assuming the filtering indeed alters the sign of the KSZ effect from the clusters, the direction agrees well also with the results of independent work using galaxies as tracers at lower distances. We make all maps and cluster templates derived by us from public data available to the scientific community to allow independent tests of our method and findings.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Simons Observatory: broadband metamaterial antireflection cuttings for large-aperture alumina optics

Here we present the design, fabrication, and measured performance of metamaterial antireflection cuttings (ARCs) for large-format alumina filters operating over more than an octave of bandwidth to be deployed at the Simons Observatory (SO). The ARC consists of subwavelength features diced into the optic’s surface using a custom dicing saw with near-micrometer accuracy. The designs achieve percent-level control over reflections at angles of incidence up to 20°. The ARCs were demonstrated on four 42 cm diameter filters covering the 75 to 170 GHz band and a 50 mm diameter prototype covering the 200 to 300 GHz band. The reflection and transmission of these samples were measured using a broadband coherent source that covers frequencies from 20 GHz to 1.2 THz. These measurements demonstrate percent-level control over reflectance across the targeted pass-bands and a rapid reduction in transmission as the wavelength approaches the length scale of the metamaterial structure where scattering dominates the optical response. The latter behavior enables use of the metamaterial ARC as a scattering filter in this limit.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

Development of Wien filter for small ion gun of surface analysis

The gas cluster ion beam (GCIB) and liquid metal ion beam have been studied in the context of ion beam usage for analytical equipment in applications such as X-ray photoelectron spectroscopy and secondary ion mass spectroscopy (SIMS). In particular, small ion sources are used for the secondary ion generation and ion etching. To set the context to this study, the SIMS project has been launched to develop ion-gun based analytical equipment for the Korea Basic Science Institute. The objective of the first stage of the project is the generation of argon beams with a GCIB system [A. Kirkpatrick, Nucl. Instrum. Methods Phys. Res., Sect. B 206, 830–837 (2003)] that consists of a nozzle, skimmer, ionizer, acceleration tube, separation system, transport system, and target. The Wien filter directs the selected cluster beam to the target system by exploiting the velocity difference of the generated particles from GCIB. In this paper, we present the theoretical modeling and three-dimensional electromagnetic analysis of the Wien filter, which can separate Ar{sup +}{sub 2500} clusters from Ar{sup +}{sub 2400} to Ar{sup +}{sub 2600} clusters with a 1-mm collimator.

43 PARTICLE ACCELERATORS↗

DOE OSTI2014

Advanced Kalman Filter for Real-Time Responsiveness in Complex Systems

Complex engineering systems pose fundamental challenges in real-time operations and control because they are highly dynamic systems consisting of a large number of elements with severe nonlinearities and discontinuities. Today’s tools for real-time complex system operations are mostly based on steady state models, unable to capture the dynamic nature and too slow to prevent system failures. We developed advanced Kalman filtering techniques and the formulation of dynamic state estimation using Kalman filtering techniques to capture complex system dynamics in aiding real-time operations and control. In this work, we looked at complex system issues including severe nonlinearity of system equations, discontinuities caused by system controls and network switches, sparse measurements in space and time, and real-time requirements of power grid operations. We sought to bridge the disciplinary boundaries between Computer Science and Power Systems Engineering, by introducing methods that leverage both existing and new techniques. While our methods were developed in the context of electrical power systems, they should generalize to other large-scale scientific and engineering applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

SU-E-J-29: Audiovisual Biofeedback Improves Tumor Motion Consistency for Lung Cancer Patients

Purpose: To investigate whether the breathing-guidance system: audiovisual (AV) biofeedback improves tumor motion consistency for lung cancer patients. This will minimize respiratory-induced tumor motion variations across cancer imaging and radiotherapy procedues. This is the first study to investigate the impact of respiratory guidance on tumor motion. Methods: Tumor motion consistency was investigated with five lung cancer patients (age: 55 to 64), who underwent a training session to get familiarized with AV biofeedback, followed by two MRI sessions across different dates (pre and mid treatment). During the training session in a CT room, two patient specific breathing patterns were obtained before (Breathing-Pattern-1) and after (Breathing-Pattern-2) training with AV biofeedback. In each MRI session, four MRI scans were performed to obtain 2D coronal and sagittal image datasets in free breathing (FB), and with AV biofeedback utilizing Breathing-Pattern-2. Image pixel values of 2D images after the normalization of 2D images per dataset and Gaussian filter per image were used to extract tumor motion using image pixel values. The tumor motion consistency of the superior-inferior (SI) direction was evaluated in terms of an average tumor motion range and period. Results: Audiovisual biofeedback improved tumor motion consistency by 60% (p value = 0.019) from 1.0±0.6 mm (FB) to 0.4±0.4 mm (AV) in SI motion range, and by 86% (p value < 0.001) from 0.7±0.6 s (FB) to 0.1±0.2 s (AV) in period. Conclusion: This study demonstrated that audiovisual biofeedback improves both breathing pattern and tumor motion consistency for lung cancer patients. These results suggest that AV biofeedback has the potential for facilitating reproducible tumor motion towards achieving more accurate medical imaging and radiation therapy procedures.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Coordinated U–Pb geochronology, trace element, Ti-in-zircon thermometry and microstructural analysis of Apollo zircons

