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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

Aubourg, Eric [APC, Paris] (ORCID:000000025592023X↗
DOE OSTI2024

Uncertainty analysis of Raman spectra for measuring ortho-parahydrogen compositions

Determining ortho-parahydrogen compositions at cryogenic temperatures is an important quality control for liquid hydrogen custody exchange. High orthohydrogen compositions lead to an exothermic reaction resulting in increased boil off and increased venting losses of liquid hydrogen product by either the supplier or consumer. Traditional methods for measuring ortho-parahydrogen compositions such as hot-wire anemometry, nuclear magnetic resonance, and infrared spectroscopy are typically inconvenient at best. As the number of cryogenic hydrogen systems continue to increase, there is an increased need for flexible, standardized techniques for post processing composition measurements. A Raman spectrometer implemented in the Cryo-Catalysis Hydrogen Experimental Facility (CHEF) has demonstrated incredible flexibility for composition measurements of cryogenic hydrogen flows through a wide range of temperatures and pressures with the Raman probe in-situ at cryogenic temperatures. This article analyzes the uncertainty of Raman spectroscopy data of cryogenic hydrogen equilibrated at temperatures in IONEX catalyst. Spectra from hydrogen catalyzed to the equilibrium ortho-parahydrogen composition are processed and compared to expected statistical distributions for method verification.

08 HYDROGEN↗
DOE OSTI2021

First 3D vector tracking of helium recoils for fast neutron measurements at Super$\mathrm{KEKB}$

Here we present results from the first deployment of novel, high definition, compact gas Time Projection Chambers (TPCs) with pixel chip readout as part of the BEAST II beam background measurement project at SuperKEKB. The TPCs provide detailed 3D imaging of ionization from neutron-induced nuclear recoils in a helium and carbon dioxide target gas mixture at standard temperature and pressure. We present the TPC performance and the neutron backgrounds observed during the initial stage of collider commissioning. We find excellent electron background rejection, leading to background-free nuclear recoil measurements above 50 keV ee , despite the extreme high-background environment. We measure an angular resolution better than 20° for recoil tracks longer than 1.7 mm, corresponding to an average ionization energy of approximately 100 keV ee . We also obtain the full 3D vector direction of helium recoils by utilizing charge profile measurements along the recoil axis, with a correct head/tail assignment efficiency of approximately 80%. With this performance, we present comparisons between measured and simulated event rates, recoil energy spectra, and directional distributions originating from beam–gas and Touschek beam losses at SuperKEKB. We utilize head/tail recognition to distinguish neutron components traveling with positive radial velocity in the Belle II coordinate system from those traveling in the opposite direction. Finally, we present a novel method of discriminating beam–gas interactions from Touschek beam losses that can eliminate the need for dedicated accelerator runs for background measurements. This method is still statistics-limited. However, future studies should be able to verify this method, which in turn could lead to neutron background analysis runs symbiotic with normal Belle II operation. The capabilities demonstrated here also suggest that high definition recoil imaging in gas TPCs is applicable to low energy, low-background experiments, such as directional dark matter searches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Estimating Code Biases for Criticality Safety Applications with Few Relevant Benchmarks

Criticality safety analyses rely on the availability of relevant benchmark experiments to determine justifiable margins of subcriticality. When a target application lacks neutronically similar benchmark experiments, validation studies must provide justification to the regulator that the impact of modeling and simulation limitations is well understood for the application and often must provide additional subcritical margin to ensure safe operating conditions. This study estimated the computational bias in the critical eigenvalue for several criticality safety applications supported by only a few relevant benchmark experiments. The accuracy of the following three methods for predicting computational biases was evaluated: the Upper Subcritical Limit STATisticS (USLSTATS) trending analysis method; the Whisper nonparametric method; and TSURFER, which is based on the generalized linear least-squares technique. Here, these methods were also applied to estimate computational biases and recommended upper subcriticality limits for several critical experiments with known biases and for several cases from a blind benchmark study. The methods are evaluated based on both the accuracy of their predicted computation bias and upper subcriticality limit estimates, as well as on the consistency of the methods’ estimates, as the model parameters, covariance data libraries, and set of available benchmark data were varied. Data assimilation methods typically have not been used for criticality safety licensing activities, and this study explores a methodology to address concerns regarding the reliability of such methods in criticality safety bias prediction applications.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2014

