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

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Generating a 4D Global CH(4) Product by Assimilating TROPOMI column CH(4) in NASA’s GEOS GCM

Examination of temporal and spatial CH4 variability is crucial for better understanding the human and natural processes driving climate change and ultimately designing mitigation strategies. Here we present an analysis framework that uses NASA’s GEOS General Circulation Model (GCM) to construct a high-resolution, time varying picture of atmospheric CH4 consistent with measurements from a variety of platforms, both in situ and remotely sensed. The resulting time varying atmospheric CH4 product can (i) support interpretation of high-resolution point source detection approaches, (ii) provide reanalysis fields for CH4 and other greenhouse gases, and (iii) supply boundary conditions for regional models. Our approach starts with a set of CH4 emissions from various inventories that have been adjusted to match the global annual growth rate over recent decades. These emissions are transported by the GEOS GCM, which in turn is constrained by meteorology from NASA’s Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) product. The simulated atmospheric field is compared with CH4 measurements, such as those from the TROPOspheric Monitoring Instrument (TROPOMI), and adjustments calculated following a Bayesian protocol. The accuracy of the resultant optimal atmospheric CH4 field can be demonstrated by its improved agreement (compared to a direct simulation of the CH4 inventories) with a host of independent CH4 measurements, such as those from the Total Carbon Column Observation Network (TCCON) and in situ observations from surface and airborne platforms.

Nikolay V. Balashov↗
DOE OSTI2024

PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments

This article describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to “enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.” This article provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate the potential of the package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Uncertainty quantification for equations of state: copper as an example

Equations of state are essential for providing a fundamental description of materials properties in thermodynamic equilibrium and are used to provide closure relations for hydrodynamics simulations. Generally, equations of state rely on simple physics-based parameterized materials models to inform on the free energy of a material through out a given thermodynamic state space. Historically the parameters of these models have been tuned by hand to fit various experimental data. However, modern optimization and uncertainty quantification techniques allow us to quickly test thousands of parameter combinations and obtain meaningful uncertainty estimates on the parameters, opening opportunities for assessing systematic uncertainties in experiments, assessing model adequacy, and more. In this report, we use Bayesian inference to fit the solid (fcc) equation of state of copper. We focus on fitting five different experimental datasets, including the isobaric density, isobaric heat capacity, room temperature isotherm, principal isentrope, and principal Hugoniot. We fit all five data types simultaneously, and then explore the extent to which combinations of 2 subsets of the 5 datasets can constrain the EOS parameters, as compared to the fit to all 5. This information is useful for investigating the extent to which different datasets can con strain EOS models and thereby help guide experimental investigations in order to best constrain the EOS. We also discuss ways that the methodologies can be used to investigate systematic discrepancies between experiments, as well as how the methods can be used to assess model uncertainty. The framework we develop is general, in that it can be used with a variety of optimization or uncertainty quantification techniques and with a variety of data sources, including both experimental and ab-inito data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗
DOE OSTI2023

PYOED: AN ETENSIBLE SUITE FOR DATA ASSIMILATION AND MODEL-CONSTRAINED OPTIMAL DESIGN OF EXPERIMENTS

SF-23-005 PyOED is a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to ``enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.'' PyOED will be continuously expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators.

ATTIA, AHMEDMOHAMED↗
NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗
NASA NTRS2026

Remote Sensing-Driven Hydrodynamic Modeling in Data-Scarce Regions: Integrating ICESat-2, Sentinel-2, SWOT and Re-analysis Models for Coastal Monitoring

Hydrodynamic models in coastal and estuarine systems are typically constrained by sparse bathymetry, boundary, and validation data, especially in regions where field campaigns are costly or impractical. Here we develop and test a fully satellite-driven framework for hydrodynamic modeling in South Africa’s Langebaan Lagoon without using any local in situ measurements. Bathymetry is derived by training multispectral Sentinel-2 reflectance against ICESat-2 ATL24 photon-derived depths using an XGBoost model optimized with Bayesian search. The final satellite-derived bathymetry reproduces independent ATL24 points with RMSE = 0.45 m and R 2 = 0.97. This bathymetry was used in a depth-averaged Delft3D Flexible Mesh model driven at the open boundary by TPXO tidal harmonics and by ERA5 winds. We validate modeled water surface elevation against 16 SWOT low-rate (250 m, unsmoothed) passes in 2023. SWOT–model comparisons yield an overall RMSE of 0.11 m and R 2 = 0.61, with typical point differences <0.10 m (∼7% of the 1.5 m tidal range), and showed consistent spatial gradients in water level from the offshore boundary, through Saldanha Bay, and into the lagoon. At the offshore boundary, TPXO and SWOT sea surface heights agree closely (R 2 = 0.86). A simple phase adjustment of ∼26,min between TPXO and SWOT lowers the RMSE from 0.18,m to 0.11,m, showing that phase offset accounts for some of the discrepancy, with additional errors likely linked to non-tidal signals. Our results demonstrate that combining passive optical, photon-counting LiDAR, radar interferometry, and global tidal/atmospheric models enables robust, transferrable hydrodynamic modeling in data-scarce coastal systems, offering a cost-effective pathway for monitoring.

