Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Posterior distribution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

Constraining Physical Models at Gigabar Pressures

High-energy-density (HED) experiments in convergent geometry are able to test physical models at pressures beyond hundreds of millions of atmospheres. The measurements from these experiments are generally highly integrated and require unique analysis techniques to procure quantitative information. This work describes a methodology to constrain the physics in convergent HED experiments by adapting the methods common to many other fields of physics. As an example, a mechanical model of an imploding shell is constrained by data from a thin-shelled direct-drive exploding-pusher experiment on the OMEGA Laser System using Bayesian inference, resulting in the reconstruction of the shell dynamics and energy transfer during the implosion. The model is tested by analyzing synthetic data from a 1-D hydrodynamics code and is sampled using a Markov chain Monte Carlo to generate the posterior distributions of the model parameters. The goal of this work is to demonstrate a general methodology that can be used to draw conclusions from a wide variety of HED experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗

BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data

We describe the BeyondPlanck project in terms of motivation, methodology and main products, and provide a guide to a set of companion papers that describe each result in fuller detail. Building directly on experience from ESA's Planck mission, we implement a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a joint posterior distribution P(omega|d), where omega represents the set of all free instrumental (gain, correlated noise, bandpass etc.), astrophysical (synchrotron, free-free, thermal dust emission etc.), and cosmological (CMB map, power spectrum etc.) parameters. Some notable advantages of this approach are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-l CMB polarization reconstruction, paying special attention to the LFI 44 GHz channel. We find evidence of significant residual systematic effects that are still not accounted for in the current processing, but must be addressed in future work. These include a break-down of the 1/f correlated noise model at 30 and 44 GHz, and scan-aligned stripes in the Southern Galactic hemisphere at 44 GHz. On the Northern hemisphere, however, we find that all results are consistent with the LCDM model, and we constrain the reionization optical depth to tau = 0.067 +/- 0.016, with a low-resolution chi-squared probability-to-exceed of 16%. The marginal CMB dipole amplitude is 3359.5 +/- 1.9 uK. (Abridged.)

Andersen, KJ↗

Bayesian Spatially Varying Multi-Regularization Image Deblurring

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Since blur and noise are inevitably present in any imaging system, the images must be \deblurred" to extract the full information content. Mathematically, image deblurring is an ill-posed inverse problem that requires regularization. The regularization, in turn, has a large effect on the deblurred image: different regularization strengths, and types, lead to drastically different reconstructions. Moreover, many images contain a mixture of smooth and sharp features which suggests the use of multi-regularization, i.e., varying the type of regularization (e.g. Tikhonov or total variation) across the image. We address these issues by formulating the image deblurring problem within a hierarchical Bayesian framework in which we spatially adapt the strength of the regularization and also vary the regularization type across the image. In this way, the image itself, along with corresponding regularization strength at each pixel, are described jointly by a posterior distribution which we can sample by Markov chain Monte Carlo (MCMC) methods. We illustrate our techniques on simplified test problems and apply them to high-energy X-ray images taken at the Nevada National Security Site. Numerical tests show that our new method is robustly applicable and increases the quality of the image reconstruction when compared to other (Bayesian) methods.

97 MATHEMATICS AND COMPUTING↗

Invertible neural networks for E3SM land model calibration and simulation

We apply an invertible neural network (INN) for E3SM land model calibration and simulation with eight parameters at the Missouri Ozark AmeriFlux forest site. INN provides bijective (two-way) mappings between inputs and outputs, thus it can solve probabilistic inverse problems and forward approximations simultaneously. We demonstrate INN's inverse and forward capability in both synthetic and real-data applications. Results indicate that INN produces accurate parameter posterior distributions similar to Markov Chain Monte Carlo sampling and it generates model outputs close to the forward model simulations. Additionally, both the inverse and forward evaluations in INN are computationally efficient which allows for rapid integration of observations for parameter estimation and fast model predictions.

