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Lossy compression of statistical data using quantum annealer

Abstract We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3–3.5 times better compression performance than the algorithm based on neural-network autoencoder. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.

97 MATHEMATICS AND COMPUTING↗

Marginal unbiased score expansion and application to CMB lensing

Here, we present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces, yielding Gaussianized asymptotically unbiased and near-optimal constraints on global parameters of interest. It is computationally much cheaper than exact alternatives like Hamiltonian Monte Carlo (HMC), excelling on funnel problems which challenge HMC, and does not require any problem-specific user supervision like other approximate methods such as variational inference or many simulation-based inference methods. MUSE makes possible the first joint Bayesian estimation of the delensed Cosmic Microwave Background (CMB) power spectrum and gravitational lensing potential power spectrum, demonstrated here on a simulated data set as large as the upcoming South Pole Telescope 3G 1500 deg 2 survey, corresponding to a latent dimensionality of ~6 million and of order 100 global bandpower parameters. On a subset of the problem where an exact but more expensive HMC solution is feasible, we verify that MUSE yields nearly optimal results. We also demonstrate that existing spectrum-based forecasting tools which ignore pixel-masking underestimate predicted error bars by only ~10%. This method is a promising path forward for fast lensing and delensing analyses which will be necessary for future CMB experiments such as SPT-3G, Simons Observatory, or CMB-S4, and can complement or supersede existing HMC approaches. The success of MUSE on this challenging problem strengthens its case as a generic procedure for a broad class of high-dimensional inference problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reliability Assessment of Remote Visual Examination

Remote visual testing (RVT) is a commonly used nondestructive examination method for inservice inspection (ISI) of reactor internals to detect cracking and gross component failures. Despite widespread use, the detection reliability of RVT and the factors that impact overall RVT performance have been unresolved issues. This report describes the results from an assessment sponsored by the U.S. Nuclear Regulatory Commission and conducted by the Pacific Northwest National Laboratory, in cooperation with the Electric Power Research Institute, for evaluating the reliability of RVT methods currently being used for [reactor] in-vessel visual inspection. The goal was to assess the performance of commercially applied RVT examination procedures implemented by qualified personnel, as well as to identify and qualitatively assess enhancements to examination procedures for detecting flaws in test specimens. The assessment was performed over three phases of research, with the results of the first phase used to identify key controllable parameters impacting RVT performance and to design the next two phases (round-robin testing). Participants in the round-robin tests included teams of inspectors from commercial nuclear power ISI vendors. Participants were asked to determine if a specimen contained a crack and its approximate location, orientation, and length. The detection and location information were used to compute estimates of the probability of detection and false call probability for various scenarios such as the placement and orientation of the flaw on the specimen, team-to-team variations in detection performance, and effects of secondary review on RVT detection. Results showed that crack opening displacement (COD) is the dominant factor in the reliability of crack detection using commercially applied RVT procedures, with crack length being weakly correlated with detection probability. The implication is that RVT detection is likely heavily dependent on the contrast produced by the crack opening, with crack detection becoming less reliable as the COD decreases. Further, the results indicated RVT will be challenged when cracks are located in the vicinity of surface features such as scratches or weld ripples, or close to the edge of welds where shadowing and/or the presence of weld undercuts may complicate the ability to detect the crack. The assessment also reinforced earlier findings on the importance of lighting in flaw detection and appeared to align with other studies that find improved reliability when using multiple inspectors or analysts. Finally, the results pointed to the importance of practice with specimens that mimic conditions likely to be found in the field. Based on the findings and limitations of the assessment, a number of recommendations are made regarding best practices for improving the reliability of RVT in a field setting and for addressing remaining informational gaps. This report describes the design and noted limitations of the three phases of research, the analysis methodology for each phase, and the results of the research. The results of this assessment provide a benchmark set of data on the reliability of RVT for detecting cracking, assuming the implementation of field-like inspection procedures. The likely impact of several uncontrolled factors on RVT detection performance are discussed, and recommendations regarding the use of these results to assess field performance are provided. Finally, recent advances in RVT technology are briefly discussed and point to the potential need for continued research to evaluate the capability and effectiveness of the technique as improvements are implemented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Quantitative Phenomena Identification and Ranking Table (QPIRT) for Bayesian uncertainty quantification