Growth of Au nanoparticle films and the effect of nanoparticle shape on plasmon peak wavelength

Metal nanoparticles (NPs) exhibit localized surface plasmon resonance (LSPR) and thus have potential for use in a wide range of applications. A facile technique for the preparation of NP films using an electron-cyclotron-resonance plasma sputtering method without a dewetting process is described. Field emission scanning electron microscopy (FE-SEM) observations revealed that the Au NPs grew independently as island-like particles during the first stage of sputtering and then coalesced with one another as sputtering time increased to ultimately form a continuous film. A plasmon absorption peak was observed via optical measurement of absorption efficiency. The LSPR peak shifted toward longer wavelengths (red shift) with an increase in sputtering time. The cause of this plasmon peak shift was theoretically investigated using the finite-difference time-domain calculation method. A realistic statistical distribution of the particle shapes based on FE-SEM observations was applied for the analysis, which has not been previously reported. It was determined that the change in the shape of the NPs from spheroidal to oval or slender due to coalescence with neighbouring NPs caused the LSPR peak shift. These results may enable the design of LSPR devices by controlling the characteristics of the nanoparticles, such as their size, shape, number density, and coverage.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

A Probabilistic Model-Based Diagnostic Framework for Nuclear Engineering Systems

A fault diagnostic framework was investigated in this study for applications in thermal–hydraulic systems of nuclear power plants. The proposed framework consists of quantitative model-based diagnosis, statistical change detection and probabilistic reasoning. The use of physics-based diagnostic models provides high detection sensitivity and allows noise and measurement uncertainty to be incorporated robustly. Performance-related parametric models for each component are constructed based on first principles. Numerical model residuals are generated using the concept of analytical redundancy. Statistical change detection methods are employed to detect non-zero residuals in the presence of uncertainty. The diagnosis task is performed using Bayesian inference to detect and localize possible faults. Application to a single-phase heat exchanger for demonstration showed that the proposed probabilistic framework can provide improved results in comparison with traditional approaches while remaining less sensitive to false alarms in the presence of measurement and modeling uncertainty.

Bayesian network↗
DOE OSTI2019

Assessing the Influence of Microphysical and Environmental Parameter Perturbations on Orographic Precipitation

Microphysical (MP) schemes contain parameters whose values can impact the amount and location of forecasted precipitation, and sensitivity is typically explored by perturbing one parameter at a time while holding the rest constant. Although much can be learned from these “one-at-a-time” studies, the results are limited as these methods do not allow for nonlinear interactions of multiple perturbed parameters. This study applies the Morris one-at-a-time (MOAT) method, a robust statistical tool allowing for simultaneous perturbation of numerous parameters, to explore orographic precipitation sensitivity to changes in microphysical and environmental parameters within an environment characteristic of an atmospheric river. Results show parameters associated with snow fall speed coefficient A s and density ρ s , ice-cloud water collection efficiency (ECI), rain accretion (WRA), relative humidity, zonal wind speed, and surface potential temperature cause the largest influence on simulated precipitation. MP and environmental parameter perturbations can cause precipitation changes of similar magnitude, but results vary by location on the mountain. Different environments are also tested, with A s being the most influential MP parameter regardless of environment. Fewer MP parameters influence precipitation in a faster-wind-speed environment, possibly due to the stronger dynamical forcing upwind and different wave dynamics downwind, compared to a slower-wind-speed environment. Finally, perturbing MP parameters within a single scheme can result in precipitation variations of similar magnitude compared to using entirely different microphysics schemes. MOAT results presented in this study have implications for Bayesian parameter estimation methods and stochastic parameterization within ensemble forecasting.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A new classification scheme of plastic wastes based upon recycling labels

