Using Parametric Matrix Models to Emulate Magnus IMSRG
Using Parametric Matrix Models to Emulate Magnus IMSRG
Clark, Benjamin Reed [Facility for Rare Isotope Be↗
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A fully Lagrangian, non-parametric bias model for dark matter halos
Here, we present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at z=0.5. Unlike the perturbative halo bias model that has been widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity δ 1 in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may lead to rising halo number counts at negative overdensities. The shape of the halo-to-mass ratio is unlikely to be described by a polynomial function of δ 1 and other quantities. Especially for massive halos with 6×10 12 h -1 M ⊙ , the halo-to-mass ratio starts soaring up at δ 1 >0, substantially different from the predictions of the bias expansion. We show that for the halo masses we consider (M>3×10 11 h -1 M ⊙ ) a non-parametric halo-to-mass ratio as a function of δ 1 and its local derivative ∇^2δ 1 can recover the halo power spectra to sub-percent level accuracy for wavenumbers k=0.01-0.1 h Mpc -1 given a proper smoothing scale to filter the initial density field, even though we do not fit the power spectrum directly. However, there is mild dependence of the recovery of the halo power spectrum on the smoothing scale and other input parameters. At k<0.01 h Mpc -1 and for massive halos with M>6x10 12 h -1 M ⊙ , our non-parametric model leads to a few percent overestimation of the halo power spectrum, indicating the need for larger or multiple smoothing scales. The halo-to-mass ratios obtained qualitatively agree with intuitions from extended Press-Schechter theory. We compare our framework to the bias expansion and discuss possible extensions.
79 ASTRONOMY AND ASTROPHYSICS↗
Parametric model-order-reduction development for unsteady convection
A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parameter space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.
leray regularization↗
A new multi-model absolute difference-based sensitivity (MMADS) analysis method to screen non-influential processes under process model and parametric uncertainty
Process-based models have been widely used for hydrologic modeling, and it is a common practice to use sensitivity analysis methods for excluding non-influential hydrologic processes from further investigation and/or model improvement. This study develops a new method called multi-model absolute difference-based sensitivity (MMADS) analysis method to screen non-influential system processes and parameters. MMADS is conceptually similar to the Morris method for addressing parametric uncertainty, but has a unique feature to address both process model uncertainty (i.e., a process may be represented by multiple process models) and process model parameter uncertainty (i.e., parameters associated with a process model are random). MMADS first evaluates absolute differences of a quantity of interest (i.e., a system model output) by varying process models and/or process model parameter values, and then calculates the mean and variance of the differences for investigating process influence. The mean measures overall influence of the process on the quantity of interest, and the variance estimates influence of nonlinear effects of the process and/or its interactions with other processes. MMADS is an extension of the Morris method from a parameter space to a joint parameter-model space for explicitly addressing both process model uncertainty and model parameter uncertainty. The performance of MMADS is evaluated by using two numerical experiments. One experiment is based on Sobol’s G*-function with ten product elements, and has analytical solutions of the MMADS mean and variance of absolute differences. The other experiment is for groundwater flow modeling which considers three processes (i.e., recharge, geology, and snowmelt) that interact with each other. Finally, results indicate that MMADS is computationally efficient and can identify non-influential processes of complex hydrological systems.
54 ENVIRONMENTAL SCIENCES↗
Energy Saving Quantification on Ductless Heat Pump (DHP) in Existing Homes
In residential retrofit applications, ductless mini-split heat pumps (DHP) are often reported to have high-energy savings potential, depending on the system they are supplementing or replacing. However, recently, there have been a number of utility studies and analyses indicating these energy savings are not being achieved when the existing system is left in place for backup heating or air conditioning. The Pacific Northwest National Laboratory conducted a three-phase project to help determine which control strategies would have the most energy savings impact in various climate zones around the United States. The first phase developed the standalone simulation model for the PNNL Lab Homes and investigated the energy-saving potential from different control strategies and HVAC system configurations. The second phase focused on conducting experiments in the PNNL Lab Homes, which tested the most promising solutions that were modeled in the first phase. The third phase used the field data to calibrate the simulation model and then extrapolated the results to different climate locations and different building sizes. This report focuses on the third phase of the study, including five major parts: model calibration, parametric model setup, results, a sensitivity analysis of air leakage rate, and conclusions.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Quantifying wildfire drivers and predictability in boreal peatlands using a two-step error-correcting machine learning framework in TeFire v1.0
Abstract. Wildfires are becoming an increasing challenge to the sustainability of boreal peatland (BP) ecosystems and can alter the stability of boreal carbon storage. However, predicting the occurrence of rare and extreme BP fires proves to be challenging, and gaining a quantitative understanding of the factors, both natural and anthropogenic, inducing BP fires remains elusive. Here, we quantified the predictability of BP fires and their primary controlling factors from 1997 to 2015 using a two-step correcting machine learning (ML) framework that combines multiple ML classifiers, regression models, and an error-correcting technique. We found that (1) the adopted oversampling algorithm effectively addressed the unbalanced data and improved the recall rate by 26.88 %–48.62 % when using multiple datasets, and the error-correcting technique tackled the overestimation of fire sizes during fire seasons; (2) nonparametric models outperformed parametric models in predicting fire occurrences, and the random forest machine learning model performed the best, with the area under the receiver operating characteristic curve ranging from 0.83 to 0.93 across multiple fire datasets; and (3) four sets of factor-control simulations consistently indicated the dominant role of temperature, air dryness, and climate extreme (i.e., frost) for boreal peatland fires, overriding the effects of precipitation, wind speed, and human activities. Our findings demonstrate the efficiency and accuracy of ML techniques in predicting rare and extreme fire events and disentangle the primary factors determining BP fires, which are critical for predicting future fire risks under climate change.