Here, we present the results of a coordinated SIMS U–Pb, trace element, Ti-in-zircon thermometry, and microstructural study of 155 lunar zircons separated from Apollo 14, 15, and 17 breccia and soil samples that help resolve discrepancies between the zircon data, the lunar whole rock history and lunar magma ocean crystallization models. The majority of lunar grains are detrital fragments, some nearly 1 mm in length, of large parent crystals suggesting that they crystallized in highly enriched KREEP magmas. The zircon age distributions for all three landing sites exhibit an abundance of ages at ~4.33 Ga, however they differ in that only Apollo 14 samples have a population of zircons with ages between 4.1 and 3.9 Ga. These younger grains comprise only 10% of all dated lunar zircons and are usually small and highly shocked making them more susceptible to Pb-loss. These observations suggest that the majority of zircons crystallized before 4.1 Ga and that KREEP magmatism had predominantly ceased by this time. We also observed that trace element analyses are easily affected by contributions from inclusions (typically injected impact melt) within SIMS analyses spots. After filtering for these effects, rare-earth element (REE) abundances of pristine zircon are consistent with one pattern characterized by a negative Eu anomaly and no positive Ce anomaly, implying that the zircons formed in a reducing environment. This inference is consistent with crystallization temperatures based on measured Ti concentrations and new estimates of oxide activities which imply temperatures ranging between 958 ± 57 and 1321 ± 100 °C, suggesting that zircon parent magmas were anhydrous. Together, the lunar zircon ages and trace elements are consistent with a ≤300 My duration of KREEP magmatism under anhydrous, reducing conditions. We also report two granular texture zircons that contain baddeleyite cores, which both yield 207 Pb– 206 Pb ages of 4.33 Ga. These grains are our best constraints on impact ages within our sample population, and suggest at least one large impact is contemporaneous with the most common time of magmatic zircon formation on the Moon’s crust visited by the Apollo missions.

58 GEOSCIENCES↗

DOE OSTI2012

Commissioning of soft and deep X-ray lithography beamline on Indus-2

Soft and Deep x-ray lithography (SDXRL) beamline is commissioned on Indus-2. The beamline can be operated between 1.5 to 20 keV and in white beam mode. Beamline consists of two x-ray mirrors, slits, Be-windows, beam diagnostics and filters assemblies and radiation safety systems. A custom built X-ray scanner is used to create 3-D high aspect ratio micro structures. The paper reports the commissioning results of this beamline.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Pedestal fluctuation measurements with charge exchange imaging at the DIII-D tokamak

A new high radial resolution 2D multichannel Charge eXchange Imaging (CXI) diagnostic is under development for deployment at DIII-D. Here, the diagnostic system will measure low-to-intermediate radial wavenumber carbon density fluctuations by observing the n = 8 – 7 (λ = 529.06 nm) C-VI emission line, resulting from charge exchange collisions between heating neutral beam atoms and the intrinsic carbon ion density. The new CXI diagnostic will provide measurements with ΔR ~ 0.4 cm to access higher k r instabilities (k r < 8 cm –1 ) predicted to arise in the steep-gradient region of the H-mode pedestal. The CXI system will feature 60 fiber bundles in a 12 × 5 arrangement, with each bundle consisting of four 1 mm fibers. A custom optical system has been designed to filter and image incoming signals onto an 8 × 8 avalanche photodiode array. Additionally, a novel electronics suite has been designed and commissioned to amplify and digitize the relatively low-intensity carbon signal at a 2 MHz bandwidth. Forward modeling results of the active C-VI emission suggest sufficient signal to noise ratios to resolve turbulent fluctuations. Prototype measurements demonstrate the ability to perform high frequency pedestal measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

UNIFICATION OF LUMINOUS TYPE 1 QUASARS THROUGH C IV EMISSION

Using a sample of {approx}30,000 quasars from the 7th Data Release of the Sloan Digital Sky Survey, we explore the range of properties exhibited by high-ionization, broad emission lines, such as C IV {lambda}1549. Specifically, we investigate the anti-correlation between continuum luminosity and emission-line equivalent width (the Baldwin Effect (BEff)) and the 'blueshifting' of the high-ionization emission lines with respect to low-ionization emission lines. Employing improved redshift determinations from Hewett and Wild, the blueshift of the C IV emission line is found to be nearly ubiquitous, with a mean shift of {approx}810 km s{sup -1} for radio-quiet (RQ) quasars and {approx}360 km s{sup -1} for radio-loud (RL) quasars. The BEff is present in both RQ and RL samples. We consider these phenomena within the context of an accretion disk-wind model that is modulated by the nonlinear correlation between ultraviolet and X-ray continuum luminosity. Composite spectra are constructed as a function of C IV emission-line properties in an attempt to reveal empirical relationships between different line species and the continuum. Within a two-component disk+wind model of the broad emission-line region (BELR), where the wind filters the continuum seen by the disk component, we find that RL quasars are consistent with being dominated by the disk component, while broad absorption line quasars are consistent with being dominated by the wind component. Some RQ objects have emission-line features similar to RL quasars; they may simply have insufficient black hole (BH) spin to form radio jets. Our results suggest that there could be significant systematic errors in the determination of L{sub bol} and BH mass that make it difficult to place these findings in a more physical context. However, it is possible to classify quasars in a paradigm where the diversity of BELR parameters is due to differences in an accretion disk wind between quasars (and over time); these differences are underlain primarily by the spectral energy distribution, which ultimately must be tied to BH mass and accretion rate.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

