Considerations for the Identification of Elasto-Plastic Material Model Parameters
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Fayad, Samuel Saiid↗
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Uncertainty quantification of material parameters in modeling coupled metal and high explosive experiments
Experiments involving the coupling of metal and high explosives (HE) are of notable defense-related interest, and we seek to refine the uncertainty quantification associated with models of such experiments. In particular, our focus is on how uncertainty related to the metal constitutive model challenges our ability to infer high explosive model parameters when analyzing focused science experiments. We consider three focused experiments involving an HE accelerating metal: small plate tests with tantalum/LX-14 and tantalum/LX-17 pairings as well as a tantalum/LX-17 cylinder test. For all three models, we perform sensitivity analysis to ascertain the influence of metal strength on the coupled experimental response. Moreover, we calibrate each model in a Bayesian setting and study the quantification of metal strength on the inference of the HE parameters. Based on our results, we offer guidance for future metal/HE experiments.
36 MATERIALS SCIENCE↗
Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model
The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. Furthermore, the combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.
54 ENVIRONMENTAL SCIENCES↗
Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics
Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .
97 MATHEMATICS AND COMPUTING↗
Using Deep Learning Models to Characterize Subsurface Physical Parameters at Modeled Underground Chemical Explosion Sources
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Harding, Jennifer Logan↗
Bayesian uncertainty quantification of tristructural isotropic particle fuel silver release: Decomposing model inadequacy plus experimental noise and parametric uncertainties
Tristructural isotropic (TRISO) particle fuel is one of the most promising fuel concepts enabling high temperature and high burnup reactor operation. One dominant source of radioactivity released from the TRISO particles is silver (Ag), which is subject to a high release fraction and long decay life compared to other fission products. Previous modeling efforts using the fuel performance code BISON indicated nonnegligible uncertainties in modeling the diffusion process of fission products in TRISO compared to the Advanced Gas Reactor experiments. The overall uncertainties observed when modeling the fission product diffusion can result from uncertainties in model parameters, noisy experimental measurements, and deficiencies in the developed models. The three types of underlying uncertainties have not yet been properly quantified in open literature. Here, this paper presents the Bayesian uncertainty quantification (UQ) using massively parallelizable Markov chain Monte Carlo samplers. The uncertainties due to model parameters, model inadequacy, and experimental measurement noise are quantified, with the σ term used to represent the sum of the model inadequacy and measurement noise uncertainties. It is worth noting that this is the first time the σ term is inferred for nuclear fuel experiments, as compared to using prescribed values for uncertainty quantification in previous work. The parallelizable Markov chain Monte Carlo samplers efficiently infer the model parameters and the σ term, giving insight into physical parameters like diffusion coefficients and the combined model discrepancy and measurement noise. A subsequent forward uncertainty quantification (UQ) is also performed based on the calibration results to generate more accurate predictions of the Ag release. The model inadequacy plus experimental noise is the most dominant source of uncertainty compared to the parametric uncertainty. All the UQ analyses presented in this work are based on the second series of the irradiation experiments in the Advanced Gas Reactor program.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling
Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.
42 ENGINEERING↗
Photosynthetic responses of switchgrass to light and CO 2 under different precipitation treatments
Switchgrass ( Panicum virgatum L .) is a prominent bioenergy crop with robust resilience to environmental stresses. However, our knowledge regarding how precipitation changes affect switchgrass photosynthesis and its responses to light and CO 2 remains limited. To address this knowledge gap, we conducted a field precipitation experiment with five different treatments, including −50%, −33%, 0%, +33%, and +50% of ambient precipitation. To determine the responses of leaf photosynthesis to CO 2 concentration and light, we measured leaf net photosynthesis of switchgrass under different CO 2 concentrations and light levels in 2020 and 2021 for each of the five precipitation treatments. We first evaluated four light and CO 2 response models (i.e., rectangular hyperbola model, nonrectangular hyperbola model, exponential model, and the modified rectangular hyperbola model) using the measurements in the ambient precipitation treatment. Based on the fitting criteria, we selected the nonrectangular hyperbola model as the optimal model and applied it to all precipitation treatments, and estimated model parameters. Overall, the model fit field measurements well for the light and CO 2 response curves. Precipitation change did not influence the maximum net photosynthetic rate ( P max ) but influenced other model parameters including quantum yield ( α ), convexity ( θ ), dark respiration ( Rd ), light compensation point ( LCP ), and saturated light point ( LSP ). Specifically, the mean P max of five precipitation treatments was 17.6 μmol CO 2 m −2 s −1 , and the ambient treatment tended to have a higher P max . The +33% treatment had the highest α , and the ambient treatment had lower θ and LCP , higher Rd , and relatively lower LSP . Furthermore, precipitation significantly influenced all model parameters of CO 2 response. The ambient treatment had the highest P max , largest α , and lowest θ , R d , and CO 2 compensation point LCP . Overall, this study improved our understanding of how switchgrass leaf photosynthesis responds to diverse environmental factors, providing valuable insights for accurately modeling switchgrass ecophysiology and productivity.