54 ENVIRONMENTAL SCIENCES↗
Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems
Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.
DC–AC power systems↗
Control systems and methods using parametric driver model
A control system of a vehicle includes: a target speed module configured to, using a parametric driver model and based on first driver parameters, second driver parameters, and vehicle parameters, determine a target vehicle speed trajectory for a future predetermined period; a driver parameters module configured to determine the first driver parameters based on conditions within a predetermined distance in front of the vehicle; and a control module configured to adjust at least one actuator of the vehicle based on the target vehicle speed trajectory and a present vehicle speed.
Hegde, Bharatkumar↗
Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. II. Bayesian model calibration
Dynamic shockless compression experiments provide the ability to explore material behavior at extreme pressures but relatively low temperatures. Typically, the data from these types of experiments are interpreted through an analytic method called Lagrangian analysis. Here, in this work, alternative analysis methods are explored using modern statistical methods. Specifically, Bayesian model calibration is applied to a new set of platinum data shocklessly compressed to 570 GPa. Several platinum equation-of-state models are evaluated, including traditional parametric forms as well as a novel non-parametric model concept. The results are compared to those in Paper I obtained by inverse Lagrangian analysis. The comparisons suggest that Bayesian calibration is not only a viable framework for precise quantification of the compression path, but also reveals insights pertaining to trade-offs surrounding model form selection, sensitivities of the relevant experimental uncertainties, and assumptions and limitations within Lagrangian analysis. The non-parametric model method, in particular, is found to give precise unbiased results and is expected to be useful over a wide range of applications. The calibration results in estimates of the platinum principal isentrope over the full range of experimental pressures to a standard error of 1.6%, which extends the results from Paper I while maintaining the high precision required for the platinum pressure standard.
Brown, Justin Lee↗
Parametric model-order reduction for radiation transport using multi-resolution proper orthogonal decomposition
For parametric high-fidelity simulations, it is often desirable to utilize a reduced-order model (ROM) to emulate, at a reduced computational cost, parametric solutions of the governing partial differential equations (PDEs) for unseen parameter values. One commonly employed option is to utilize a data-driven, projection-based ROM supplemented with subspace identification via proper orthogonal decomposition (POD). POD discovers the ROM subspace by computing the singular value decomposition (SVD) of a set of training data from the full-order model (FOM). In streaming-dominated radiation transport simulations with localized sources, solutions often greatly vary over the spatial domain by many orders of magnitude. In such cases, machine-precision arithmetic can be insufficient to obtain an accurate SVD, resulting in a poorly performing ROM. We present a method called multiresolution POD (mrPOD) that mitigates these inaccuracies. The mrPOD method works by decomposing the spatial domain into regions and performing proper orthogonal decomposition on the training dataset separately in each region. In conclusion, mrPOD is tested on single energy group and multigroup atmospheric shielding transport problems and is shown to outperform classic POD.
