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DOE OSTI2023

Autonomous Inversion of In Situ Deformation Measurement Data for Injection-Induced Stress Change

Geologic carbon storage (GCS) is likely to play a key part of the global effort to dramatically reduce CO2 emissions and perhaps even reduce atmospheric CO2 concentrations through carbon negative operations. A critical part of effort to commercialize and widely deploy this technology is developing the capability to rapidly assimilate real-time monitoring data into a form that will enable site operators to make decisions to manage the safe and efficient operations. Two of the risks associate with GCS are the risk of inducing fractures in the sealing formations that can create leakage pathways and the risk of inducing earthquakes of sufficient magnitude to cause public concern, property damage, or safety risks. To properly manage these risks the site operator needs to know the initial state of stress, the change in stress induced by injection, and the relationship between operational parameters such as injection rate and pressure and the change in stress. Current methods of estimating the change in stress require choosing the type of constitutive model and the model parameters based on core, log, and geophysical data during the characterization phase, with little feedback from operational observations to validate or refine these choices. These characterization methods interrogate the geologic formations using length scales, loading rates or magnitudes that are quite different from those encountered by the actual storage system. It is shown that errors in the assumed constitutive response, even when informed by laboratory tests on core samples, are likely to be common, large, and underestimate the magnitude of stress change caused by injection. Recent advances in borehole-based strain instruments and borehole and surface-based tilt and displacement instruments have now enabled monitoring of the deformation of the storage system throughout its operational lifespan. This data can enable validation and refinement of the knowledge of the geomechanical properties and state of the system, but brings with it a challenge to transform the raw data into actionable knowledge. We demonstrate a method that uses automatic differentiation and a finite-element based geomechanical model perform a gradient-based deterministic inversion of geomechanical monitoring data. This approach allows autonomous integration of the instrument data without the need for time consuming manual interpretation and selection of updated model parameters. Furthermore, only isotropic linear elasticity is considered in this paper, the approach presented is very flexible as to what type of geomechanical constitutive response can be used. The approach is easily adaptable to nonlinear physics-based constitutive models to account for common rock behaviors such as creep and plasticity. The approach also enables training of machine learning-based constitutive models by allowing back propagation of errors through the finite element calculations. This enables strongly enforcing known physics, such as conservation of momentum and continuity, while allowing data-driven models to learn the truly unknown physics such as the constitutive or petrophysical responses.

Burghardt, Jeffrey A.↗

DOE OSTI2024

Quasilinear modelling of collisional trapped electron modes

The simplification of collision operators is necessary for quasilinear turbulence modelling used with integrated modelling frameworks, such as the gyrokinetic code QuaLiKiz. The treatment of collisions greatly impacts the accuracy of trapped electron mode (TEM) modelling, which is necessary to predict the electron heat flux and the balance between inward and outward particle fluxes. In particular, accurate particle flux predictions are necessary to successfully model density peaking in the tokamak core. We explored two ways of improving collisional TEM model reduction for tokamak core plasmas. First, we carried out linear GENE simulations to study the complex interplay between collisions and trapped electrons. We then used these simulations to define an effective trapped fraction to characterize the collisional TEM based on two key parameters, the local inverse-aspect ratio $\epsilon$ and the collisionality $\nu ^\ast$. One aspect missing from analytical TEM research is that the collisional frequency and the bounce-transit frequency are both velocity dependent; this effective trapped fraction takes both into account. In doing so, we determined that two parameters are not enough to model the collisional TEM, as an additional third free parameter was necessary. We determined that this model, as currently formulated, is not suitable for integrated modelling purposes. Second, we directly improved QuaLiKiz's Krook operator, which relies on two free parameters. We determined that these parameters required adjustments against higher-fidelity collisional models. In order to improve density profile predictions when paired with integrated models, we refined the Krook operator by using GENE simulations as a higher-fidelity point of comparison. We then demonstrate strong improvement of density peaking predictions of QuaLiKiz within the integrated modelling framework JETTO.

