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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A phenomenological rate of injection model for predicting fuel injection with application to mixture formation in light-duty diesel engines

Fuel injection rate laws are one of the most important pieces of information needed when modeling engine combustion with computational fluid dynamics. In this study, a simple phenomenological model of a common-rail injector was developed and calibrated for the Bosch CRI2.2 platform. The model requires three tunable parameter fits, making it relatively easy to calibrate and suitable for injector modeling when high-fidelity information about the internal injector’s geometry and electrical circuit details are not available. Each injection pulse is modeled as a sequence of up to four stages: an injection needle mechanical opening transient, a full-lift viscous flow inertial transient, a Bernoulli steady-state stage, and a needle descent transient. Parameters for each stage are obtained as polynomial fits from measured injection rate properties. The model enforces total injected mass, and the intermediate stages are only introduced if the injection pulse duration is long enough. Experimental rates of injection from two separate campaigns on the same injector were used to calibrate the model. The model was first validated against measured injection rate laws featuring pilot injections, short partially premixed combustion pulses, and conventional diesel combustion injection strategies. Then, it was employed as an input to engine computational fluid dynamics simulations, which were run to simulate experiments of mixture formation in an optically accessible light-duty diesel engine. It was found that, though simple, this model is capable of predicting both pilot and main injection pulse mass flow rates well: the simulations yielded accurate predictions of in-cylinder equivalence ratio distributions from injection strategies for both partially premixed combustion and pilot injections. Also, once calibrated, the model produced appropriate results for a wide range of injected mass and rail pressure values. Finally, it was observed that usage of such a relatively simple model can be a good choice when high-fidelity injection rate input and highly detailed information of the injector’s geometry and operation are not available, particularly as noticeable discrepancies can be present also among different experimental campaigns on similar hardware.

42 ENGINEERING↗
DOE OSTI2016

Recent Advances in Analytical Electron Microscopy for Irradiated Materials

Analytical electron microscopy (AEM) in the scanning transmission electron microscope (STEM) has long been a staple of post-irradiation examination (PIE) and materials development campaigns. Recently, new advances in both STEM hardware and post-processing data-analysis software, along with ancillary advances such as in focused ion beam (FIB) sample preparation, has led to exciting advances in the quantity and quality of data that can be obtained. This talk will summarize recent experiments performed at Oak Ridge National Laboratory (ORNL), especially work on neutron-irradiated materials and fuels taking advantage of a newly-installed latest-generation AEM tool in the ORNL irradiated materials laboratories. ORNL installed a new FEI Talos F200X microscope, a 200 keV, high-brightness Schottky emission AEM system optimized for high-speed, high-efficiency X-ray mapping experiments. The F200X features the FEI 'SuperX' four-sector silicon drift detector (SDD) X-ray detector, which provides 0.9 sr solid angle of collection. By combining the high-brightness electron source, latest-generation electron optics, and fast computers and pulse processors, X-ray mapping speed is increased by a factor of 50-100 x compared to the previous-generation instruments. In addition to improvements in hardware, data mining via multivariate statistical analysis (MVSA) allows for maximum insight to the data obtained from the new hardware. MVSA data mining of the X-ray maps allows, for instance, unbiased computational identification of the phases present, and discovery of small phases or precipitates not expected by the human analyst. This talk will present examples of experiments performed using the most modern AEM tools and software. Silicon carbide is a major candidate for next-generation nuclear applications. Nano-infiltration by transient eutectic (NITE) SiC requires low sintering temperatures. X-ray mapping of the NITE structure find pockets of different oxides, such as Zr-Y-oxide, Y-Al-oxide, and yttria. MVSA data mining finds the regions where different oxides are present and indicates that Y additions preferentially wet grain boundaries, where Zr additions are preferentially concentrated at grain triple points. SiC coatings from AGR-I experiment TRISO particles were found to contain significant quantities of fission products (e.g., Pd) as well as actinides (U, Pu). MVSA data mining found complex precipitates and grain boundary films of the fission products and actinides deep (∼several microns) into the SiC layer. Advanced AEM methods, combined with MVSA data mining, makes possible both rapid and detailed PIE. Ferritic alloys, such as accident-tolerant FeCrAl grades, benefit greatly from advanced AEM examination. Neutron-irradiated FeCrAl precipitates the detrimental Cr-rich α' phase. Because the SuperX SDD system has four detectors, it is possible to obtain high X-ray count rates even on a highly tilted specimen, as might be needed to obtain STEM images of dislocation loops. Results on neutron-irradiated FeCrAl indicates that α' size and number density can be obtained by AEM, and MVSA results determine that minor elements (such as Si) has complex radiation-induced segregation behavior at grain boundaries. We have also developed and validated computer models of the AEM experiment, allowing different microstructures' X-ray map results to be simulated for different STEM instruments. This allows X-ray mapping to be more quantitative, such as by estimating what size nanoclusters in an oxide-dispersion strengthened steel would be visible or invisible in STEM. In summary, new advanced AEM technology provides a major leap forward in experiments possible in PIE of irradiated materials. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2019