09 BIOMASS FUELS↗
PINN surrogate of Li-ion battery models for parameter inference, Part II: Regularization and application of the pseudo-2D model
Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of ~2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. Finally, in the low-data availability scenario, the testing error was estimated to ~2 mV for the SPM surrogate and ~10 mV for the P2D surrogate which could be mitigated with additional data.
25 ENERGY STORAGE↗
Improved geophysical monitoring of carbon sequestration through parameter linkage to reservoir modeling
Predictive reservoir modeling, even if present in the form of only basic hydrogeological model assumptions, is expected to accompany the majority of carbon capture and sequestration monitoring activities. It thus represents a source of prior information about the migration of injected fluids that can benefit geophysical survey planning and ensuing monitoring. Constraining the imaging of geophysical monitoring data with reservoir modeling is preferable over standalone geophysical imaging because of additional complementary hydrogeological information. However, fully coupled hydrogeophysical data inversion for flow-modeling parameters that control saturation predictions is an involved process. Within the context of three-dimensional electromagnetic (EM) inversion of data from borehole-to-surface layouts, we employ a "poor people's" alternative. The approach constrains geophysical inversion parameters through saturation predictions. The coupling is realized through spatially variable lower and upper parameter bounds that scale with gas saturation magnitudes, the latter provided by reservoir modeling. In this work, enhancement of three-dimensional time-lapse plume EM imaging is demonstrated for simulated sequestration into a depleted gas reservoir.
58 GEOSCIENCES↗
Robust Statistical Approach for Determination of Graphite Nitridation Using Bayesian Model Comparison
A better estimation of surface reaction efficiency of semiconductor-grade graphite with atomic nitrogen, as well as the calibration error are calculated using Bayesian updating based on experimental data. Compared with a conventional deterministic model, the stochastic model approach is a powerful tool in the sense that the model is capable of taking into account underlying error correlations among the data quantities. In this paper, we investigate four different stochastic models (called “stochastic system model classes” herein) corresponding to different descriptions of modeling and measurement error structures, given one deterministic physical model. These stochastic system model classes differ in the covariance matrix structure that is used in the uncertainty model to represent uncertainties associated with the physical model and experimental measurements. For each model class, Bayesian inference is used to estimate the posterior probabilities of the physical model parameters as well as of the stochastic model parameters. Model comparison and selection are then applied based on two measures including Bayesian evidence and Bayesian information criterion, as well as the deviance information criterion. Both measures suggest the stochastic model class, which considers that a correlation between errors in two data quantities among different data points is the most plausible. With the stochastic model class, the range of uncertainty in surface reaction efficiency is estimated to be about two orders of magnitude at [Formula: see text].
Engineering↗
Contrasting Parametric Sensitivities in Two Global Vegetation Models Using Parameter Perturbation Ensembles
Uncertainty in land model projections remains high and the roles of parametric and structural uncertainty are difficult to disentangle. To compare parametric sensitivity across model structures we present two parameter perturbation ensembles using the Community Land Model (CLM) operating in satellite phenology mode. The ensembles contrast two vegetation modules: (a) the default CLM vegetation module and (b) the Functionally Assembled Terrestrial Ecosystem Simulator (CLM-FATES). We perturbed over 300 parameters and quantified their effects on biophysical fluxes globally and across biomes. Most parameters have minimal impact on biophysical fluxes, with only a few substantially influencing results. While both models exhibit similar parameter sensitivity for some fluxes, CLM-FATES shows larger spread in gross primary productivity (GPP), driven by strong sensitivity to carboxylation rate. CLM-FATES also shows a weaker GPP response to soil hydrology parameters and exhibits higher water use efficiency (WUE). Cross-model comparisons reveal similar sensitivities for some parameters (e.g., leaf dimension) but divergent responses to others (e.g., stomatal intercept), highlighting underlying structural differences. Differences in WUE and sensitivity to hydrology and stomatal conductance parameters underscore how model structure fundamentally alters parametric sensitivity. The data sets generated from these ensembles can be used to identify influential parameters and guide future calibration efforts.
Foster, A. C. [NSF National Center for Atmospheric↗
Modelling type 1 quasar colours in the era of Rubin and Euclid
We construct a parametric SED model which is able to reproduce the average observed SDSS–UKIDSS–WISE quasar colours to within one-tenth of a magnitude across a wide range of redshift (0 < z < 5) and luminosity (–22 > M i > –29). This model is shown to provide accurate predictions for the colours of known quasars which are less luminous than those used to calibrate the model parameters, and also those at higher redshifts z > 5. Using a single parameter, the model encapsulates an up-to-date understanding of the intra-population variance in the rest-frame ultraviolet and optical emission lines of luminous quasars. At fixed redshift, there are systematic changes in the average quasar colours with apparent i-band magnitude, which we find to be well explained by the contribution from the host galaxy and our parametrization of the emission-line properties. By including redshift as an additional free parameter, the model could be used to provide photometric redshifts for individual objects. For the population as a whole we find that the average emission line and host-galaxy contributions can be well described by simple functions of luminosity which account for the observed changes in the average quasar colours across 18.1 < i AB < 21.5. Finally, we use these trends to provide predictions for quasar colours at the luminosities and redshifts which will be probed by the Rubin Observatory LSST and ESA-Euclid wide survey. The model code is applicable to a wide range of upcoming photometric and spectroscopic surveys, and is made publicly available.