fusion plasma↗

DOE OSTI2020

Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Machine Learning (ML) Classifier to Assist Metadata Creation

The Atmospheric Radiation Measurement (ARM) Data Center is responsible for the timely collection, archival, and curation of science data products. These products are freely available through an online data repository. Metadata creation is paramount for scientific users to find and access over seven petabytes of atmospheric science data. The hierarchical metadata structure allows users to search for information at both broad and narrow levels. This project aims to leverage 30 years’ worth of manually created metadata to enable machine predictions of broad-term classifications from narrow-term descriptions. These classification predictions would assist metadata coordinators with their term selections. This paper discusses the cleaning and preprocessing of the training data, the pipeline developed to determine the best model for this task, and the creation of an API metadata classifier for ARM measurement metadata. Our results show that the Linear Support Vector Classification (LinearSVC) algorithm, along with the Term Frequency – Inverse Document Frequency (TF-IDF) vectorizer, is well-suited for our multi-class classification task. Lengthier input training data led to better results, and artificial balancing was unnecessary for this particular use case. This predictive classifier enhances efficiency in metadata creation, as well as supports greater consistency and accuracy in metadata tagging.

Collier, Hannah [ORNL] (ORCID:0000000341284292)↗

DOE OSTI2024

Simulations and models for the Richtmyer– Meshkov instability with broadband perturbations

The Richtmyer–Meshkov instability (RMI) is shock driven and affects many phenomena from inertial fusion to supernova explosions. The behavior of single-modes in the RMI has been studied extensively but less is known with the broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with an initial power spectrum of the form P∝ k m , where k is the wavenumber. The hydrodynamic condition is the same as in the $\theta$-Group Collaboration [Thornber et al., “Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The $\theta$-group collaboration,” Phys. Fluids 29, 105107 (2017)] with a Mach ~1.86 shock and gamma-law = 5/3 fluids with Atwood number A = 0.5. The bubble amplitude h B is found to grow in two stages. Initially, h B undergoes a phase-inversion and grows linearly in time (t) at a rate consistent with a linear theory. Asymptotically, h B grows as a power law $~t^{\theta}$ when $\langle{k}\rangle{|h_B|}$ > O(1), where $\langle{k}\rangle$ is the average wavenumber for the initial spectrum. The RMI behavior in simulations and modeling agree over a wide range of exponent m, spectral width, initial amplitude, and time. The agreement is quantified objectively using statistical analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Machine-learning prediction for quasiparton distribution function matrix elements

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-x dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken x) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small- x reliably. This means that very fine lattice spacing to minimize lattice artifacts at order $(P_za)^n$ will become crucial for next-generation LaMET-like structure calculations. Furthermore, such calculations require operators with long Wilson-link displacements, especially in finer lattice units, increasing the communication costs relative to that of the propagator inversion. In this work, we explore whether machine-learning algorithms can make predictions of correlators to reduce the computational cost of these LQCD calculations. We consider two algorithms, gradient-boosting decision tree and linear models, applied to LaMET data, the matrix elements needed to determine the kaon and $η_s$ unpolarized parton distribution functions (PDFs), meson distribution amplitude (DA), and the nucleon gluon PDF. We find that both algorithms can reliably predict the target observables with different prediction accuracy and systematic errors. The predictions from smaller displacement z to larger ones work better than those for momentum p due to the higher correlation among the data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗

DOE OSTI2022

Clump survival and migration in VDI galaxies: an analytical model versus simulations and observations