Eigenvalue Problems for Exponential-Type Kernels

Here, We study approximations of eigenvalue problems for integral operators associated with kernel functions of exponential type. We show convergence rate | λ k - λ k , h | ≤ C k h 2 in the case of lowest order approximation for both Galerkin and Nystrom methods, where h is the mesh size, λ k and λ k , h are the exact and approximate k th largest eigenvalues, respectively. We prove that the two methods are numerically equivalent in the sense that | λ k , h ( G ) - λ k , h ( N ) | ≤ C h 2 , where λ k , h ( G ) and λ k , h ( N ) denote the k th largest eigenvalues computed by Galerkin and Nystrom methods, respectively, and C is a eigenvalue independent constant. The theoretical results are accompanied by a series of numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Localization of fluorescent targets in deep tissue with expanded beam illumination for studies of cancer and the brain

Imaging fluorescence through millimeters or centimeters of tissue has important in vivo applications, such as guiding surgery and studying the brain. Often, the important information is the location of one of more optical reporters, rather than the specifics of the local geometry, motivating the need for a localization method that provides this information. We present an optimization approach based on a diffusion model for the fast localization of fluorescent inhomogeneities in deep tissue with expanded beam illumination that simplifies the experiment and the reconstruction. We show that the position of a fluorescent inhomogeneity can be estimated while assuming homogeneous tissue parameters and without having to model the excitation profile, reducing the computational burden and improving the utility of the method. We perform two experiments as a demonstration. First, a tumor in a mouse is localized using a near infrared folate-targeted fluorescent agent (OTL38). This result shows that localization can quickly provide tumor depth information, which could reduce damage to healthy tissue during fluorescence-guided surgery. Second, another near infrared fluorescent agent (ATTO647N) is injected into the brain of a rat, and localized through the intact skull and surface tissue. This result will enable studies of protein aggregation and neuron signaling.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Evaluating Portable Parallelization Strategies for Heterogeneous Architectures in High Energy Physics

High-energy physics (HEP) experiments have developed millions of lines of code over decades that are optimized to run on traditional x86 CPU systems. However, we are seeing a rapidly increasing fraction of floating point computing power in leadership-class computing facilities and traditional data centers coming from new accelerator architectures, such as GPUs. HEP experiments are now faced with the untenable prospect of rewriting millions of lines of x86 CPU code, for the increasingly dominant architectures found in these computational accelerators. This task is made more challenging by the architecture-specific languages and APIs promoted by manufacturers such as NVIDIA, Intel and AMD. Producing multiple, architecture-specific implementations is not a viable scenario, given the available person power and code maintenance issues. The Portable Parallelization Strategies team of the HEP Center for Computational Excellence is investigating the use of Kokkos, SYCL, OpenMP, std::execution::parallel and alpaka as potential portability solutions that promise to execute on multiple architectures from the same source code, using representative use cases from major HEP experiments, including the DUNE experiment of the Long Baseline Neutrino Facility, and the ATLAS and CMS experiments of the Large Hadron Collider. This cross-cutting evaluation of portability solutions using real applications will help inform and guide the HEP community when choosing their software and hardware suites for the next generation of experimental frameworks. We present the outcomes of our studies, including performance metrics, porting challenges, API evaluations, and build system integration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Viscosity Control Experiment Feasibility Study