Highlights: • PET, HPDE or PP types of plastics are considered. • An automated classification of plastic bottles based on the feature extraction and classification methods is performed. • The decision mechanism consists of PCA, Kernel PCA, FLDA, SVD and Laplacian Eigenmaps methods. • SVM is selected to achieve the classification task and majority voting technique is used. - Abstract: Since recycling of materials is widely assumed to be environmentally and economically beneficial, reliable sorting and processing of waste packaging materials such as plastics is very important for recycling with high efficiency. An automated system that can quickly categorize these materials is certainly needed for obtaining maximum classification while maintaining high throughput. In this paper, first of all, the photographs of the plastic bottles have been taken and several preprocessing steps were carried out. The first preprocessing step is to extract the plastic area of a bottle from the background. Then, the morphological image operations are implemented. These operations are edge detection, noise removal, hole removing, image enhancement, and image segmentation. These morphological operations can be generally defined in terms of the combinations of erosion and dilation. The effect of bottle color as well as label are eliminated using these operations. Secondly, the pixel-wise intensity values of the plastic bottle images have been used together with the most popular subspace and statistical feature extraction methods to construct the feature vectors in this study. Only three types of plastics are considered due to higher existence ratio of them than the other plastic types in the world. The decision mechanism consists of five different feature extraction methods including as Principal Component Analysis (PCA), Kernel PCA (KPCA), Fisher’s Linear Discriminant Analysis (FLDA), Singular Value Decomposition (SVD) and Laplacian Eigenmaps (LEMAP) and uses a simple experimental setup with a camera and homogenous backlighting. Due to the giving global solution for a classification problem, Support Vector Machine (SVM) is selected to achieve the classification task and majority voting technique is used as the decision mechanism. This technique equally weights each classification result and assigns the given plastic object to the class that the most classification results agree on. The proposed classification scheme provides high accuracy rate, and also it is able to run in real-time applications. It can automatically classify the plastic bottle types with approximately 90% recognition accuracy. Besides this, the proposed methodology yields approximately 96% classification rate for the separation of PET or non-PET plastic types. It also gives 92% accuracy for the categorization of non-PET plastic types into HPDE or PP.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Impact of parametric uncertainty on estimation of the energy deposition into an irradiated brain tumor

Predictions of the total energy deposited into a brain tumor through X-ray irradiation are notoriously error-prone. We investigate how this predictive uncertainty is affected by uncertainty in both the location of the region occupied by a dose-enhancing iodinated contrast agent and the agent's concentration. This is done within the probabilistic framework in which these uncertain parameters are modeled as random variables. We employ the stochastic collocation (SC) method to estimate statistical moments of the deposited energy in terms of statistical moments of the random inputs, and the global sensitivity analysis (GSA) to quantify the relative importance of uncertainty in these parameters on the overall predictive uncertainty. A nonlinear radiation–diffusion equation dramatically magnifies the coefficient of variation of the uncertain parameters, yielding a large coefficient of variation for the predicted energy deposition. This demonstrates that accurate prediction of the energy deposition requires a proper treatment of even small parametric uncertainty. Our analysis also reveals that SC outperforms standard Monte Carlo, but its relative efficiency decreases as the number of uncertain parameters increases from one to three. A robust GSA ameliorates this problem by reducing this number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

CHARACTERIZING THE GALACTIC WHITE DWARF BINARY POPULATION WITH SPARSELY SAMPLED RADIAL VELOCITY DATA

We present a method to characterize statistically the parameters of a detached binary sample-binary fraction, separation distribution, and mass-ratio distribution-using noisy radial velocity data with as few as two, randomly spaced, epochs per object. To do this, we analyze the distribution of {Delta}RV{sub max}, the maximum radial velocity difference between any two epochs for the same object. At low values, the core of this distribution is dominated by measurement errors, but for large enough samples there is a high-velocity tail that can effectively constrain the parameters of the binary population. We discuss our approach for the case of a population of detached white dwarf (WD) binaries with separations that are decaying via gravitational wave emission. We derive analytic expressions for the present-day distribution of separations, integrated over the star formation history of the Galaxy, for parameterized initial WD separation distributions at the end of the common-envelope phase. We use Monte Carlo techniques to produce grids of simulated {Delta}RV{sub max} distributions with specific binary population parameters, and the same sampling cadences and radial velocity errors as the observations, and we compare them to the real {Delta}RV{sub max} distribution to constrain the properties of the binary population. We illustrate the sensitivity of the method to both the model and observational parameters. In the particular case of binary WDs, every model population predicts a merger rate per star which can easily be compared to specific Type Ia supernova rates. In a companion paper, we apply the method to a sample of {approx}4000 WDs from the Sloan Digital Sky Survey. The binary fractions and separation distribution parameters allowed by the data indicate a rate of WD-WD mergers per unit stellar mass in the Galactic disk, {approx}1 Multiplication-Sign 10{sup -13} mergers yr{sup -1} M{sup -1}{sub Sun }, remarkably similar to the rate per unit mass of Type Ia supernovae in Milky Way like galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