ABSTRACT We address the nature of the giant clumps in high-z galaxies that undergo violent disc instability, distinguishing between long-lived and short-lived clumps. We study the evolution of long-lived clumps during migration through the disc via an analytical model tested by simulations and confront theory with CANDELS-HST observations. The clump ‘bathtub’ model, which considers gas and stellar gain and loss, involves four parameters: the accretion efficiency α, the star formation rate (SFR) efficiency ϵd, and the outflow mass-loading factors for gas and stars, η and ηs. The corresponding time-scales are comparable to the migration time, two-three orbital times. The accretion-rate dependence on clump mass, gas, and stars, allows an analytical solution involving exponential growing and decaying modes. For the fiducial parameter values there is a main evolution phase where the SFR and gas mass are constant and the stellar mass is rising linearly with time. This makes the inverse specific SFR an observable proxy for clump age. When η or ϵd are high, or α is low, the decaying mode induces a decline of SFR and gas mass till the migration ends. Later, the masses and SFR approach an hypothetical exponential growth with a constant specific SFR. The model matches simulations with different, moderate feedbacks, both in isolated and cosmological settings. The observed clumps agree with our predictions, indicating that the massive clumps are long-lived and migrating. A challenge is to model feedback that is non-disruptive in massive clumps but suppresses SFR to match the galactic stellar-to-halo mass ratio.

Dekel, Avishai↗

DOE OSTI2021

Modeling Volatility-Based Aerosol Phase State Predictions in the Amazon Rainforest

Organic aerosol (OA) is a complex matrix of various constituents—fresh (primary organic aerosols—POA) and aged via oxidation (secondary organic aerosols—SOA), generated from biogenic, anthropogenic, and biomass burning sources. The viscosity of OA can be critical in influencing new particle formation, reactive uptake processes that impact evaporation-growth kinetics, and the lifetime of particles in the atmosphere. We report this work utilizes a well-defined relationship between volatility and viscosity for pure compounds, which we incorporated within the Weather Research and Forecasting Model coupled to chemistry (WRF-Chem) to simulate the phase state and viscosity of bulk OA during the dry-to-wet transition season (September–October) in the Amazon rainforest during 2014. Our simulations indicate spatial and temporal heterogeneity in aerosol phase state often not captured by global-scale models. We show the strong role of water associated with organic aerosol ($w_s$) as the dominant factor that can be used to quantitatively estimate OA viscosity. Analysis of WRF-Chem simulations across the entire atmospheric column indicates a strong inverse log-linear relationship between $w_s$ and OA viscosity with a correlation coefficient approaching 1, in the background and biomass burning-influenced conditions. At high altitudes where relative humidity (RH) and temperatures are low, our simulations indicate that OA exists in a semisolid-/solid-like phase state, consistent with previous studies. OA hygroscopicity is strongly correlated (ca. –0.8) with OA viscosity at RH ca. 30–50%, but this RH range is found mostly at low OA concentrations and the middle troposphere (ca. 6–10 km altitudes) in our simulated domain. OA hygroscopicity is uncorrelated with viscosity at higher-RH (near surface) and lower-RH (upper troposphere) regimes. At the urban site near surface, where day–night differences in RH are significant, RH is found to drive the phase state. At the background forested site near surface, where day–night RH differences are small, biomass burning-influenced OA is semisolid and a significant OA associated with background conditions is liquid-like. Simulations indicate a long tail of OA viscosity frequency distributions extending in the semisolid/solid regimes over background biogenic-influenced conditions due to the role of low-volatility OA components such as monoterpene oxidation products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗

DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗

DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗

DOE OSTI2024

Permeability and Induced Polarization of Mudstones

Electrical measurements can be used to estimate hydraulic properties such as permeability ( k ) in sedimentary rocks. Previous work has focused on sandstones, siltstones, and carbonates, while investigations on mudstones have rarely been reported. In this study, we report on electrical geophysical measurements for 23 mudstone samples using an experimental approach designed to reliably saturate these low permeability mudstones. The modified Hagen-Poiseuille model linking permeability to the formation factor ( F ) and an effective pore radius ( r ) provides an excellent fit to the data set with a near-constant pore radius, indicating that the effective porosity (1/ F ) is the controlling factor on k . In these samples, the surface area normalized to pore volume ( S por ), frequently used in permeability estimation models, varies by 1–2 orders of magnitude and is thus not a reliable proxy of the inverse effective hydraulic radius. The formation factor also exerts the primary control on induced polarization (IP) parameters, whereas Spor shows no relation to the IP parameters. A strong linear relationship is found between IP parameters (imaginary conductivity and normalized chargeability) and surface conductivity, although the proportionality factor is significantly lower than those observed in more permeable rocks and sediments. Apparent relationships between the polarization strength-derived and time constant-derived geophysical length scales and the effective hydraulic radius appear to be driven by variations in the electrochemical parameters (i.e., specific polarizability and diffusion coefficient). Overall, these findings emphasize that predicting hydraulic properties from electrical measurements in fine-grained rocks remains challenging and requires further investigation into the electrochemical properties involved.