Turbulent mix has been invoked to explain many results in Inertial Confinement Fusion (ICF) and High Energy Density (HED) physics, such as reduced yield in capsule implosions. Many ICF capsule implosions exhibit interfacial instabilities seeded by the drive shock, but it is not clear that fully developed turbulence results from this. Many simulations use turbulent mix models to help match simulation results to data, but this is not appropriate if turbulence is not present. It would be useful to have an experiment where turbulent mixing could be turned on or off by design. The use of high-Z dopants to modify viscosity and the resulting influence on turbulence is considered here. A complicating factor is that the plasma in some implosions can become strongly coupled, which makes the Spitzer expression for viscosity invalid. We first consider equations that cover a broad parameter space in temperature and density to address regimes for various experimental applications. Next, a previous shock-tube and other ICF experiments that investigate viscosity or use doping to examine the effects on yield are reviewed. How viscosity and dopants play a role in capsule yield depends on the region and process under consideration. Experiments and simulations have been performed to study the effects of viscosity on both the hot spot and the fuel/ablator mix. Increases in yield have been seen for some designs, but not all. We then discuss the effect of adding krypton dopant to the gas region of a typical OMEGA and a 2-shock NIF implosion to determine approximately the effect of adding dopant on the computed Reynolds number. Recommendations for a path forward for possible experiments using high-Z dopants to affect viscosity and turbulence are made.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Computationally Directed Discovery of MoBi 2

Incorporating bismuth, the heaviest element stable to radioactive decay, into new materials enables the creation of emergent properties such as permanent magnetism, superconductivity, and nontrivial topology. Understanding the factors that drive Bi reactivity is critical for the realization of these properties. Using pressure as a tunable synthetic vector, we can access unexplored regions of phase space to foster reactivity between elements that do not react under ambient conditions. Furthermore, combining computational and experimental methods for materials discovery at high-pressures provides broader insight into the thermodynamic landscape than can be achieved through experiment alone, informing our understanding of the dominant chemical factors governing structure formation. Herein, we report our combined computational and experimental exploration of the Mo–Bi system, for which no binary intermetallic structures were previously known. Using the ab initio random structure searching (AIRSS) approach, we identified multiple synthetic targets between 0–50 GPa. Highpressure in situ powder X-ray diffraction experiments performed in diamond anvil cells confirmed that Mo–Bi mixtures exhibit rich chemistry upon the application of pressure, including experimental realization of the computationally predicted CuAl 2 -type MoBi 2 structure at 35.8(5) GPa. Electronic structure and phonon dispersion calculations on MoBi 2 revealed a correlation between valence electron count and bonding in high-pressure transition metal–Bi structures as well as identified two dynamically stable ambient pressure polymorphs. Our study demonstrates the power of the combined computational–experimental approach in capturing highpressure reactivity for efficient materials discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