4D ML reconstruction as a tool for volumetric PET-based treatment verification in ion beam radiotherapy

Purpose: An innovative strategy to improve the sensitivity of positron emission tomography (PET)-based treatment verification in ion beam radiotherapy is proposed. Methods: Low counting statistics PET images acquired during or shortly after the treatment (Measured PET) and a Monte Carlo estimate of the same PET images derived from the treatment plan (Expected PET) are considered as two frames of a 4D dataset. A 4D maximum likelihood reconstruction strategy was adapted to iteratively estimate the annihilation events distribution in a reference frame and the deformation motion fields that map it in the Expected PET and Measured PET frames. The outputs generated by the proposed strategy are as follows: (1) an estimate of the Measured PET with an image quality comparable to the Expected PET and (2) an estimate of the motion field mapping Expected PET to Measured PET. The details of the algorithm are presented and the strategy is preliminarily tested on analytically simulated datasets. Results: The algorithm demonstrates (1) robustness against noise, even in the worst conditions where 1.5 × 10{sup 4} true coincidences and a random fraction of 73% are simulated; (2) a proper sensitivity to different kind and grade of mismatches ranging between 1 and 10 mm; (3) robustness against bias due to incorrect washout modeling in the Monte Carlo simulation up to 1/3 of the original signal amplitude; and (4) an ability to describe the mismatch even in presence of complex annihilation distributions such as those induced by two perpendicular superimposed ion fields. Conclusions: The promising results obtained in this work suggest the applicability of the method as a quantification tool for PET-based treatment verification in ion beam radiotherapy. An extensive assessment of the proposed strategy on real treatment verification data is planned.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Entity Resolution at Large Scale: Benchmarking and Algorithmics

We seek scalable benchmarks for entity resolution problems. Solutions to these problems range from trivial approaches such as string sorting to sophisticated methods such as statistical relational learning. The theoretical and practical complexity of these approaches varies widely, so one of the primary purposes of a benchmark will be to quantify the trade-off between solution quality and runtime. We are motivated by the ubiquitous nature of entity resolution as a fundamental problem faced by any organization that ingests large amounts of noisy text data. A benchmark is typically a rigid specification that provides an objective measure usable for ranking implementations of an algorithm. For example the Top500 and HPCG500 bench- marks rank supercomputers based on their performance of dense and sparse linear algebra problems (respectively). These two benchmarks require participants to report FLOPS counts attainable on various machines. Our purpose is slightly different. Whereas the supercomputing benchmarks mentioned above hold algorithms constant and aim to rank machines, we are primarily interested in ranking algorithms. As mentioned above, entity resolution problems can be approached in completely different ways. We believe that users of our benchmarks must decide what sort of procedure to run before comparing implementations and architectures. Eventually, we also wish to provide a mechanism for ranking machines while holding algorithmic approach constant . Our primary contributions are parallel algorithms for computing solution quality mea- sures per entity. We find in some real datasets that many entities are quite easy to resolve while others are difficult, with a heavy skew toward the former case. Therefore, measures such as global confusion matrices, F measures, etc. do not meet our benchmarking needs. We design methods for computing solution quality at the granularity of a single entity in order to know when proposed solutions do well in difficult situations (perhaps justifying extra computational), or struggling in easy situations. We report on progress toward a viable benchmark for comparing entity resolution algo- rithms. Our work is incomplete, but we have designed and prototyped several algorithms to help evalute the solution quality of competing approaches to these problems. We envision a benchmark in which the objective measure is a ratio of solution quality to runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Experimental evidence of intermittent chaos in a glow discharge plasma without external forcing and its numerical modelling

Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noise level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Data for Transposon Signatures of Allopolyploid Genome Evolution

Hybridization brings together chromosome sets from two or more distinct progenitor species. Genome duplication associated with hybridization, or allopolyploidy, allows these chromosome sets to persist as distinct subgenomes during subsequent meioses. Here, we present a general method for identifying the subgenomes of a polyploid based on shared ancestry as revealed by the genomic distribution of repetitive elements that were active in the progenitors. This subgenome-enriched transposable element signal is intrinsic to the polyploid, allowing broader applicability than other approaches that depend on the availability of sequenced diploid relatives. We develop the statistical basis of the method, demonstrate its applicability in the well-studied cases of tobacco, cotton, and Brassica napus, and apply it to several cases: allotetraploid cyprinids, allohexaploid false flax, and allooctoploid strawberry. These analyses provide insight into the origins of these polyploids, revise the subgenome identities of strawberry, and provide perspective on subgenome dominance in higher polyploids.