42 ENGINEERING↗
Overview of Base Model in Parametric Studies Specific to Performance of U-Mo Plates
This paper provides an overview of the base model specifically developed to perform parametric sensitivity studies on the U-10Mo monolithic fuel system. U-Mo monolithic fuels are being considered for the conversion of test reactors into high-performance research reactors that operate using proliferation-resistant, low-enriched uranium (LEU) fuels. These plate-type fuels contain a high-density, low-enrichment fuel sandwiched between zirconium diffusion barriers and encapsulated in aluminum claddings. All U.S. high-performance research reactors have released the designs of their LEU monolithic fuel reactor cores. These designs include nearly 50 distinct fuel plate geometries with different operational parameters. Consequently, a single generic plate geometry representing all the extreme points in this design matrix is unrealistic. To evaluate the performance for various parameters, a set of sensitivity studies was performed. These studies considered various input parameters (i.e., geometric, operational, and material property-related). The results revealed valuable information about plate performance and the sensitivity of this performance to various modeling inputs. To establish a reference state for comparing these result, base model featuring representative irradiation conditions was developed. To capture in-reactor behavior accurately, incorporation of representative constitutive models capable of evolving properties with respect to temperature, irradiation time, and burnup was needed. The behavioral models considered burnup-dependent properties, swelling, creep, and degradation. This paper introduces the base model created for the parametric sensitivity studies. The detailed description of the procedure includes the model geometry, model discretization, thermo-mechanical coupling, material properties and behavioral models. This paper also provides selected results and assesses the performance of the base model.
42 ENGINEERING↗
Parametric raytracing modeling for NSTX-U scenario development with high harmonic fast waves and neutral beam injection
High harmonic fast waves (HHFW) are a versatile heating and current drive tool for scenario development. Extensive modeling scans were performed to find optimal parameters for different uses of HHFW in National Spherical Tokamak Experiment (NSTX-U). Scans of plasma density, temperature, magnetic field, and antenna phasing were performed both with and without neutral beam injection. For speed of calculation, the ray-tracing code GENRAY coupled to the quasilinear Fokker–Planck code CQL3D was used. CQL3D allows for a more accurate description of the fast ion population, as well as for quasilinear effects such as HHFW-induced modifications of the distribution function. Best current drive results are obtained at elevated electron temperatures and with the lowest k φ phasing. Adding neutral beams however typically strongly reduces the HHFW current drive efficiency at the low density cases due to HHFW absorption on beam ions. Results of this parametric study will feed into scenario development and predict-first whole-shot modeling of NSTX-U discharges.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Dynamical Mass Estimates of the β Pictoris Planetary System through Gaussian Process Stellar Activity Modeling
Nearly 15 yr of radial velocity (RV) monitoring and direct imaging enabled the detection of two giant planets orbiting the young, nearby star β Pictoris. The δ Scuti pulsations of the star, which overwhelm planetary signals, need to be carefully suppressed. In this work, we independently revisit the analysis of the RV data following a different approach than available in the literature to model the activity of the star. We show that a Gaussian process (GP) with a stochastically driven damped harmonic oscillator kernel can model the δ Scuti pulsations. It provides similar results to parametric models but with a simpler framework, using only three hyperparameters. It also enables us to model poorly sampled RV data that were excluded from previous analyses, hence extending the RV baseline by nearly five years. Altogether, the orbit and mass of both planets can be constrained from RV only, which was not possible with the parametric modeling. To characterize the system more accurately, we also perform a joint fit of all available relative astrometry and RV data. Our orbital solutions for β Pic b favor a low eccentricity of 0.029$_{−0.024}^{+0.061}$ and a relatively short period of 21.1$_{−0.8}^{+2.0}$ yr. The orbit of β Pic c is eccentric with 0.206$_{−0.063}^{+0.074}$ with a period of 3.36 ± 0.03 yr. We find model-independent masses of 11.7 ± 1.4 and 8.5 ± 0.5 M Jup for β Pic b and c, respectively, assuming coplanarity. The mass of β Pic b is consistent with the hottest start evolutionary models, at an age of 25 ± 3 Myr. A direct detection of β Pic c would provide a second calibration measurement in a coeval system.
79 ASTRONOMY AND ASTROPHYSICS↗
Accurate and Efficient Parametric Model-Order Reduction for Turbulent Thermal Transport
This project produced new algorithms and software for low-cost exploration of turbulent thermal-fluids behavior under parametric variation by using reduced-order models (ROMs). The ROMs numerically solve the governing equations for fluid motion by using a small set of basis functions (typically, N=20-200 modes) to represent the solution. The base modes are computed as optimal combinations of solutions from expensive high-fidelity "anchor-point" solutions involving millions of unknowns, which are typically generated by solving the full Navier-Stokes equations on a supercomputer. The ROM solution is itself a combination of the base modes, where the basis coefficients are determined by evolving an NxN system of nonlinear equations. The overarching idea is to use the inexpensive ROM to predict solutions under conditions where the parameters differ from the anchor-point conditions. Several ingredients are required to make ROMs useful for thermal hydraulics analysis. These include: a stable and accurate ROM that is capable of reproducing the large-scale dynamics of turbulent flow, error indicators than can guide the choice of anchor points, and low-cost mechanisms for evaluating nonlinear terms in the reduced equations.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models
In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.
