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Results for “Bayesian parameter estimation”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

In this work we present a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

42 ENGINEERING↗
DOE OSTI2022

Bayesian optimized collection strategies for fatigue strength testing

Abstract A statistical framework is presented enabling optimal sampling and analysis of constant life fatigue data. Protocols using Bayesian maximum entropy sampling are built based on conventional staircase and stress step methods, reducing the requirement of prior knowledge for data collection. The Bayesian Staircase method shows improved parameter estimation efficiency, and the Bayesian Stress Step method shows equal accuracy to the standard method at larger step size allowing experimentalists to lessen concerns of loading history. Statistical methods for determining model suitability are shown, highlighting the influence of protocol. Experimental validation is performed, showing the applicability of the methods in laboratory testing.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗
DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗
DOE OSTI2025

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗
DOE OSTI2021

Statistically-informed deep learning for gravitational wave parameter estimation

We introduce deep learning models to estimate the masses of the binary components of black hole mergers, $(m_1,m_2)$, and three astrophysical properties of the post-merger compact remnant, namely, the final spin, $a_\mathrm f$, and the frequency and damping time of the ringdown oscillations of the fundamental $\ell = m = 2$ bar mode, $(\omega_\mathrm R, \omega_\mathrm I)$. Our neural networks combine a modified WaveNet architecture with contrastive learning and normalizing flow. We validate these models against a Gaussian conjugate prior family whose posterior distribution is described by a closed analytical expression. Upon confirming that our models produce statistically consistent results, we used them to estimate the astrophysical parameters $(m_1,m_2, a_\mathrm f, \omega_\mathrm R, \omega_\mathrm I)$ of five binary black holes: GW150914, GW170104, GW170814, GW190521 and GW190630. We use PyCBC Inference to directly compare traditional Bayesian methodologies for parameter estimation with our deep learning based posterior distributions. Our results show that our neural network models predict posterior distributions that encode physical correlations, and that our data-driven median results and 90% confidence intervals are similar to those produced with gravitational wave Bayesian analyses. This methodology requires a single V100 NVIDIA GPU to produce median values and posterior distributions within two milliseconds for each event. Furthermore, this neural network, and a tutorial for its use, are available at the Data and Learning Hub for Science.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Model-Data for Joint Estimation of Biogeochemical Model Parameters from Multiple Experiments: A Bayesian Approach Applied to Mercury Methylation

This modeling archive supports the manuscript submitted for publication in the Environmental Modeling and Software. This study is supported by ORNL-SFA and IDEAS-Watershed. This study aims to improve calibration of complex biogeochemical models using datasets from multiple experiments targeting specific subprocesses. The proposed Bayesian joint-fitting scheme calibrates the entire biogeochemical model in one go using all the available datasets and estimate parameter uncertainties using Markov Chain Monte Carlo (MCMC). This allows for complete propagation of uncertainties and utilization of the information shared between different datasets. Mapping joint distribution of parameters guides model improvement by identifying null spaces in the parameter space. This archive contains files used to perform MCMC, post-process outputs and visualize results.

East Fork Poplar Creek↗
DOE OSTI2022

Joint estimation of biogeochemical model parameters from multiple experiments: A bayesian approach applied to mercury methylation

Here, to characterize complex biogeochemical systems, results from multiple experiments, where each targets a specific subprocess, are commonly combined. The resulting datasets are interpreted through the calibration of biogeochemical models for process inference and predictions. Commonly used calibration approaches of fitting datasets from individual experiments to subprocess models one at a time is prone to missing information shared between datasets and incomplete uncertainty propagation. We propose a Bayesian joint-fitting scheme addressing the above-mentioned concerns by jointly fitting all the available datasets, thus calibrating the entire biogeochemical model in one go using Markov Chain Monte Carlo (MCMC). The identification of null spaces in the parameter distributions from MCMC guided the simplification of certain subprocess models. For example, fast kinetic sorption was replaced by equilibrium sorption, and Monod demethylation was replaced by first-order demethylation. Joint fitting of datasets resulted in complete uncertainty propagation with parameter estimates informed by all available data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Informational approach to cosmological parameter estimation

Here, we introduce a new approach for cosmological parameter estimation based on the information-theoretical Jensen-Shannon divergence ($\mathscr{D}$ JS ), calculating it for models in the restricted parameter space {H 0 , w 0 , w a }, where H 0 is the value of the Hubble constant today, and w 0 and w a are dark energy parameters, with the other parameters held fixed at their best-fit values from the Planck 2018 data. As an application, we investigate the H 0 tension between the Planck temperature power spectrum data (TT) and the local astronomical data by comparing the ΛCDM model with the wCDM and the w 0 w a CDM dynamic dark energy models. We find agreement with other works using the standard Bayesian inference for parameter estimation; in addition, we show that while the $\mathscr{D}$ JS is equally minimized for both values of H 0 along the (w 0 , w a ) plane, the lines of degeneracy are different for each value of H 0 . This allows for distinguishing between the two, once the value of either w 0 or w a is known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Deep Neural Network Informed Markov Chain Monte Carlo Methods