Lu, Dan↗

Strong Lensing Parameter Estimation on Ground-Based Imaging Data Using Simulation-Based Inference

Current ground-based cosmological surveys, such as the Dark Energy Survey (DES), are predicted to discover thousands of galaxy-scale strong lenses, while future surveys, such as the Vera Rubin Observatory Legacy Survey of Space and Time (LSST) will increase that number by 1-2 orders of magnitude. The large number of strong lenses discoverable in future surveys will make strong lensing a highly competitive and complementary cosmic probe. To leverage the increased statistical power of the lenses that will be discovered through upcoming surveys, automated lens analysis techniques are necessary. We present two Simulation-Based Inference (SBI) approaches for lens parameter estimation of galaxy-galaxy lenses. We demonstrate the successful application of Neural Posterior Estimation (NPE) to automate the inference of a 12-parameter lens mass model for DES-like ground-based imaging data. We compare our NPE constraints to a Bayesian Neural Network (BNN) and find that it outperforms the BNN, producing posterior distributions that are for the most part both more accurate and more precise; in particular, several source-light model parameters are systematically biased in the BNN implementation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Bayesian analysis for estimating statistical parameter distributions of elasto-viscoplastic material models

High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.

42 ENGINEERING↗

Predicting Li-Ion Battery Capacity Fade Using Early-Life Data and a Hybrid Data-Driven Gaussian Process-Bayesian Regression Approach

Accurately predicting Li-ion battery capacity trajectories using early-life data can dramatically improve battery-life understandings and be used to rapidly evaluate design/cost/performance trade-offs when developing new battery materials. Accurate early-life predictions enable researchers to quickly iterate over cell designs and material precursor properties without consistently cycling cells to failure. To this end, we present a toolbox that uses a combined Gaussian Process and Bayesian regression approach that capitalizes on signals other than just capacity (e.g., dQ/dV, voltage drops) to rapidly predict capacity-fade trajectories. The prediction tool uses Bayesian regression to fit functional forms, e.g., power law, sigmoids, etc., to predict capacity-fade dynamics. By fitting functional forms, the capacity fade can be interrogated at any point in the future, allowing for early cell-failure prediction. Additionally, Bayesian regression allows for accurate uncertainty estimates that account for cell-to-cell variability (aleatoric uncertainty) and the lack of observation data (epistemic uncertainty). By only using early cycle data to predict the capacity fade trajectory, uncertainty bounds at end-of-life can be extremely large. The large uncertainty bounds are further exacerbated because there is no systematic way to define the prior distribution of the functional forms' parameters. We improve our the predicted trajectory confidence interval of our predicted trajectory using two methods. First, we shows that a small amount of held-out cycling data is sufficientuse some train cells, that have been cycled to failure to derive information regarding the appropriate prior distributions for the functional forms' parameters of the functional form, effectively leading to data-driven priors.. We propose constructing the data-driven priors by first running a Bayesian regression starting with uninformed priors to generate intermediate cell-specific posterior parameter distributions. These posterior distributions are combined using a Ggaussian mixture model for each parameter to create the data-driven priors. These mixture models serve as the data-driven prior distributions for the parameters for. Second, we derive multiple features, e.g., C_dchg 0.5 DoD 0.5, log (|mean(dQ/dV_(w_3-w_0 ) (V)|), etc., from the train cellsheld-out cycling data, identify which the features are that best predicting capacity at early/mid-life cycles, and then create Ggaussian process regression models that are used for predicting capacity at early/mid-life cycles for the test cells (see blue dots with error bars in Fig 1b). Finally, these predicted data-points are used in addition to the actual early cycle data capacity fade to construct the Bayesian regression trajectory for the test cell s. Notably. We note that these two methods are complementary and can be combined with each other. We evaluate the performance of our proposed method on an testing open-source dataset from Iowa State University and Iowa Lakes Community College (ISU-ILCC). This dataset comprises of 251 nickel-manganese-cobalt/graphite Lithium-ion cells that are cycled under 63 different conditions. We compute the mean average percentage error (MAPE) and negative log predictive density (NLPD) to quantify the efficacy of our method. Our initial findings suggest that, when only few observations are available, for test cells, when using only Bayesian regression with uninformed priors, a power law functional provides the most accurate predictions. with very few data points. However, asHowever, a the number of data points increases, a twin sigmoidal function becomes more accurate as the number of observations further increases. We also find that using as little as 10% of the data set towards generating data-driven priors can lead to significant improvement in prediction accuracy when using early cycle data. Lastly, we found that augmenting early-cycle data with Gaussian process-predicted capacity data for Bayesian regression greatly improves the prediction accuracy. We will present a comprehensive comparison of our methods to other methods available in the literature and apply this method to additional battery datasets.