DETERMINING THE STRUCTURE OF SOLAR CORONAL LOOPS USING THEIR EVOLUTION

Despite significant progress in understanding the dynamics of the corona, there remain several unanswered questions about the basic physical properties of coronal loops. Recent observations from different instruments have yielded contradictory results about some characteristics of coronal loops, specifically as to whether the observed loops are spatially resolved. In this paper, we examine the evolution of coronal loops through two extreme-ultraviolet filters and determine if they evolve as a single cooling strand. We measure the temporal evolution of eight active region loops previously studied and found to be isothermal and resolved by Aschwanden and Nightingale. All eight loops appear in 'hotter' TRACE filter images (Fe XII 195 A) before appearing in the 'cooler' (Fe IX/Fe X 171 A) TRACE filter images. We use the measured delay between the two filters to calculate a cooling time and then determine if that cooling time is consistent with the observed lifetime of the loop. We do this twice: once when the loop appears (rise phase) and once when it disappears (decay phase). We find that only one loop appears consistent with a single cooling strand and hence could be considered to be resolved by TRACE. For the remaining seven loops, their observed lifetimes are longer than expected for a single cooling strand. We suggest that these loops could be formed of multiple cooling strands, each at a different temperature. These findings indicate that the majority of loops observed by TRACE are unresolved.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Single-particle imaging without symmetry constraints at an X-ray free-electron laser

The analysis of a single-particle imaging (SPI) experiment performed at the AMO beamline at LCLS as part of the SPI initiative is presented here. A workflow for the three-dimensional virus reconstruction of the PR772 bacteriophage from measured single-particle data is developed. It consists of several well defined steps including single-hit diffraction data classification, refined filtering of the classified data, reconstruction of three-dimensional scattered intensity from the experimental diffraction patterns by orientation determination and a final three-dimensional reconstruction of the virus electron density without symmetry constraints. The analysis developed here revealed and quantified nanoscale features of the PR772 virus measured in this experiment, with the obtained resolution better than 10 nm, with a clear indication that the structure was compressed in one direction and, as such, deviates from ideal icosahedral symmetry.

47 OTHER INSTRUMENTATION↗

DOE OSTI2012

TOPAS: An innovative proton Monte Carlo platform for research and clinical applications

Purpose: While Monte Carlo particle transport has proven useful in many areas (treatment head design, dose calculation, shielding design, and imaging studies) and has been particularly important for proton therapy (due to the conformal dose distributions and a finite beam range in the patient), the available general purpose Monte Carlo codes in proton therapy have been overly complex for most clinical medical physicists. The learning process has large costs not only in time but also in reliability. To address this issue, we developed an innovative proton Monte Carlo platform and tested the tool in a variety of proton therapy applications. Methods: Our approach was to take one of the already-established general purpose Monte Carlo codes and wrap and extend it to create a specialized user-friendly tool for proton therapy. The resulting tool, TOol for PArticle Simulation (TOPAS), should make Monte Carlo simulation more readily available for research and clinical physicists. TOPAS can model a passive scattering or scanning beam treatment head, model a patient geometry based on computed tomography (CT) images, score dose, fluence, etc., save and restart a phase space, provides advanced graphics, and is fully four-dimensional (4D) to handle variations in beam delivery and patient geometry during treatment. A custom-designed TOPAS parameter control system was placed at the heart of the code to meet requirements for ease of use, reliability, and repeatability without sacrificing flexibility. Results: We built and tested the TOPAS code. We have shown that the TOPAS parameter system provides easy yet flexible control over all key simulation areas such as geometry setup, particle source setup, scoring setup, etc. Through design consistency, we have insured that user experience gained in configuring one component, scorer or filter applies equally well to configuring any other component, scorer or filter. We have incorporated key lessons from safety management, proactively removing possible sources of user error such as line-ordering mistakes. We have modeled proton therapy treatment examples including the UCSF eye treatment head, the MGH stereotactic alignment in radiosurgery treatment head and the MGH gantry treatment heads in passive scattering and scanning modes, and we have demonstrated dose calculation based on patient-specific CT data. Initial validation results show agreement with measured data and demonstrate the capabilities of TOPAS in simulating beam delivery in 3D and 4D. Conclusions: We have demonstrated TOPAS accuracy and usability in a variety of proton therapy setups. As we are preparing to make this tool freely available for researchers in medical physics, we anticipate widespread use of this tool in the growing proton therapy community.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

Xie, Xuping↗