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Results for “Bayesian inversion modeling”

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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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Venus gravity

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter (PVO) by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter was evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Reasenberg, Robert D.↗
DOE OSTI2021

Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. Furthermore, the combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Parameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo

Bayesian-inference-based approaches, in particular the random-walk Markov Chain Monte Carlo (MCMC) method, have received much attention recently for X-ray scattering analysis. Hamiltonian MCMC, a state-of-the-art development in the field of MCMC, has become popular in recent years. It utilizes Hamiltonian dynamics for indirect but much more efficient drawings of the model parameters. We described the principle of the Hamiltonian MCMC for inversion problems in X-ray scattering analysis by estimating high-dimensional models for several motivating scenarios in small-angle X-ray scattering, reflectivity, and X-ray fluorescence holography. Hamiltonian MCMC with appropriate preconditioning can deliver superior performance over the random-walk MCMC, and thus can be used as an efficient tool for the statistical analysis of the parameter distributions, as well as model predictions and confidence analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗
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 OSTI2019

Bayesian inference and predictive performance of soil respiration models in the presence of model discrepancy

Bayesian inference of microbial soil respiration models is often based on the assumptions that the residuals are independent (i.e., no temporal or spatial correlation), identically distributed (i.e., Gaussian noise), and have constant variance (i.e., homoscedastic). In the presence of model discrepancy, as no model is perfect, this study shows that these assumptions are generally invalid in soil respiration modeling such that residuals have high temporal correlation, an increasing variance with increasing magnitude of CO 2 efflux, and non-Gaussian distribution. Relaxing these three assumptions stepwise results in eight data models. Data models are the basis of formulating likelihood functions of Bayesian inference. This study presents a systematic and comprehensive investigation of the impacts of data model selection on Bayesian inference and predictive performance. We use three mechanistic soil respiration models with different levels of model fidelity (i.e., model discrepancy) with respect to the number of carbon pools and the explicit representations of soil moisture controls on carbon degradation; therefore, we have different levels of model complexity with respect to the number of model parameters. The study shows that data models have substantial impacts on Bayesian inference and predictive performance of the soil respiration models such that the following points are true: (i) the level of complexity of the best model is generally justified by the cross-validation results for different data models; (ii) not accounting for heteroscedasticity and autocorrelation might not necessarily result in biased parameter estimates or predictions, but will definitely underestimate uncertainty; (iii) using a non-Gaussian data model improves the parameter estimates and the predictive performance; and (iv) accounting for autocorrelation only or joint inversion of correlation and heteroscedasticity can be problematic and requires special treatment. Although the conclusions of this study are empirical, the analysis may provide insights for selecting appropriate data models for soil respiration modeling.

58 GEOSCIENCES↗
DOE OSTI2024

Deriving cloud droplet number concentration from surface-based remote sensors with an emphasis on lidar measurements

Abstract. Given the importance of constraining cloud droplet number concentrations (Nd) in low-level clouds, we explore two methods for retrieving Nd from surface-based remote sensing that emphasize the information content in lidar measurements. Because Nd is the zeroth moment of the droplet size distribution (DSD), and all remote sensing approaches respond to DSD moments that are at least 2 orders of magnitude greater than the zeroth moment, deriving Nd from remote sensing measurements has significant uncertainty. At minimum, such algorithms require the extrapolation of information from two other measurements that respond to different moments of the DSD. Lidar, for instance, is sensitive to the second moment (cross-sectional area) of the DSD, while other measures from microwave sensors respond to higher-order moments. We develop methods using a simple lidar forward model that demonstrates that the depth to the maximum in lidar-attenuated backscatter (Rmax⁡) is strongly sensitive to Nd when some measure of the liquid water content vertical profile is given or assumed. Knowledge of Rmax⁡ to within 5 m can constrain Nd to within several tens of percent. However, operational lidar networks provide vertical resolutions of > 15 m, making a direct calculation of Nd from Rmax⁡ very uncertain. Therefore, we develop a Bayesian optimal estimation algorithm that brings additional information to the inversion such as lidar-derived extinction and radar reflectivity near the cloud top. This statistical approach provides reasonable characterizations of Nd and effective radius (re) to within approximately a factor of 2 and 30 %, respectively. By comparing surface-derived cloud properties with MODIS satellite and aircraft data collected during the MARCUS and CAPRICORN II campaigns, we demonstrate the utility of the methodology.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Model-Based Localizatiion in a Shallow Ocean Environment: A Sequential Bayesian/Optimization Approach