58 GEOSCIENCES↗

DOE OSTI2025

The Efficiency of Water Vapor on Top‐of‐Atmosphere Radiation

Earth's climate sensitivity is greatly affected by the compensation between temperature feedback and water vapor (WV) feedback. Using abrupt 4xCO 2 experiments, we show that the global-mean WV feedback is nearly a linear function of the temperature feedback, the slope of which is explained by the longwave radiative efficiency of WV (ϵ). Although ϵ remains constant across models in the global mean, it exhibits substantial spatial variations and is particularly weak in Antarctica, where near-surface inversions decouple the surface from the free troposphere. We introduce a surface–free troposphere temperature difference (SFTD) metric, showing that positive SFTD (e.g., high lifting condensation level) amplifies ϵ, while negative SFTD (e.g., strong surface inversion) suppresses it. These findings provide a clear explanation of how local climate conditions modulate the radiative compensation between temperature and WV feedbacks.

climate feedback↗

DOE OSTI2021

Shear reflectivity compensation in full-waveform inversion using least-squares reverse-time migration

SUMMARY The computational cost of elastic-waveform inversion is too high for inverting PP reflections, while using acoustic full-waveform inversion (FWI) is inaccurate because it does not depend on the shear modulus/velocity/impedance that affects elastic PP wavefield amplitudes. To solve this problem, we develop a waveform inversion method that uses acoustic least-squares reverse-time migration (LSRTM) to compensate the shear reflectivity for acoustic FWI. Our method is based on the quasi-elastic-wave equation developed by Chapman et al. (2014). The quasi-elastic-wave equation uses a linearized acoustic-wave equation with shear modulus μ as a virtual source to correct the acoustic PP wavefield amplitudes toward elastic ones. Our waveform inversion method inverts for elastic parameters by minimizing the L2 norm of the difference between recorded and predicted PP reflections modelled using the quasi-elastic-wave equation. Numerical tests on synthetic and field data show that our method can properly handle the amplitudes of elastic PP reflections and provides an accurate estimate of the P- and S-wave velocities/impedances and, in some cases, the density. The method does not need the computationally expensive numerical solution to the elastic-wave equation. It also gives a better estimate of elastic parameters than a pure LSRTM method for elastic PP reflections.

Feng, Zongcai↗

DOE OSTI2020

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↗

DOE OSTI2024

MatCal Users Guide: Release 1.3.0

Any continuum mechanics model will require three components: (1) a discretized geometry of the boundary value problem being studied, (2) the partial differential equations to be solved, and (3) the initial conditions and boundary conditions for the problem. To describe material behavior in these computational models, material models contribute to (2) the underlying equations and, occasionally, to (3) the initial conditions for the simulation. These material models can exhibit a mathematical form that is empirically based, based on first principles, or developed from both empirical observations and known physics. In general, these models are meant to represent a class of materials with well understood behavior. As a result, material models have parameters that must be tuned or calibrated so that the model response matches characterization data available for the specific material it is intended to represent when used to simulate a specific system. For simple models, such as isotropic, linear elastic materials in solid mechanics, this calibration process can be a simple analytical calculation directly extracting the parameters from experimental measurements. For complex models that have many inputs and require many characterization datasets to adequately identify the material behavior, the model calibration process can require an inverse problem approach where an optimization is performed to tune the model parameters to the available data.

36 MATERIALS SCIENCE↗