STAR Data Production Workflow on HPC: Lessons Learned & Best Practices

The Solenoidal Tracker at RHIC (STAR) is a multi-national supported experiment located at Brookhaven National Lab. The raw physics data captured from the detector is on the order of tens of PBytes per data acquisition campaign, which makes STAR fit well within the definition of a big data science experiment. The production of the data has typically run on standard nodes or on standard Grid computing environments. All embedding simulations (complex workflow mixing real and simulated events) have been run on standard Linux resources at the National Energy Research Scientific Computing Center (NERSC) aka PDSF. However, HPC resources such as Cori have become available for STAR's data production as well as embedding, and STAR has been the very first experiment to show feasibility of running a sustainable data production campaign on this computing resource. The use of Docker containers with Shifter is required to run on HPC @ NERSC - this approach encapsulates the environment in which a standard STAR workflow runs. From the deployment of a tailored Scientific Linux environment (requiring many of its own libraries and special configurations required to run) to the deployment of third-party software and the STAR specific software stack, it has become impractical to rely on a set of containers containing each specific software release. To this extent, solutions based on the CERN VM File System (CVMFS) for the deployment of software and services have been employed in HENP, but one needs to make careful scalability considerations when using a resource like Cori, such as not allowing all software to be deployed in containers or bare node. Additionally, CVMFS clients are not compatible on Cori nodes and one needs to rely on an indirect NFS/DVS mount scheme. In our contribution, we will discuss our strategies from the past and our current solution based on CVMFS. Furthermore, running on HPC is not a simple task as each aspect of the workflow must be enabled to scale, run efficiently, and the workflow needs to fit within the boundaries of the provided queue system (SLURM in this case). Lastly, we will also discuss what we have learned so far about what is the best method for grouping jobs to maximize a single 48 core HPC node within a specific time frame and maximize our workflow efficiency.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

High Performance Equilibrium Solvers for Integrated Magnetic Fusion Simulations

With the funding provided by this award, we developed numerical codes for the study of magnetically confined plasmas for fusion applications. Accordingly, our work can be divided into two separate categories: 1) the design and analysis of novel numerical methods providing high accuracy and high efficiency; 2) the study of the equilibrium and stability of magnetically confined plasmas with some of these numerical codes, as well as the study of the nature of the turbulent behavior which may arise in the presence of instabilities. We first developed new numerical schemes based on integral equation methods for the computation of steady-state magnetic configurations in fusion experiments, providing high accuracy for the magnetic field and its derivatives, which are required for stability and turbulence calculations. We employed different integral formulations depending on the application of interest: axisymmetric or non-axisymmetric equilibria, force-free or magnetohydrodynamic equilibria, fixed-boundary equilibria or free-boundary equilibria. While efficient, these methods do not yet apply to plasma boundaries which are not smooth, a situation which is fairly common in magnetic confinement experiments. To address this temporary weakness, we also constructed a new steady-state solver based on the Hybridizable Discontinuous Galerkin (HDG) method, which provides full geometric flexibility. In addition to these numerical tools focused on steady-states, we also contributed to the improvement of the speed and accuracy of codes simulating the plasma dynamics of fusion plasmas, by developing a novel velocity space representation for the efficient solution of kinetic equations, which most accurately describe the time evolution of hot plasmas in fusion experiments. Using the tools discussed above, we studied several questions pertaining to the equilibrium and stability of magnetically confined plasmas. In particular, we derived a new simple model for axisymmetric devices called tokamaks, to predict how elongated a fusion plasma can be before it becomes unstable and collapses. We also looked at the effect of the shape of the outer plasma surface on key properties of the steady-state magnetic configurations, and how these properties impact turbulence in fusion plasmas, and the corresponding transport of momentum. Likewise, we studied the role of large localized flows on the steady-state magnetic configurations, and how they may influence plasma stability and turbulence. Non-axisymmetric steady-state magnetic configurations are inherently more complex than axisymmetric steady-state configurations, and the subject of ongoing controversies regarding the regularity of the equations determining such steady-states, and their solutions. Implementing an existing NYU code in a new geometry, we studied the nature of the singularity of the solutions observed in the code, and methods to eliminate them. Our main conclusion is that by appropriately tailoring the plasma boundary, it is possible to eliminate the singularities otherwise appearing in our simulations, and to obtain steady-states which appear to be smooth. To gain further insights on incompletely understood turbulence phenomena, we proposed a new reduced model capturing most of these phenomena, which is simple enough to not require expensive numerical simulations on massive supercomputers to investigate them. We demonstrated the strong similarity between our simulations and published results obtained from computationally expensive simulations, and plan to rely on our reduced model to identify the key mechanisms determining the evolution and strength turbulent driven transport in fusion plasmas. Finally, we proposed a new framework for tokamak reactor design studies, enabling us to consider the relative merits of steady-state versus pulsed fusion reactors. We found that pulsed fusion reactors may benefit most from recent advances in magnet technology, and the availability of very high field magnets. As such, they may become more desirable than steady-state tokamak reactors for cost efficient electricity generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning

We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor-critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection-diffusion field. As a result, we provide explanation for the policy behaviors using knowledge of the underlying physical process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

PARVMEC: An Efficient, Scalable Implementation of the Variational Moments Equilibrium Code

The ability to sustain magnetically confined plasma in a state of stable equilibrium is crucial for optimal and cost-effective operations of fusion devices like tokamaks and stellarators. The Variational Moments Equilibrium Code (VMEC) is the de-facto serial application used by fusion scientists to compute magnetohydrodynamics (MHD) equilibria and study the physics of three dimensional plasmas in confined configurations. Modern fusion energy experiments have larger system scales with more interactive experimental workflows, both demanding faster analysis turnaround times on computational workloads that are stressing the capabilities of sequential VMEC. In this paper, we present PARVMEC, an efficient, parallel version of its sequential counterpart, capable of scaling to thousands of processors on distributed memory machines. PARVMEC is a non-linear code, with multiple numerical physics modules, each with its own computational complexity. A detailed speedup analysis supported by scaling results on 1,024 cores of a Cray XC30 supercomputer is presented. Depending on the mode of PARVMEC execution, speedup improvements of one to two orders of magnitude are reported. PARVMEC equips fusion scientists for the first time with a state-of-theart capability for rapid, high fidelity analyses of magnetically confined plasmas at unprecedented scales.

Seal, Sudip K↗
DOE OSTI2015

High-resolution computational algorithms for simulating offshore wind turbines and farms: Model development and validation

The present project involves the development of modeling and analysis design tools for assessing offshore wind turbine technologies. The computational tools developed herein are able to resolve the effects of the coupled interaction of atmospheric turbulence and ocean waves on aerodynamic performance and structural stability and reliability of offshore wind turbines and farms. Laboratory scale experiments have been carried out to derive data sets for validating the computational models.

17 WIND ENERGY↗
DOE OSTI2024

Empowering Scientific Innovation Through An Integrated Research Infrastructure: The Role of the Advanced Computing Ecosystem

As the landscape of computational science evolves, the Department of Energy (DOE) is reimagining the roles of its large-scale computing facilities to meet emerging research challenges. The Integrated Research Infrastructure (IRI) program aims to transform how experiments are designed, conducted, and shared, with significant impacts on all stakeholders. In response, the Oak Ridge Leadership Computing Facility (OLCF) has established the Advanced Computing Ecosystem (ACE), a strategic framework to prepare its hardware, software, and experimental capabilities for the IRI era. ACE focuses on integrating novel compute environments, orchestrating advanced workflows, and developing foundational technologies, ensuring a seamless transition to IRI while accelerating scientific discovery. This paper outlines ACE's role in advancing OLCF's mission and its impact on the future of computational science.

Widener, Patrick↗
DOE OSTI2026

Nuclear Data Adjustment for Nonlinear Applications in the OECD/NEA WPNCS SG14 Benchmark—A Bayesian Inverse UQ-Based Approach for Data Assimilation