79 ASTRONOMY AND ASTROPHYSICS↗
Updated parameters of the LArQL model
The need for a microscopic description of scintillation light generation in liquid argon becomes increasingly desirable with the upcoming operation of large scale LArTPCs in the next decade. While a detailed mathematical account of the process is still to be achieved, a phenomenological model for simultaneously treating ionization and scintillation, LArQL, has been successfully employed to describe the range of electric fields from 0 to 0.75 kV/cm and dE/dx from 2 to 40 MeV/cm providing the anti-correlation between the free ionization charge and scintillation light. A reanalysis of the original model parameter values has been performed within a global fit procedure and is presented.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Mathematical modeling and parameter estimation of MFI membranes for para/ortho‐xylene separation
Abstract A mathematical model of a membrane with a thin, oriented, and selective MFI layer, which also includes contributions from defects, pore blockages, support layer, and external mass transfer, was formulated based on the Maxwell‐Stefan equations. It was validated using reported (Kim et al., Angew Chemie Int Ed, 2018, 57:480–485; Jeon et al., Nature, 2017, 543:690–694) para/ortho‐xylene separation data from five MFI membranes. The diffusivities of the xylenes were considered to be the same for all membranes, while the thickness and the density of defects and pore blockage were treated as unique properties of each membrane, and their contributions were estimated by fitting the model to the corresponding separation data. The effects of these properties and the role of permeate pressure on the separation performance were subsequently analyzed. The proposed modeling, parameter estimation, and analysis framework allow one to quantitatively interpret the variation of separation performance, to understand separation bottlenecks, and to provide guidance for designing membranes with desired performance.
Liu, Jingjun↗
Machine learning assisted modeling of mixing timescale for LES/PDF of high-Karlovitz turbulent premixed combustion
Accurate modeling of mixing in the transported probability density function (PDF) method remains a great challenge, especially for turbulent premixed combustion under extreme conditions such as high Karlovitz number Ka. Recently, a power-law based mixing timescale model was developed for the large-eddy simulations (LES)/PDF modeling of high-Ka number turbulent premixed flames. It is found in this work that the power-law mixing timescale model is highly sensitive to the model parameters. It is thus critically needed to develop accurate calibration of these model parameters. The empirical specification of the model parameters developed in Zhang et. al. is found to be inadequate for accurate modeling of the mixing timescale. Here, machine learning is introduced as an attractive alternative in this work for the specification of the model parameters. A high-Ka number DNS jet flame is used as the training and validation of the machine learning models. The choices of the input parameters are discussed and compared for the machine learning models. The effect of differential molecular diffusion on mixing is examined by including the effect of the Lewis number in the training of the machine learning models. The performance of different machine learning algorithms is compared for the specification of the mixing model parameters. Overall, excellent performance of the machine learning models is observed for assisting the mixing modeling. The feasibility, interpretability, applicability, generality, and portability of using machine learning are discussed in general to provide a perspective on applying data-driven machine learning for turbulent combustion modeling studies.
42 ENGINEERING↗
LANL end of the year report (2023)
This report summarizes the advances made by LANL in the XMAT-H2 program over FY23. In summary LANL was tasked with leading efforts related to (1) the development of models predicting hydrogen (H) redistribution within polycrystals (H redistribution model), (2) the development of models for the mechanical performance of metals/steels under H environments (Model for H effects on plasticity), The development of a framework to quantify the uncertainty in model parameters (Uncertainty in model parameters), (3) small scale characterization of the mechanical response of 347H (Microstructure characterization).
08 HYDROGEN↗
Spread Spectrum Time Domain Reflectometry and Steepest Descent Inversion to Measure Complex Impedance
In this paper, we present a method for estimating complex impedances using reflectometry and a modified steepest descent inversion algorithm. We simulate spread spectrum time domain reflectometry (SSTDR), which can measure complex impedances on energized systems for an experimental setup with resistive and capacitive loads. A parametric function, which includes both a misfit function and stabilizer function, is created. The misfit function is a least squares estimate of how close the model data matches observed data. The stabilizer function prevents the steepest descent algorithm from becoming unstable and diverging. Steepest descent iteratively identifies the model parameters that minimize the parametric function. We validate the algorithm by correctly identifying the model parameters (capacitance and resistance) associated with simulated SSTDR data, with added 3 dB white Gaussian noise. With the stabilizer function, the steepest descent algorithm estimates of the model parameters are bounded within a specified range. Furthermore, the errors for capacitance (220pF to 820pF) and resistance (50 Ω to 270 Ω) are < 10%, corresponding to a complex impedance magnitude |R +1/jωC| of 53 Ω to 510 Ω.
14 SOLAR ENERGY↗