The shallow ocean is a dynamically changing medium leading to nonstationary statistical behavior when subjected to temperature, wind, surface variations, bottom interactions, noise and extraneous disturbances as well as other conditions that render it a uniquely challenging environment — especially from a signal processing perspective. Processors must account for and adapt to such instantaneous changes in order to be effective. Thus, a processor is required to “adapt” to these environmental variations while simultaneously providing meaningful estimates that are necessary for such applications as detection, localization, inversion and enhancement. In this paper, we develop a parametrically adaptive, sequential Bayesian processor capable of jointly estimating both modal functions and environmental parameters to provide enhanced estimates for a focused optimizer capable locating a target in the noisy shallow ocean environment.

42 ENGINEERING↗
DOE OSTI2024

Estimating coccidioidomycosis endemicity while accounting for imperfect detection using spatio - temporal occupancy modeling

Coccidioidomycosis, or Valley fever, is an infectious disease caused by inhaling Coccidioides fungal spores. Incidence has risen in recent years, and it is believed the endemic region for Coccidioides is expanding in response to climate change. While Valley fever case data can help us understand trends in disease risk, using case data as a proxy for Coccidioides endemicity is not ideal because case data suffers from imperfect detection, including false positives (e.g., travel-related cases reported outside of endemic area) and false negatives (e.g., misdiagnosis or underreporting). Here we proposed a Bayesian, spatio-temporal occupancy model to relate monthly, county-level presence/absence data on Valley fever cases to latent endemicity of Coccidioides, accounting for imperfect detection. We used our model to estimate endemicity in the western United States. We estimated high probability of endemicity in southern California, Arizona, and New Mexico, but also in regions without mandated reporting, including western Texas, eastern Colorado, and southeastern Washington. We also quantified spatio-temporal variability in detectability of Valley fever, given an area is endemic to Coccidioides. We estimated an inverse relationship between lagged 3- and 9-month precipitation and case detection, and a positive association with agriculture. This work can help inform public health surveillance needs and identify areas that would benefit from mandatory case reporting.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2010

A Model-Based Probabilistic Inversion Framework for Wire Fault Detection Using TDR

Time-domain reflectometry (TDR) is one of the standard methods for diagnosing faults in electrical wiring and interconnect systems, with a long-standing history focused mainly on hardware development of both high-fidelity systems for laboratory use and portable hand-held devices for field deployment. While these devices can easily assess distance to hard faults such as sustained opens or shorts, their ability to assess subtle but important degradation such as chafing remains an open question. This paper presents a unified framework for TDR-based chafing fault detection in lossy coaxial cables by combining an S-parameter based forward modeling approach with a probabilistic (Bayesian) inference algorithm. Results are presented for the estimation of nominal and faulty cable parameters from laboratory data.

Schuet, Stefan R.↗
DOE OSTI2022

Probabilistic constrained Bayesian inversion for transpiration cooling

Abstract To enable safe operations in applications such as rocket combustion chambers, the materials require cooling to avoid material damage. Here, transpiration cooling is a promising cooling technique. Numerous studies investigate possibilities to simulate and evaluate the complex cooling mechanism. One naturally arising question is the amount of coolant required to ensure a safe operation. To study this, we introduce an approach that determines the posterior probability distribution of the Reynolds number using an inverse problem and constraining the maximum temperature of the system under parameter uncertainties. Mathematically, this chance inequality constraint is dealt with by a generalized polynomial chaos expansion of the system. The posterior distribution will be evaluated by different Markov chain Monte Carlo based methods. A novel method for the constrained case is proposed and tested among others on two‐dimensional transpiration cooling models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Arctic Cloud‐Base Ice Precipitation Properties Retrieved Using Bayesian Inference