Propagating parameter uncertainty for a nuclear reactor system code is a challenging problem due to often non-linear system response to the numerous parameters involved and lengthy computational times; issues that compound when a statistical sampling procedure is adopted, since the code must be run many times. The number of parameters sampled must therefore be limited to as few as possible that still accurately characterize the uncertainty in the system response. A Quantitative Phenomena Identification and Ranking Table (QPIRT) was developed to accomplish this goal. The QPIRT consists of two steps: a 'Top-Down' step focusing on identifying the dominant physical phenomena controlling the system response, and a 'Bottom-Up' step which focuses on determining the correlations from those key physical phenomena that significantly contribute to the response uncertainty. The Top-Down step evaluates phenomena using the governing equations of the system code at nominal parameter values, providing a 'fast' screening step. The Bottom-Up step then analyzes the correlations and models for the phenomena identified from the Top-Down step to find which parameters to sample. The QPIRT, through the Top-Down and Bottom-Up steps thus provides a systematic approach to determining the limited set of physically relevant parameters that influence the uncertainty of the system response. This strategy was demonstrated through an application to the RELAP5-based analysis of a PWR Total Loss of main Feedwater Flow (TLOFW) accident, also known as feed and bleed' scenario, . Ultimately, this work is the first component in a larger task of building a calibrated uncertainty propagation framework. The QPIRT is an essential piece because the uncertainty of those selected parameters will be calibrated to data from both Separate and Integral Effect Tests (SETs and IETs). Therefore the system response uncertainty will incorporate the knowledge gained from the database of past large IETs. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Deformable Image Registration for Adaptive Radiation Therapy of Head and Neck Cancer: Accuracy and Precision in the Presence of Tumor Changes

Purpose: To compare deformable image registration (DIR) accuracy and precision for normal and tumor tissues in head and neck cancer patients during the course of radiation therapy (RT). Methods and Materials: Thirteen patients with oropharyngeal tumors, who underwent submucosal implantation of small gold markers (average 6, range 4-10) around the tumor and were treated with RT were retrospectively selected. Two observers identified 15 anatomical features (landmarks) representative of normal tissues in the planning computed tomography (pCT) scan and in weekly cone beam CTs (CBCTs). Gold markers were digitally removed after semiautomatic identification in pCTs and CBCTs. Subsequently, landmarks and gold markers on pCT were propagated to CBCTs, using a b-spline-based DIR and, for comparison, rigid registration (RR). To account for observer variability, the pair-wise difference analysis of variance method was applied. DIR accuracy (systematic error) and precision (random error) for landmarks and gold markers were quantified. Time trend of the precisions for RR and DIR over the weekly CBCTs were evaluated. Results: DIR accuracies were submillimeter and similar for normal and tumor tissue. DIR precision (1 SD) on the other hand was significantly different (P<.01), with 2.2 mm vector length in normal tissue versus 3.3 mm in tumor tissue. No significant time trend in DIR precision was found for normal tissue, whereas in tumor, DIR precision was significantly (P<.009) degraded during the course of treatment by 0.21 mm/week. Conclusions: DIR for tumor registration proved to be less precise than that for normal tissues due to limited contrast and complex non-elastic tumor response. Caution should therefore be exercised when applying DIR for tumor changes in adaptive procedures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Gamma Knife irradiation method based on dosimetric controls to target small areas in rat brains

Purpose: Targeted and whole-brain irradiation in humans can result in significant side effects causing decreased patient quality of life. To adequately investigate structural and functional alterations after stereotactic radiosurgery, preclinical studies are needed. The purpose of this work is to establish a robust standardized method of targeted irradiation on small regions of the rat brain. Methods: Euthanized male Fischer rats were imaged in a stereotactic bed, by computed tomography (CT), to estimate positioning variations relative to the bregma skull reference point. Using a rat brain atlas and the stereotactic bregma coordinates obtained from CT images, different regions of the brain were delimited and a treatment plan was generated. A single isocenter treatment plan delivering ≥100 Gy in 100% of the target volume was produced by Leksell GammaPlan using the 4 mm diameter collimator of sectors 4, 5, 7, and 8 of the Gamma Knife unit. Impact of positioning deviations of the rat brain on dose deposition was simulated by GammaPlan and validated with dosimetric measurements. Results: The authors’ results showed that 90% of the target volume received 100 ± 8 Gy and the maximum of deposited dose was 125 ± 0.7 Gy, which corresponds to an excellent relative standard deviation of 0.6%. This dose deposition calculated with GammaPlan was validated with dosimetric films resulting in a dose-profile agreement within 5%, both in X- and Z-axes. Conclusions: The authors’ results demonstrate the feasibility of standardizing the irradiation procedure of a small volume in the rat brain using a Gamma Knife.