ICESat-2↗
DOE OSTI2019

Bayesian performance evaluation of evapotranspiration models based on eddy covariance systems in an arid region

Abstract. Evapotranspiration (ET) is a major component of the land surface processinvolved in energy fluxes and energy balance, especially in the hydrologicalcycle of agricultural ecosystems. While many models have been developed aspowerful tools to simulate ET, there is no agreement on which model bestdescribes the loss of water to the atmosphere. This study focuses on twoaspects, evaluating the performance of four widely used ET models andidentifying parameters, and the physical mechanisms that havesignificant impacts on the model performance. The four tested models arethe Shuttleworth–Wallace (SW) model, Penman–Monteith (PM) model,Priestley–Taylor and Flint–Childs (PT–FC) model, and advection–aridity (AA)model. By incorporating the mathematically rigorous thermodynamicintegration algorithm, the Bayesian model evidence (BME) approach is adoptedto select the optimal model with half-hourly ET observations obtained at aspring maize field in an arid region. Our results reveal that the SW model has thebest performance, and the extinction coefficient is not merely partitioningthe total available energy into the canopy and surface but also includingthe energy imbalance correction. The extinction coefficient is wellconstrained in the SW model and poorly constrained in the PM model but notconsidered in PT–FC and AA models. This is one of the main reasons that theSW model outperforms the other models. Meanwhile, the good fitting of SWmodel to observations can counterbalance its higher complexity. In addition,the detailed analysis of the discrepancies between observations and modelsimulations during the crop growth season indicate that explicit treatmentof energy imbalance and energy interaction will be the primary way offurther improving ET model performance.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Jensen–Shannon divergence based novel loss functions for Bayesian neural networks

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback–Leibler (KL) divergence-based variational inference used in BNNs suffer from unstable optimization and challenges in approximating light-tailed posteriors due to the unbounded nature of the KL divergence. To resolve these issues, we formulate a novel loss function for BNNs based on a new modification to the generalized Jensen–Shannon (JS) divergence, which is bounded. In addition, we propose a Geometric JS divergence-based loss, which is computationally efficient since it can be evaluated analytically. We found that the JS divergence-based variational inference is intractable, and hence employed a constrained optimization framework to formulate these losses. Our theoretical analysis and empirical experiments on multiple regression and classification data sets suggest that the proposed losses perform better than the KL divergence-based loss, especially when the data sets are noisy or biased. Specifically, there are approximately 5% and 8% improvements in accuracy for a noise-added CIFAR-10 dataset and a regression dataset, respectively. There is about 13% reduction in false negative predictions of a biased histopathology dataset. Additionally, we quantify and compare the uncertainty metrics for the regression and classification tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parameter estimation from spontaneous imbibition into volcanic tuff

Two-phase fluid flow properties underlie quantitative prediction of water and gas movement, but constraining these properties typically requires multiple time-consuming laboratory methods. The estimation of two-phase flow properties (van Genuchten parameters, porosity, and intrinsic permeability) is illustrated in cores of vitric nonwelded volcanic tuff using Bayesian parameter estimation that fits numerical models to observations from spontaneous imbibition experiments. The uniqueness and correlation of the estimated parameters is explored using different modeling assumptions and subsets of the observed data. The resulting estimation process is sensitive to both moisture retention and relative permeability functions, thereby offering a comprehensive method for constraining both functions. The data collected during this relatively simple laboratory experiment, used in conjunction with a numerical model and a global optimizer, result in a viable approach for augmenting more traditional capillary pressure data obtained from hanging water column, membrane plate extractor, or mercury intrusion methods. This method may be useful when imbibition rather than drainage parameters are sought, when larger samples (e.g., including heterogeneity or fractures) need to be tested that cannot be accommodated in more traditional methods, or when in educational laboratory settings.