The Organisation for Economic Co-operation and Development Working Party on Nuclear Criticality Safety has proposed a benchmark exercise to assess the performance of current nuclear data adjustment techniques applied to nonlinear applications and experiments with low correlation to applications. This work introduces Bayesian inverse uncertainty quantification (IUQ) employing scientific machine learning surrogate models as a method for nuclear data adjustments in this benchmark, and compares IUQ to the more traditional methods of generalized linear least squares (GLLS) and Monte Carlo Bayes (MOCABA). Posterior predictions from IUQ showed agreement with GLLS and MOCABA for linear applications. Here, when comparing GLLS, MOCABA, and IUQ posterior predictions to computed model responses using adjusted parameters, we observe that the GLLS predictions failed to replicate the computed response distributions for nonlinear applications, while MOCABA showed near agreement, and IUQ used the computed model responses directly. We also discuss observations on why experiments with low correlation to applications can be informative to nuclear data adjustments and identify some properties useful in selecting experiments for inclusion in nuclear data adjustment. Performance in this benchmark indicates potential for Bayesian IUQ in nuclear data adjustments.

Bayesian calibration↗
DOE OSTI2016

Sediment Resuspension and Transport in Water Distribution Storage Tanks

Computational and experimental studies were conducted to better understand conditions that affect particle resuspension and movement in water storage tanks. Parameters that were investigated included inlet/outlet (I/O) line location and diameter, flow rate, particle size, and filling versus draining cycles. Simulation results showed that smaller particle sizes, higher flow rates, and draining cycles yielded the greatest potential for particle resuspension, which was generally limited to regions near the I/O line. Small‐scale experiments were also performed using different sizes of glass beads and silica sand; the results generally validated the models. Mitigation methods were also presented to reduce the amount of particle resuspension. A pipe that extended from the I/O line into the tank (slightly above the bottom floor) was found to significantly reduce the potential for particle resuspension in both the computational models and experiments.

Ho, Clifford K.↗
DOE OSTI2025

Accelerating detector simulations with Celeritas: Profiling and performance optimizations

Celeritas is a GPU-optimized Monte Carlo (MC) particle transport code designed to meet the growing computational demands of next-generation high energy physics (HEP) experiments. It provides efficient simulation of electromagnetic (EM) physics processes in complex geometries with magnetic fields, detector hit scoring, and seamless integration into Geant4-driven applications to offload EM physics to GPUs. Recent efforts have focused on performance optimizations and expanding profiling capabilities. This paper presents some key advancements, including the integration of the Perfetto system profiling tool for detailed performance analysis and the development of track-sorting methods to improve computational efficiency.

Lund, Amanda [Argonne National Laboratory (ANL)]↗
DOE OSTI2017

The OSG Open Facility: an on-ramp for opportunistic scientific computing

The Open Science Grid (OSG) is a large, robust computing grid that started primarily as a collection of sites associated with large HEP experiments such as ATLAS, CDF, CMS, and DZero, but has evolved in recent years to a much larger user and resource platform. In addition to meeting the US LHC community’s computational needs, the OSG continues to be one of the largest providers of distributed high-throughput computing (DHTC) to researchers from a wide variety of disciplines via the OSG Open Facility. The Open Facility consists of OSG resources that are available opportunistically to users other than resource owners and their collaborators. In the past two years, the Open Facility has doubled its annual throughput to over 200 million wall hours. More than half of these resources are used by over 100 individual researchers from over 60 institutions in fields such as biology, medicine, math, economics, and many others. Over 10% of these individual users utilized in excess of 1 million computational hours each in the past year. The largest source of these cycles is temporary unused capacity at institutions affiliated with US LHC computational sites. An increasing fraction, however, comes from university HPC clusters and large national infrastructure supercomputers offering unused capacity. Such expansions have allowed the OSG to provide ample computational resources to both individual researchers and small groups as well as sizable international science collaborations such as LIGO, AMS, IceCube, and sPHENIX. Opening up access to the Fermilab FabrIc for Frontier Experiments (FIFE) project has also allowed experiments such as mu2e and NOvA to make substantial use of Open Facility resources, the former with over 40 million wall hours in a year. We present how this expansion was accomplished as well as future plans for keeping the OSG Open Facility at the forefront of enabling scientific research by way of DHTC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Bilevel parameter optimization for learning nonlocal image denoising models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the space-dependent fidelity weight and weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and we introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