In subsurface flow modeling, quantifying the uncertainty of model parameters and the corresponding uncertainly on output quantities is a crucial task for groundwater management. Markov chain Monte Carlo (MCMC) methods can take advantage of observed data to estimate parameters in a Bayesian setting. However, MCMC can be slow to converge and produce highly correlated samples when the dimensions of the parameters is high. Using gradients for the posterior distribution can help samplers explore the parameter space more efficiently, but obtaining gradients can be computationally challenging.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data

Here, we perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg 2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be ${A}_{\phi }=0.949\,\pm \,0.122$ using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist "bias hardening" or linear bias correction, and reducing the systematic uncertainty on A Φ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A Φ along with A L , the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A Φ and seven times lower effective lensing reconstruction noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Estimating uncertainty: A Bayesian approach to modelling photosynthesis in C3 leaves

The Farquhar-von Caemmerer-Berry (FvCB) model is extensively used to model pho-tosynthesis from gas exchange measurements. Since its publication, many methods have been developed to measure, or more accurately estimate, parameters of this model. Here, we have created a tool that uses Bayesian statistics to fit photosyn-thetic parameters using concurrent gas exchange and chlorophyll fluorescence mea-surements whilst evaluating the reliability of the parameter estimation. We have tested this tool on synthetic data and experimental data from rice leaves. Our results indicate that reliable parameter estimation can be achieved whilst only keeping one parameter, Km, that is, Michaelis constant for CO2 by Rubisco, prefixed. Additionally, we show that including detailed low CO2 measurements at low light levels increases reliability and suggests this as a new standard measurement protocol. By providing an estimated distribution of parameter values, the tool can be used to evaluate the quality of data from gas exchange and chlorophyll fluorescence measurement proto-cols. Compared to earlier model fitting methods, the use of a Bayesian statistics-based tool minimizes human interaction during fitting, reducing the subjectivity which is essential to most existing tools. A user friendly, interactive Bayesian tool script is provided.

Bayesian statistics, leaf photosynthesis, mesophyl↗
DOE OSTI2026

Bayesian Physics Informed Spatio-Temporal Network for Streamflow Data Imputation

Reliable reconstruction of incomplete streamflow records is critical for improving hydrological forecasting, flood preparedness, and water resource management. However, large observational gaps and uncertainties in governing physical parameters limit the accuracy of traditional statistical and machinelearning imputation frameworks. To address these challenges, we develop a Bayesian Physics-Informed Spatio-Temporal Network (BPI-STNet) that jointly captures spatial and temporal dependencies while enforcing hydrologic consistency through embedded physical constraints. The framework integrates a GraphSAGE-LSTM architecture to model spatial connectivity across gauges and temporal flow dynamics, coupled with a Bayesian update mechanism to estimate uncertain parameters in a simplified water-balance framework. Unlike conventional physics-informed networks that rely on sampling-based posterior estimation, BPI-STNet derives an analytic solution to the inverse problem, allowing closed-form Bayesian updates of uncertain parameters Λ={α,β,k} using Gaussian priors and likelihoods. Applied to daily observations from the Susquehanna River Basin (1980-2022), BPI-STNet achieves substantial improvements over a purely data-driven RGNN baseline, which reduced RMSE by 23 % and MAE by 9 %, and achieving an average NSE values up to 0.96. The results demonstrate that coupling Bayesian inference with physics-informed learning yields physically consistent, uncertainty-aware reconstructions that preserve the temporal persistence and statistical distribution of observed flows. The proposed framework establishes a generalizable paradigm for data-sparse hydrologic systems where both data fidelity and physical interpretability are essential.

Krishnan Kutty Ambika, Anukesh [ORNL] (ORCID:00000↗
DOE OSTI2023

BeyondPlanck: XII. Cosmological parameter constraints with end-to-end error propagation

We present cosmological parameter constraints estimated using the Bayesian BEYONDPLANCK analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered Planck LFI observations, combined with selected external data (WMAP 33–61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter amounting about 1σ when considering only temperature multipoles between 30 ≤ ℓ ≤ 600. In cases where there are differences, we note that the BEYONDPLANCK results are generally slightly closer to the high-ℓ HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low-ℓ polarization information from LFI and WMAP, we find a best-fit value of τ = 0.066 ± 0.013, which is higher than the low value of τ = 0.052 ± 0.008 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the BEYONDPLANCK processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion

In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Risk-informed Predictive Analytics To Achieve Cost-effective Condition-based Monitoring And Maintenance Strategy

The research involves developing risk-informed predictive analytic capabilities to achieve condition-based monitoring and maintenance strategies to reduce overall maintenance costs. The research utilizes data (real-time data, periodic data, and institutional knowledge) related to a particular plant asset from a specific nuclear plant site to develop risk-informed predictive analytic algorithms. The developed algorithms and codes are used to optimize the maintenance strategy and estimate/forecast generation costs based on the state of health of the plant asset. Developed codes specifically include 1. Parameter estimation code based on Bayesian inference 2. Statistical data analysis code 3. Feature engineering code 4. Health classifier code 5. Diagnosis code 6. Prognosis code 7. Hazard code 8. Generation risk code 9. Economic code

Agarwal, Vivek↗