Genomics↗
DOE OSTI2015

Contactless Determination of Electrical Conductivity of One-Dimensional Nanomaterials by Solution-Based Electro-orientation Spectroscopy

For nanowires of the same composition, and even fabricated within the same batch, often exhibit electrical conductivities that can vary by orders of magnitude. Unfortunately, existing electrical characterization methods are time-consuming, making the statistical survey of highly variable samples essentially impractical. Here, we demonstrate a contactless, solution-based method to efficiently measure the electrical conductivity of 1D nanomaterials based on their transient alignment behavior in ac electric fields of different frequencies. In comparison with direct transport measurements by probe-based scanning tunneling microscopy shows that electro-orientation spectroscopy can quantitatively measure nanowire conductivity over a 5-order-of-magnitude range, 10–5–1 Ω–1 m–1 (corresponding to resistivities in the range 102–107 Ω·cm). With this method, we statistically characterize the conductivity of a variety of nanowires and find significant variability in silicon nanowires grown by metal-assisted chemical etching from the same wafer. We also find that the active carrier concentration of n-type silicon nanowires is greatly reduced by surface traps and that surface passivation increases the effective conductivity by an order of magnitude. Moreover, this simple method makes electrical characterization of insulating and semiconducting 1D nanomaterials far more efficient and accessible to more researchers than current approaches. Electro-orientation spectroscopy also has the potential to be integrated with other solution-based methods for the high-throughput sorting and manipulation of 1D nanomaterials for postgrowth device assembly.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Field‐Induced Ferroelectric Phase Evolution During Polarization “Wake‐Up” in Hf 0.5 Zr 0.5 O 2 Thin Film Capacitors

Abstract As an emerging nonvolatile memory technology, HfO 2 ‐based ferroelectrics exhibit excellent compatibility with silicon CMOS process flows; however, the reliability of polarization switching in these materials remains a major challenge. During repeated field programming and erase of the polarization state of initially pristine HfO 2 ‐based ferroelectric capacitors, the magnitude of the measured polarization increases, a phenomenon known as “wake‐up”. In this study, the authors attempt to understand what causes the wake‐up effect in Hf 0.5 Zr 0.5 O 2 (HZO) capacitors using nondestructive methods that probe statistically significant sample volumes. Synchrotron X‐ray diffraction reveals a concerted shift in HZO Bragg peak position as a function of polarization switching cycle number in films prepared under conditions such that they exhibit extremely large (≈3000%) wake‐up. In contrast, a control sample with insignificant wake‐up shows no such peak shift. Capacitance – voltage measurements show evolution in the capacitance loop with switching cycle number for the wake‐up sample and no change for the control sample. Piezoresponse force microscopy measurements are utilized to visualize the domain switching with wake‐up. The combination of these observations clearly demonstrates that wake‐up is caused by a field‐driven phase transformation of the tetragonal phase to the metastable ferroelectric orthorhombic phase during polarization switching of HZO capacitors.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Novel Non‐Destructive Rapid Tool for Estimating Amino Acid Composition and Secondary Structures of Proteins in Solution

Abstract Amino‐acid protein composition plays an important role in biology, medicine, and nutrition. Here, a groundbreaking protein analysis technique that quickly estimates amino acid composition and secondary structure across various protein sizes, while maintaining their natural states is introduced and validated. This method combines multivariate statistics and the thermostable Raman interaction profiling (TRIP) technique, eliminating the need for complex preparations. In order to validate the approach, the Raman spectra are constructed of seven proteins of varying sizes by utilizing their amino acid frequencies and the Raman spectra of individual amino acids. These constructed spectra exhibit a close resemblance to the actual measured Raman spectra. Specific vibrational modes tied to free amino and carboxyl termini of the amino acids disappear as signals linked to secondary structures emerged under TRIP conditions. Furthermore, the technique is used inversely to successfully estimate amino acid compositions and secondary structures of unknown proteins across a range of sizes, achieving impressive accuracy ranging between 1.47% and 5.77% of root mean square errors (RMSE). These results extend the uses for TRIP beyond interaction profiling, to probe amino acid composition and structure.

Chemistry↗
DOE OSTI2025

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