97 MATHEMATICS AND COMPUTING↗
Process Interactions Can Change Process Ranking in a Coupled Complex System Under Process Model and Parametric Uncertainty
For a complex hydrologic system with multiple processes and process interactions, global sensitivity analysis is often used to identify important or influential parameters for model development and improvement. The identification is complicated by process model uncertainty, when a system process can be represented by multiple process models. This study develops a new total-effect process sensitivity index to identify influential processes under model uncertainty. This is done by extending Sobol's total-effect parameter sensitivity index for one system model to total-effect process sensitivity index for multiple system models to account for uncertainty in process models and model parameters. The total-effect process sensitivity index includes not only the first-order process sensitivity index for measuring the importance of individual processes but also higher-order indices that account for process interactions. The total-effect process sensitivity index can identify an influential process that itself and its interactions with other processes influence a model output. Here, the total-effect process sensitivity index is applied to two numerical examples: (a) Sobol's G*-functions with analytical solutions of first-order and total-effect process sensitivity indices, and (b) groundwater flow models with interactions between recharge, geology, and snowmelt processes. The second evaluation shows that, due to second-order and higher-order process interactions, the first-order and total-effect process sensitivity indices give different process ranking. It is thus necessary to estimate both first-order and total-effect process sensitivity indices to appreciate the difference between the first-order impact of a process alone and the overall total-effect impact of the process itself and its interactions with other processes on a model output.
54 ENVIRONMENTAL SCIENCES↗
Numerical Modeling and Parametric Study of a Dual Purpose Underground Thermal Battery
Buildings’ thermal energy systems for providing space heating/cooling consume a considerable amount of electricity nationwide. Integrating thermal energy storage with buildings’ thermal systems has the potential to shave the peak electric demand and to overcome the mismatch between the intermittent renewable power and the fluctuating daily demand for electricity. A novel dual-purpose underground thermal battery (DPUTB) has been developed to provide diurnal thermal energy storage in conjunction with a dual-source heat pump (DSHP)system. A two-dimensional numerical model is developed to simulate the transient performance of the DPUTB. This model has similar accuracy as a detailed three-dimensional model developed with commercial heat transfer and fluid dynamics simulation program but with 1000 times faster computational speed. A parametric study is performed to identify a design of the DPUTB that can provide 14 kWh thermal storage capacity for each charging and discharging cycle. A system simulation has been developed to assess the performance of the designed DPUTB when it is integrated with a DSHP for conditioning a typical residential building in summer and winter. Simulation results indicate that the DPUTB can meet all the design requirements in both summer and winter with the simple rule-based control strategy and the overall integrated DPUTB and DSHP system can shift the electric load for meeting the thermal demand from the peak hours to off-peak hours during a day, which would result in considerable energy cost savings if a Time of Use electricity tariff is applicable.
25 ENERGY STORAGE↗
Characterization of the Atmosphere of Super-Earth 55 Cancri e Using High-resolution Ground-based Spectroscopy
The nearby super-Earth 55 Cnc e orbits a bright (V = 5.95 mag) star with a period of -18 hr and a mass of -8M {sub ⊕}. Its atmosphere may be water-rich and have a large-scale height; though, attempts to characterize it have yielded ambiguous results. Here we present a sensitive search for water and TiO in its atmosphere at high spectral resolution using the Gemini North telescope and the GRACES spectrograph. We combine observations with previous observations from Subaru and CFHT, improving the constraints on the presence of water vapor. We adopt parametric models with an updated planet radius based on recent measurements, and use a cross-correlation technique to maximize sensitivity. Our results are consistent with atmospheres that are cloudy or contain minimal amounts of water and TiO. Using these parametric models, we rule out a water-rich atmosphere (VMR ≥ 0.1%) with a mean molecular weight of ≤ 15 g mol{sup -1} at a 3σ confidence level, improving on the previous limit by a significant margin. For TiO, we rule out a mean molecular weight of ≤ 5 g mol{sup -1} with a 3σ confidence level for a VMR greater than 10{sup -8}; for a VMR of greater than 10{sup -7}, the limit rises to a mean molecular weight of ≤ 10 g mol{sup -1}. We can rule out low mean-molecular-weight chemical equilibrium models both including and excluding TiO/VO at very high confidence levels (>10σ). Overall, our results are consistent with an atmosphere with a high mean molecular weight and/or clouds, or no atmosphere.
79 ASTRONOMY AND ASTROPHYSICS↗