Abstract Cloud‐climate feedbacks are still the greatest source of uncertainty in current climate projections. Arctic clouds, which are predominantly stratiform and supercooled, often long‐lived, and nearly continuously precipitate ice particles, contribute roughly 10% of the uncertainty attributed to the global cloud feedback. This Arctic cloud uncertainty is driven by incomplete observational and theoretical knowledge required to estimate and explain the state and active processes occurring in those clouds. A focus on ice precipitation properties at Arctic cloud base rather than the surface deconfounds the product of cloud condensate sink processes from the influence of the atmospheric thermodynamic state below cloud base, rendering cloud‐base properties a more appealing target for inference and evaluation of model simulations. Here I describe an inverse model for the estimation of cloud base ice precipitation properties over Utqiagvik, North Slope of Alaska, using the synthesis of ground‐based radar and lidar measurements. By leveraging a Markov Chain Monte Carlo algorithm as the core of the inverse model, a wide range of particle size distributions are sampled, and different combinations of ice habit models are examined, both of which are typically fixed in other retrieval methods. Results show intriguing links between different cloud base thermodynamic and ice precipitation properties. Apparent ice number concentration enhancements at temperatures of −5 and −15°C suggest possible secondary ice production (SIP). The analysis alludes to an overestimation of SIP occurrence and intensity, especially in studies relying only on radar or lidar measurements. Finally, reflectivity‐dependent ice precipitation rate and ice water content parameterizations are presented.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Far-field thermal imaging below diffraction limit

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.

42 ENGINEERING↗
DOE OSTI2026

Observation of quantum effects on radiation reaction in strong fields

Radiation reaction, the force experienced by an accelerated charge due to radiation emission, has long been the subject of extensive theoretical and experimental research. Experimental verification of a quantum, strong-field description of radiation reaction is fundamentally important, and has wide-ranging implications for astrophysics, laser-driven particle acceleration, next-generation particle colliders and inverse-Compton photon sources for medical and industrial applications. However, the difficulty of accessing regimes where strong field and quantum effects dominate inhibited previous efforts to observe quantum radiation reaction in charged particle dynamics with high significance. We report the first high significance (> 5σ) observation of strong-field radiation reaction on electron spectra where quantum effects are substantial. We obtain the first, quantitative, strong evidence favouring the quantum-continuous and quantum-stochastic models over the classical model; the quantum models perform comparably. The lower electron energy losses predicted by the quantum models accounts for their improved performance. Model comparison was performed using a novel Bayesian framework which has widespread utility for laser-particle collision experiments, including those utilising conventional accelerators, where some collision parameters cannot be measured directly.

Los, Eva E. [Imperial College London (United Kingd↗
NASA NTRS2018

A Singular Value Decomposition Framework for Retrievals with Vertical Distribution Information from Greenhouse Gas Column Absorption Spectroscopy Measurements

We review the singular value decomposition (SVD) framework and use it for quantifying and discerning vertical information in greenhouse gas retrievals from column integrated absorption measurements. While the commonly used traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We review the SVD method, explicitly recognize the use of an uninformative prior and show it to incur no bias from the choice of the prior. We also make the connection between the SVD method and the pseudo-inverse, which makes it more intuitive and easy to understand. We illustrate the use of the SVD method on an integrated path differential absorption CO2 lidar measurement model and verify our derivations and bias-free properties versus optimal estimation using numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. Hence, the SVD method is particularly useful for situations in which knowledge of the prior mean and prior covariance of the true state (e.g., greenhouse gas profiles) is inadequate.

Ramanathan, Anand K.↗
DOE OSTI2025

High-throughput spin-bath characterization of spin defects in semiconductors

Detailed knowledge of the local environments of spin defects in semiconductors, such as nitrogenvacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, at present a direct experimental characterization of individual defect environments is not scalable, as conventional spin-bath measurements are time consuming and difficult to automate. Achieving high-throughput characterization requires short experiments to probe the spin bath. However, with fewer and noisier measurements, the inverse problem of recovering spin-bath properties from measured data becomes ill posed, with multiple spin baths having a high likelihood of yielding the same data. In this work, we present a set of computational tools to resolve the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin defects from sparse, noisy experimental coherence data, which can be obtained in hours. Here, we use a trans-dimensional Bayesian approach that incorporates ab initio data to yield full posterior distributions over nuclear spin environments, enabling robust recovery from limited data. We also provide practical tools and guidelines to determine the limits of detectability for hyperfine couplings under specific dynamical decoupling sequences and sampling conditions. In addition, we demonstrate how the tools developed here, in combination with ab initio simulations of spin baths, can guide the design of efficient experimental protocols for application-specific high-throughput screening. To showcase the utility of our approach, we apply it to design fast dynamical decoupling experiments to characterize the spin baths often individual NV centers in diamond. While the primary focus is on accelerating spin-bath characterization of spin defects, this Bayesian approach also lays the foundation for digital-twin studies of spin defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin defects in semiconductors for quantum sensing and information applications.

Bayesian methods↗