60 APPLIED LIFE SCIENCES↗

Rad-Hydro with a High-Order, Low-Order Method

Moment-based acceleration via the development of “high-order, low-order” (HO-LO) algorithms has provided substantial accuracy and efficiency enhancements for solutions of the nonlinear, thermal radiative transfer equations by CCS-2 and T-3 staff members. Accuracy enhancements over traditional, linearized methods are obtained by solving a nonlinear, time-implicit HO-LO system via a Jacobian-free Newton Krylov procedure. This also prevents the appearance of non-physical maximum principle violations (“temperature spikes”) associated with linearization. Efficiency enhancements are obtained in part by removing “effective scattering” from the linearized system. In this highlight, we summarize recent work in which we formally extended the HO-LO radiation algorithm to include operator-split radiation-hydrodynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Identification and Quantification of Beta-Emitters in Waste Packages by Segmented Gamma-Scanning - 20114

A commonly applied method for the non-destructive characterization of the radioactive inventory of waste packages (e.g. 200-l drums) is segmented gamma-scanning. The gamma-emitting inventory is identified via their characteristic lines in the measured spectra. The corresponding net peak areas allow for quantification applying appropriate models. The identification and quantification of beta-emitters present in the waste package require further evaluation. While some of them emit gamma-rays, too, which can be used for identification and quantification, pure beta-emitters contribute to the gamma-spectra only by their Bremsstrahlung-spectra. {sup 32}P, {sup 90}Sr and {sup 90}Y are typical representatives of these isotopes. A method is developed for identification and quantification of these pure beta-emitters in radioactive waste packages. Origin of the procedure is the evaluation of the measured gamma-spectrum. After the identification of all lines present in the spectrum (characteristic gamma-lines, single- and double-escape-lines, X-ray-lines, annihilation peak etc.) this information is used together with calibration data of the detection system and further a-priori information like matrix composition, cross-section data from databases etc. to simulate the spectra without the Bremsstrahlung-components by an appropriate method. This may be Monte Carlo simulations or, like in our case, a computer code taking into account mathematical descriptions of the physical effects like photo effect, (multiple) Compton scattering, backscattering etc. and the attenuation effects of the waste matrix. In any case, the resulting spectrum must simulate the real spectrum without its Bremsstrahlung-component as good as possible. Subtracting the simulated from the measured spectrum then results in the Bremsstrahlung-components caused by the beta-emitters. Prior to evaluation, a set of Bremsstrahlung-spectra is calculated and stored for different beta-emitters in different matrices using the Bethe-Heitler equation. This data set can be extended for new conditions, if necessary, and is allocated in a data base for future application. Applying a non-linear optimization using the generalized reduced gradient method for comparing the calculated with the derived Bremsstrahlung-spectra results in the identification of the beta-emitter and a factor, which is proportional to its activity. The proportionality is determined by previous calibration measurements. The application of the method is demonstrated by measurements on a 200-l mock-up drum and a real waste package. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

Bayesian optimal experimental design for constitutive model calibration

Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. Further, this framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration. Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.

42 ENGINEERING↗

Novel Radiometry for In-Pipe Robotic Inspection of Holdup Deposits in Gaseous Diffusion Piping - 19503