42 ENGINEERING↗

Preliminary Results on Bayesian Inverse UQ for OECD/NEA WPNCS Subgroup 14 Benchmark Exercise for Error Recovery and Experimental Coverage

The Organization for Economic Cooperation and Development (OECD) Working Party on Nucelar Criticality Safety (WPNCS) has proposed a benchmark exercise representative of neutronic behavior in criticality experiments. Here, the goal is to develop confidence in data assimilation techniques used to adjust nuclear data. Participants are given synthetic experimental models with associated measured data and asked to estimate the model parameters given the model and measurements as well as provide predictions for separate application models. In this work, we performed data assimilation using Bayesian inverse Uncertainty Quantification (UQ) with machine learning surrogate models to produce posterior parameter distributions for the requested parameters and posterior predictive distributions for the requested responses. Several experimental models are shown to insufficiently inform the posterior parameter distributions for the applications involved. However, given sufficient experimental data, posterior parameter estimates yielded reduced uncertainty in the response predictions of interest while covering the experimental data.

Bayesian Inference↗

Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations

Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high- delity simulations of radiation transport within an urban domain. The model is constructed to employ a source location (x, y, z) as input and return the estimated count rate for a set of speci ed detector locations. Because MCNP simulations are computationally expensive, we develop e cient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes (GP) and neural networks (NN) that we train and verify using the MCNP simulations. The trained surrogate models provide an e cient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo (MCMC) algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source's location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Direct Bayesian inference for fault severity assessment in Digital-Twin-Based fault diagnosis

For applications in condition-based maintenance of nuclear systems, the assessment of fault severity is crucial. In this work, we developed a framework that allows for direct inference of the probability distributions of possible faults in a system. Here, we employed a model-based approach with model residuals generated from analytical redundancy relations provided by physics-based models of the system components. From real-time sensor readings, the values of the model residuals can be calculated, and the posterior probability distributions of the faults can be computed directly using the methods of Bayesian networks. From the posterior distribution of each fault, one can estimate the fault probability based on a chosen threshold and assess the severity of the fault. By eliminating the discretization and simplifications in middle steps, this approach allows us to leverage the available computational resources to provide more accurate fault probability estimates and severity assessments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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↗

Challenges in Markov Chain Monte Carlo for Bayesian Neural Networks

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such challenges culminate to lack of convergence to the parameter posterior. Nevertheless, this paper shows that a nonconverged Markov chain, generated via MCMC sampling from the parameter space of a neural network, can yield via Bayesian marginalization a valuable posterior predictive distribution of the output of the neural network. Further, classification examples based on multilayer perceptrons showcase highly accurate posterior predictive distributions. The postulate of limited scope for MCMC developments in BNNs is partially valid; an asymptotically exact parameter posterior seems less plausible, yet an accurate posterior predictive distribution is a tenable research avenue.