58 GEOSCIENCES↗
DOE OSTI2023

BEYONDPLANCK VI. Noise characterization and modeling

We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BeyondPlanck Gibbs sampling framework, and apply this to Planck Low Frequency Instrument (LFI) time-ordered data. Following previous literature, we initially adopt a 1/ f model for the noise power spectral density (PSD), but find the need for an additional lognormal component in the noise model for the 30 and 44 GHz bands. We implement an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then use this procedure to both estimate the gapless correlated noise in the time-domain, n corr , and to sample the noise PSD parameters, ξ n = {σ 0 , f knee , α, A p }. In contrast to previous Planck analyses, we assume piecewise stationary noise only within each pointing period (PID), not throughout the full mission, but we adopt the LFI Data Processing Center (DPC) results as priors on α and f knee . On average, we find best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results reveals many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/ f model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise not described by a 1/ f model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/ f at the 2–3σ level in each one hour pointing period, motivating the addition of the lognormal noise component for these bands. For some periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/ f profile is not adequate to fully characterize the Planck LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the Planck LFI data, and the current work is a first attempt at understanding and mitigating these issues.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2016

Constraining the Sulfur Dioxide Degassing Flux from Turrialba Volcano, Costa Rica Using Unmanned Aerial System Measurements

Observed sulfur dioxide (SO2)mixing ratios onboard unmanned aerial systems (UAS) duringMarch 11-13, 2013 are used to constrain the three-day averaged SO2 degassing flux fromTurrialba volcanowithin a Bayesian inverse modeling framework. A mesoscale model coupled with Lagrangian stochastic particle backward trajectories is used to quantify the source-receptor relationships at very high spatial resolutions (i.e., b1 km). The model shows better performance in reproducing the near-surface meteorological properties and observed SO2 variations when using a first-order closure non-local planetary boundary layer (PBL) scheme. The optimized SO2 degassing fluxes vary from 0.59 +/- 0.37 to 0.83 +/- 0.33 kt d−1 depending on the PBL scheme used. These fluxes are in good agreement with ground-based gas flux measurements, and correspond to corrective scale factors of 8-12 to the posteruptive SO2 degassing rate in the AeroCom emission inventory. The maximum a posteriori solution for the SO2 flux is highly sensitive to the specification of prior and observational errors, and relatively insensitive to the SO2 loss term and temporal averaging of observations. Our results indicate relatively low degassing activity but sustained sulfur emissions from Turrialba volcano to the troposphere during March 2013. This study demonstrates the utility of low-cost small UAS platforms for volcanic gas composition and flux analysis.

Xi, Xin↗
DOE OSTI2016

Bayesian optimization of the Community Land Model simulated biosphere-atmosphere exchange using CO 2 observations from a dense tower network and aircraft campaigns over Oregon

Here, the vast forests and natural areas of the Pacific Northwest comprise one of the most productive ecosystems in the northern hemisphere. The heterogeneous landscape of Oregon poses a particular challenge to ecosystem models. We present a framework using a scaling factor Bayesian inversion to improve the modeled atmosphere-biosphere exchange of carbon dioxide. Observations from 5 CO/CO 2 towers, eddy covariance towers, and airborne campaigns were used to constrain the Community Land Model CLM4.5 simulated terrestrial CO 2 exchange at a high spatial and temporal resolution (1/24°, 3-hourly). To balance aggregation errors and the degrees of freedom in the inverse modeling system, we applied an unsupervised clustering approach for the spatial structuring of our model domain. Data from flight campaigns were used to quantify the uncertainty introduced by the Lagrangian particle dispersion model that was applied for the inversions. The average annual statewide net ecosystem productivity (NEP) was increased by 32% to 29.7 TgC per year by assimilating the tropospheric mixing ratio data. The associated uncertainty was decreased by 28.4% to 29%, on average over the entire Oregon model domain with the lowest uncertainties of 11% in western Oregon. The largest differences between posterior and prior CO 2 fluxes were found for the Coast Range ecoregion of Oregon that also exhibits the highest availability of atmospheric observations and associated footprints. In this area, covered by highly productive Douglas-fir forest, the differences between the prior and posterior estimate of NEP averaged 3.84 TgC per year during the study period from 2012 through 2014.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Recent advances in the quantification of uncertainties in reaction theory