This paper details the first complete, DOE approved, deployed and operational radiometry for robotic nondestructive assay (NDA) of holdup deposits in gaseous diffusion piping. Some features, like peak-finding, Compton correction, detector efficiency, and material properties are characteristic of typical manual methods. Most features are specific to in-pipe robotic deployment. These include in-motion radiometry, self-determined location, geometric modeling of thick deposits, bounding of self-attenuation thickness and auto-checking of replicate measurements. Significant are the means for determining all the properties, equations, and constants for automatically computing and displaying all the quantities, uncertainties and information needed for NDA reporting, analysis, and review. Earlier work by this team demonstrated rudimentary but convincing robotic in-pipe NDA of holdup deposits in pipes. Cold testing with high-enrichment mat sources and hot tests with low U-235 loadings together succeeded to exhibit convincing proof-of-principle. This research-grade radiometry implementation lacked accurate odometry, efficiency calibration, high-fidelity detector modeling, attenuation modeling, forward geometric modeling, auto-segmenting, uncertainty modeling, replicate checking, deconvolution and much more. This work explains the technical basis behind robotic in-pipe NDA. It includes discussion of a new method for modeling of self-attenuation using in-pipe deposit geometry information, detail of the method's total measurement uncertainty, and explanation of calibration methods and results. Beyond development of automation-specific radiometric elements, the paper highlights analyses, testing, and technical bases specific to and supportive of the methodology. Examples include collimation characterization, detector efficiency determination, auto-calibration methodology, and odometric replicate-checking. Results of this methodology are formalized in a DOE EM Technical Basis Document, implemented in software, formally verified in review and acceptance testing and proceduralized as a means for D and D NDA at the Portsmouth enrichment facility. Measurement of U-235 quantity is a well-known cost and schedule driver in D and D of every defunct gaseous diffusion enrichment facility in the world. The radiometry methodologies and results detailed in this paper were the high hurdles. Having established the technical basis for this automated NDA, the opportunity is to apply this to many sizes and robot forms for addressing holdup deposit NDA throughout the D and D community. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Group Structure Optimization Using the PyGroup Code

Group constants are used as coefficients in the energy domain discretized Linear Boltzmann Equation (LBE), in which the Continuous-Energy (CE) fluxes are also integrated over energy bins and transformed into group fluxes. This procedure, based on the Multi-Group (MG) theory, is widely applied in radiation transport and diffusion simulations Careful preparation of MG cross section data, or group constants, is thus a prerequisite for success in acquiring high-fidelity LBE solutions. Generation of MG cross section data itself is a complicated multi-step task, since group constants are indispensably coupled with the solution of the LBE, i.e. the flux spectrum in the problem to be solved. Theoretically, a MG cross section library is only valid for the problem that it is built upon. Nevertheless, in practice MG cross section libraries are prepared for similar type of problems, such as thermal reactors, fast reactors, etc., to facilitate the neutronic simulations. Generally, CE point-wise cross section data set, generated by both theoretical models and experimental data, is first converted to Fine-Group (FG) libraries using a pre-defined or precalculated flux spectra, then, Broad-Group (BG) libraries are collapsed from the fine-group libraries using problem-dependent flux spectra. Proper treatments of energy and spatial self-shielding and resonance cross section are required in the CE-to-MG converting process Previously, we have developed a computer code, YGROUP, for fine-to-broad group cross section collapsing. To maintain high accuracy of the resulting BG libraries, YGROUP provides users several options on collapsing strategies and weighting schemes for group binning and evaluation of BG cross section data in users' specific problems.. An approach based on Particle Swarm Optimization was applied to automatically determine the optimal group structure. We also developed a hybrid weighting scheme to further improve BG library performance for Special Nuclear Materials (SNM) detection applications. In this work, a new computer code, PyGroup, has been developed to implement the PSO approach with an improved simulation-driven fitness function design that includes both response and forward/adjoint flux errors. Together with YGROUP, and deterministic transport code TITAN/PENMSHXP, the PyGroup code package is tested on a Dual Range Coincident Counter (DRCC) model. In this paper, we demonstrated the capability of the PyGroup code for group structure optimization using the DRCC detector model. In the future, an iteration scheme can be implemented to determine the number of broad groups based on a user-defined tolerance. we will also apply PyGroup to more complicated reactor models, and investigate physics-based fitness function designs to further reduce computational cost. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MIDA: A Multimodal Imaging-Based Detailed Anatomical Model of the Human Head and Neck