97 MATHEMATICS AND COMPUTING↗

A Bayesian approach to the long-baseline neutrino oscillation sensitivity of DUNE

The sensitivity of the Deep Underground Neutrino Experiment (DUNE) to neutrino oscillation is evaluated using a Bayesian Markov Chain Monte Carlo (MCMC) approach. This analysis uses the same underlying sensitivity inputs as previous DUNE studies [Eur. Phys. J. C 80, 978 (2020)], and therefore does not present updated DUNE sensitivities, but instead explores the additional inferences accessible using a Bayesian approach. We present four-dimensional posterior probability distributions of the oscillation parameters, highlighting the breadth of correlation in the parameter space of interest, especially between $\sin^2 θ_{23}$ and $\sin^2 θ_{13}$. We exploit the flexibility of the Bayesian framework to incorporate parameter constraints post hoc and assess the impact of applying a reactor short-baseline $θ_{13}$ constraint. A significant increase in the sensitivity to the $θ_{23}$ octant is found when including the constraint. Posterior distributions of derived quantities can be easily constructed from MCMC results. This work presents the first study of DUNE's sensitivity to the Jarlskog invariant, $J$, a quantity that provides a parametrisation-independent measure of charge-parity violation in the leptonic sector.

Abbaslu, Saeed [IPM, Tehran] (ORCID:00000003356771↗

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

State of Stress Uncertainty Quantification and Geomechanical Risk Analysis for Subsurface Engineering

All subsurface stress measurement methods available for deep subsurface applications are indirect and involve a significant amount of uncertainty. Quantifying these uncertainties is critical for applications where the state of stress is a component of a risk analysis with significant safety, environmental, and economic considerations. A publicly available and open source tool called the State of Stress Analysis Tool (SOSAT) has been developed to aid in performing a Bayesian uncertainty quantification and geomechanical risk analysis using many types of commonly available data. A new feature of this tool is using data from the FutureGen 2.0 site. The new feature of the tool was uses information about the absence or presence of borehole breakouts to constrain the state of stress. This new feature allows the user to specify probability distributions for the relevant parameters such as the drilling mud pressure, temperature, and the formation strength properties. The tool computes the posterior joint probability distribution of the horizontal principal stresses. Using random samples from this posterior distribution the tool then computes the probability of activating a critically oriented fault at a range of pore pressures. This latter feature can be used to aid in the assessment of the risk of induced seismicity and leakage in geologic carbon sequestration and enhanced geothermal systems.

Burghardt, Jeffrey A.↗

Proxy-based Bayesian inversion of strain tensor data measured during well tests

Recent instrument developments have made it possible to measure the strain tensor caused by injecting or pumping fluid from aquifers or reservoirs, but the full value of these data is limited because the long runtimes of poroelastic forward models makes it impractical to use many inversion schemes. This limits the interpretation of strain data for managing the recovery of resources or storage of wastes in the subsurface. This paper describes a method of inverting deformation data using a poroelastic numerical simulator so the results can be used to manage reservoirs or aquifers. We developed a workflow designed to reduce the number of simulations sufficiently to make it feasible to use DREAMzs, an advanced Bayesian inversion method that translates the uncertainties from different sources into unbiased posterior parameter distributions and uncertainty envelopes around the field data. Using a KNN proxy model for the poroelastic simulator is key to reducing the overall computations, and the workflow includes a strategy for ensuring the proxy model results converge on the results from the simulator. The workflow is tested using an idealized example that verifies the ability to correctly identify parameters and characterize noise used to perturb the data. Field data from an injection test at an oil reservoir near Tulsa, Oklahoma, are also used to evaluate the efficacy of the workflow with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), where the results were used to characterize posterior parameter distribution and evaluate the prediction uncertainty. Furthermore, this workflow is significant because it enables strain tensor, or other geomechanical measurements to be interpreted to guide decision-making during energy and environmental processes in the subsurface.

42 ENGINEERING↗

Bayesian Monte Carlo Evaluation of Imperfect (n, 233 U) Data and Model

Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