Uncertainty quantification has become increasingly more prominent in nuclear physics over the past several years. In few-body reaction theory, there are four main sources that contribute to the uncertainties in the calculated observables: the effective potentials, approximations made to the few-body problem, structure functions, and degrees of freedom left out of the model space. In this work, we illustrate some of the features that can be obtained when modern statistical tools are applied in the context of nuclear reactions. This work consists of a summary of the progress that has been made in quantifying theoretical uncertainties in this domain, focusing primarily on those uncertainties coming from the effective optical potential as well as their propagation within various reaction theories. We use, as the central example, reactions on the doubly-magic stable nucleus 40 Ca, namely neutron and proton elastic scattering and single-nucleon transfer 40 Ca(d,p) 41 Ca. First, we show different optimization schemes used to constrain the optical potential from differential cross sections and other experimental constraints; we then discuss how these uncertainties propagate to the transfer cross section, comparing two reaction theories. Finally, we finish by laying out our future plans.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Bayesian optimization with active learning of design constraints using an entropy-based approach

Abstract The design of alloys for use in gas turbine engine blades is a complex task that involves balancing multiple objectives and constraints. Candidate alloys must be ductile at room temperature and retain their yield strength at high temperatures, as well as possess low density, high thermal conductivity, narrow solidification range, high solidus temperature, and a small linear thermal expansion coefficient. Traditional Integrated Computational Materials Engineering (ICME) methods are not sufficient for exploring combinatorially-vast alloy design spaces, optimizing for multiple objectives, nor ensuring that multiple constraints are met. In this work, we propose an approach for solving a constrained multi-objective materials design problem over a large composition space, specifically focusing on the Mo-Nb-Ti-V-W system as a representative Multi-Principal Element Alloy (MPEA) for potential use in next-generation gas turbine blades. Our approach is able to learn and adapt to unknown constraints in the design space, making decisions about the best course of action at each stage of the process. As a result, we identify 21 Pareto-optimal alloys that satisfy all constraints. Our proposed framework is significantly more efficient and faster than a brute force approach.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Using a surrogate-assisted Bayesian framework to calibrate the runoff-generation scheme in the Energy Exascale Earth System Model (E3SM) v1

Abstract. Runoff is a critical component of the terrestrial water cycle, and Earth system models (ESMs) are essential tools to study its spatiotemporal variability. Runoff schemes in ESMs typically include many parameters so that model calibration is necessary to improve the accuracy of simulated runoff. However, runoff calibration at a global scale is challenging because of the high computational cost and the lack of reliable observational datasets. In this study, we calibrated 11 runoff relevant parameters in the Energy Exascale Earth System Model (E3SM) Land Model (ELM) using a surrogate-assisted Bayesian framework. First, the polynomial chaos expansion machinery with Bayesian compressed sensing is used to construct computationally inexpensive surrogate models for ELM-simulated runoff at 0.5∘ × 0.5∘ for 1991–2010. The error metric between the ELM simulations and the benchmark data is selected to construct the surrogates, which facilitates efficient calibration and avoids the more conventional, but challenging, construction of high-dimensional surrogates for the ELM simulated runoff. Second, the Sobol' index sensitivity analysis is performed using the surrogate models to identify the most sensitive parameters, and our results show that, in most regions, ELM-simulated runoff is strongly sensitive to 3 of the 11 uncertain parameters. Third, a Bayesian method is used to infer the optimal values of the most sensitive parameters using an observation-based global runoff dataset as the benchmark. Our results show that model performance is significantly improved with the inferred parameter values. Although the parametric uncertainty of simulated runoff is reduced after the parameter inference, it remains comparable to the multimodel ensemble uncertainty represented by the global hydrological models in ISMIP2a. Additionally, the annual global runoff trend during the simulation period is not well constrained by the inferred parameter values, suggesting the importance of including parametric uncertainty in future runoff projections.

58 GEOSCIENCES↗
DOE OSTI2018

Bayesian optimization of generalized data

Direct application of Bayes' theorem to generalized data yields a posterior probability distribution function (PDF) that is a product of a prior PDF of generalized data and a likelihood function, where generalized data consists of model parameters, measured data, and model defect data. The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. A set of constraints imposed on the posterior expectation values and covariances of generalized data via a given model is formally solved by the method of Lagrange multipliers. Posterior expectation values of the constraints and their covariance matrix are conventionally set to zero, leading to a likelihood function that is a Dirac delta function of the constraining equation. It is shown that setting constraints to values other than zero is analogous to introducing a model defect. Since posterior expectation values of any function of generalized data are integrals of that function over all generalized data weighted by the posterior PDF, all elements of generalized data may be viewed as nuisance parameters marginalized by this integration. One simple form of posterior PDF is obtained when the prior PDF and the likelihood function are normal PDFs. For linear models without a defect this PDF becomes equivalent to constrained least squares (CLS) method, that is, the χ2 minimization method.

Arbanas, Goran↗
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↗