Computational modeling and simulations are increasingly being used to complement experimental testing for analysis of safety and efficacy of medical devices. Multiple voxel- and surface-based whole- and partial-body models have been proposed in the literature, typically with spatial resolution in the range of 1–2 mm and with 10–50 different tissue types resolved. We have developed a multimodal imaging-based detailed anatomical model of the human head and neck, named “MIDA”. The model was obtained by integrating three different magnetic resonance imaging (MRI) modalities, the parameters of which were tailored to enhance the signals of specific tissues: i) structural T1- and T2-weighted MRIs; a specific heavily T2-weighted MRI slab with high nerve contrast optimized to enhance the structures of the ear and eye; ii) magnetic resonance angiography (MRA) data to image the vasculature, and iii) diffusion tensor imaging (DTI) to obtain information on anisotropy and fiber orientation. The unique multimodal high-resolution approach allowed resolving 153 structures, including several distinct muscles, bones and skull layers, arteries and veins, nerves, as well as salivary glands. The model offers also a detailed characterization of eyes, ears, and deep brain structures. A special automatic atlas-based segmentation procedure was adopted to include a detailed map of the nuclei of the thalamus and midbrain into the head model. The suitability of the model to simulations involving different numerical methods, discretization approaches, as well as DTI-based tensorial electrical conductivity, was examined in a case-study, in which the electric field was generated by transcranial alternating current stimulation. The voxel- and the surface-based versions of the models are freely available to the scientific community.

59 BASIC BIOLOGICAL SCIENCES↗

A new yield and failure theory for composite materials under static and dynamic loading

In order to facilitate and accelerate the process of introducing, evaluating and adopting new material systems, it is important to develop/establish comprehensive and effective procedures of characterization, modeling and failure prediction of composite structures based on the properties of the constituent materials, e. g., fibers, matrix, and the single ply or lamina. A new yield/failure theory is proposed for predicting lamina yielding and failure under multi-axial states of stress including strain rate effects. It is based on the equivalent stress concept derived from energy principles and is expressed in terms of a single criterion. It is presented in the form of master yield and failure envelopes incorporating strain rate effects. The theory can be further adapted and extended to the prediction of in situ first ply yielding and failure (FPY and FPF) and progressive damage of multi-directional laminates under static and dynamic loadings. The significance of this theory is that it allows for rapid screening of new composite materials without extensive testing and offers easily implemented design tools.

36 MATERIALS SCIENCE↗

TH-E-209-00: Radiation Dose Monitoring and Protocol Management

Radiation dose monitoring solutions have opened up new opportunities for medical physicists to be more involved in modern clinical radiology practices. In particular, with the help of comprehensive radiation dose data, data-driven protocol management and informed case follow up are now feasible. Significant challenges remain however and the problems faced by medical physicists are highly heterogeneous. Imaging systems from multiple vendors and a wide range of vintages co-exist in the same department and employ data communication protocols that are not fully standardized or implemented making harmonization complex. Many different solutions for radiation dose monitoring have been implemented by imaging facilities over the past few years. Such systems are based on commercial software, home-grown IT solutions, manual PACS data dumping, etc., and diverse pathways can be used to bring the data to impact clinical practice. The speakers will share their experiences with creating or tailoring radiation dose monitoring/management systems and procedures over the past few years, which vary significantly in design and scope. Topics to cover: (1) fluoroscopic dose monitoring and high radiation event handling from a large academic hospital; (2) dose monitoring and protocol optimization in pediatric radiology; and (3) development of a home-grown IT solution and dose data analysis framework. Learning Objectives: Describe the scope and range of radiation dose monitoring and protocol management in a modern radiology practice Review examples of data available from a variety of systems and how it managed and conveyed. Reflect on the role of the physicist in radiation dose awareness.

60 APPLIED LIFE SCIENCES↗

Design Optimization of A generic Fissile Solution for Mo99 production using Electron Beam-based Neutron Generator using MCNP+CFD

Molybdenum-99 ( 99 Mo) is a medical isotope used in 80% of all medical imaging procedures today. However, 99 Mo is not directly administered to patients for imaging; its decay product, technetium-99m ( 99 mTc), is a metastable isotope with a half-life of ~6 hours. Such a short half-life does not allow for production, separation, and application to a patient before decaying further. Therefore, the solution is to produce the precursor to 99 mTc, 99 Mo. 99 Mo has a half-life of 66 hours, long enough to produce the material and send it to the desired location before it fully decays. Under National Nuclear Security Administration’s (NNSA) highly enriched uranium (HEU) minimization mission, the Material Management and Minimization (M3) office leads the Molybdenum-99 (Mo-99) program. A major goal of the Mo-99 program is to develop methods of producing 99 Mo using low enriched uranium (LEU) opposed to the traditionally used HEU domestically in the U.S. Internationally, LEU is the new standard for use in research reactors and isotope production facility. In this study, we introduce a generic fissile solution system for 99 Mo production facility meeting the design requirement of 1) LEU usage as fissile material and 2) subcritical fissile system coupled with a horizontal electron beam (E-beam) accelerator. The focus of this research is to optimize a fissile solution configuration for maximum 99 Mo production yield using MCNP model, and ultimately implement the optimized design with computational fluid dynamics (CFD) model to understand thermal hydraulic behavior and solution convection characteristic. The report consists of two parts: 1) isotope yield calculation and criticality analysis with a wide range of parametric test matrix, and 2) thermal hydraulic analysis for solution mixing and cooling assessment.

60 APPLIED LIFE SCIENCES↗

Robot Adaptation to Unstructured Terrains by Joint Representation and Apprenticeship Learning

When a mobile robot is deployed in a field environment, e.g., during a disaster response application, the capability of adapting its navigational behaviors to unstructured terrains is essential for effective and safe robot navigation. In this paper, we introduce a novel joint terrain representation and apprenticeship learning approach to implement robot adaptation to unstructured terrains. Different from conventional learning-based adaptation techniques, our approach provides a unified problem formulation that integrates representation and apprenticeship learning under a unified regularized optimization framework, instead of treating them as separate and independent procedures. Our approach also has the capability to automatically identify discriminative feature modalities, which can improve the robustness of robot adaptation. In addition, we implement a new optimization algorithm to solve the formulated problem, which provides a theoretical guarantee to converge to the global optimal solution. In the experiments, we extensively evaluate the proposed approach in real-world scenarios, in which a mobile robot navigates on familiar and unfamiliar unstructured terrains. Experimental results have shown that the proposed approach is able to transfer human expertise to robots with small errors, achieve superior performance compared with previous and baseline methods, and provide intuitive insights on the importance of terrain feature modalities.

42 ENGINEERING↗

Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations

In this work, we introduce a new residual distribution (RD) framework for the design of bound-preserving high-resolution finite element schemes. The continuous and discontinuous Galerkin discretizations of the linear advection equation are modified to construct local extremum diminishing (LED) approximations. To that end, we perform mass lumping and redistribute the element residuals in a manner which guarantees the LED property. The hierarchical correction procedure for high-order Bernstein finite element discretizations involves localization to subcells and definition of bound-preserving weights for subcell contributions. Using strong stability preserving (SSP) Runge–Kutta methods for time integration, we prove the validity of discrete maximum principles under CFL-like time step restrictions. The low-order version of our method has roughly the same accuracy as the one derived from a piecewise (multi)-linear approximation on a submesh with the same nodal points. In high-order extensions, we use an element-based flux-corrected transport (FCT) algorithm which can be interpreted as a nonlinear RD scheme. The proposed LED corrections are tailor-made for matrix-free implementations which avoid the rapidly growing cost of matrix assembly for high-order Bernstein elements. The results for 1D, 2D, and 3D test problems compare favorably to those obtained with the best matrix-based approaches.

97 MATHEMATICS AND COMPUTING↗

Simulation-driven optimization of high-order meshes in ALE hydrodynamics

Here we propose tools for high-order mesh optimization and demonstrate their benefits in the context of multi-material Arbitrary Lagrangian-Eulerian (ALE) compressible shock hydrodynamic applications. The mesh optimization process is driven by information provided by the simulation which uses the optimized mesh, such as shock positions, material regions, known error estimates, etc. These simulation features are usually represented discretely, for instance, as finite element functions on the Lagrangian mesh. The discrete nature of the input is critical for the practical applicability of the algorithms we propose and distinguishes this work from approaches that strictly require analytical information. Our methods are based on node movement through a high-order extension of the Target-Matrix Optimization Paradigm (TMOP). The proposed formulation is fully algebraic and relies only on local Jacobian matrices, so it is applicable to all types of mesh elements, in 2D and 3D, and any order of the mesh. We discuss the notions of constructing adaptive target matrices and obtaining their derivatives, reconstructing discrete data in intermediate meshes, node limiting that enables improvement of global mesh quality while preserving space-dependent local mesh features, and appropriate normalization of the objective function. The adaptivity methods are combined with automatic ALE triggers that can provide robustness of the mesh evolution and avoid excessive remap procedures. The benefits of the new high-order TMOP technology are illustrated on several simulations performed in the high-order ALE application BLAST.

97 MATHEMATICS AND COMPUTING↗