Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “process uncertainty”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

Integrating field observations and process-based modeling to predict watershed water quality under environmental perturbations

Watersheds play a critical role in supplying water resources needed for human use and ecosystem health. Understanding and predicting how, when, and where changes in the quantity and quality of water resources occur under different environmental stresses including extreme events is crucial for sustainable management of water resources under a changing environment. However, few studies have attempted to quantify or identify the factors and process interactions controlling the impact of extreme events across water-shed systems. Only few large-scale studies include coordinated monitoring and modeling efforts, which limits our ability to assess the large-scale impact of extreme events on water supply and quality. Methods are lacking to propagate uncertainty in process understanding through an integrated hydro-biogeochemical model framework and evaluate its importance, thus failing to take full advantage of the information potentially available through transformative advances in characterization technologies from high-resolution mass spectrometry to airborne and satellite-based remote sensing. There are consequent risks to our nations water security and to human and ecosystem health that may become exacerbated with the increasing frequency of extreme events that is projected for the coming decades. This paper reviews the current status of watershed science for both water quantity and quality and identifies critical gaps in our current knowledge and modeling capability in addressing the emergent needs in predicting watershed hydrologic and biogeochemical responses (i.e., water quantity and quality) under natural and anthropogenic perturbations. We highlight the need to (1) understand how environmental perturbations including extreme events like floods and droughts propagate through watershed systems and assess their short- and long-term impacts on watershed biogeochemistry, water quality and their recovery pathways; (2) develop and improve a watershed water quality model that reflects the state of scientific understanding gained from observations; and (3) construct a data-model fusion system for watershed characterization, process identification, and mechanistic model parameterization. A large base of modeling, monitoring and data capabilities have been built by various federal government agencies given the relevance of water to their critical missions. An emerging need is to build an integrated national capability for watershed water availability and quality that can address water-related missions across multiple federal agencies.

13 HYDRO ENERGY↗

Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield

The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely matched the measured surface pressures. This observation is somewhat surprising, given that stress-limiting models have generally been developed to better predict shock-separated flows. All of the models considered also failed to properly predict the shape and extent of the separated flow region caused by the shock boundary layer interactions. However, the best performing models were able to predict the isolator shock train length (an important metric for isolator operability margin) to within 1 isolator duct height.

Baurle, Robert A.↗

TPSAS-NF1676L-32640-DND

Computational fluid dynamics is now considered to be an indispensable tool for the design and development of scramjet engine components. Unfortunately, the quantification of uncertainties is rarely addressed with anything other than sensitivity studies, so the degree of confidence associated with the numerical results remains exclusively with the subject matter expert that generated them. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Given the limitations of current hypersonic ground test facilities, this expanded role is believed to be a requirement by some in the hypersonics community if scramjet engines are to be given serious consideration as a viable propulsion system. The present effort describes a simple, relatively low cost, nonintrusive approach to uncertainty quantification that includes the basic ingredients required to handle both aleatoric (random) and epistemic (lack of knowledge) sources of uncertainty.

Robert A Baurle↗

Sources of Uncertainty in Predicting Land Surface Fluxes Using Diverse Data and Models

In the domain of predicting land surface fluxes, models are used to bring data from large observation networks and satellite remote sensing together to make predictions about present and future states of the Earth. Characterizing the uncertainty about such predictions is a complex process and one that is not yet fully understood. Uncertainty exists about initialization, measurement and interpolation of input variables; model parameters; model structure; and mixed spatial and temporal supports. Multiple models or structures often exist to describe the same processes. Uncertainty about structure is currently addressed by running an ensemble of different models and examining the distribution of model outputs. To illustrate structural uncertainty, a multi-model ensemble experiment we have been conducting using the Terrestrial Observation and Prediction System (TOPS) will be discussed. TOPS uses public versions of process-based ecosystem models that use satellite-derived inputs along with surface climate data and land surface characterization to produce predictions of ecosystem fluxes including gross and net primary production and net ecosystem exchange. Using the TOPS framework, we have explored the uncertainty arising from the application of models with different assumptions, structures, parameters, and variable definitions. With a small number of models, this only begins to capture the range of possible spatial fields of ecosystem fluxes. Few attempts have been made to systematically address the components of uncertainty in such a framework. We discuss the characterization of uncertainty for this approach including both quantifiable and poorly known aspects.

Dungan, Jennifer L.↗

A Monte Carlo study of photochemical model uncertainties affecting the calculation of subsonic perturbations in the upper troposphere

Monte Carlo methods are frequently applied to the evaluation of uncertainties in models with multiple inputs that themselves have associated imprecisions. In the case of photochemical models used to evaluate changes in O3 or OH, inputs analyzed include rate coefficients measured in the laboratory, and chemical and physical constituents measured in the atmosphere. The Monte Carlo method was used with the 1-dimensional GSFC tropospheric photochemical model to examine uncertainty propagation to calculation of NO(x) and the major oxidants (O3, OH) in the upper troposphere. In all cases chemical kinetics inputs are varied and the NO(x) perturbation of a subsonic fleet is simulated. A series of model runs is used to explore sensitivities of model-computed parameters to other parameters: heterogeneous processes, the uncertainty in upper tropospheric H2O vapor measurements, aircraft emissions at different latitudes.

Thompson, Anne M.↗

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

Calibration of Predictor Models Using Multiple Validation Experiments

This paper presents a framework for calibrating computational models using data from several and possibly dissimilar validation experiments. The offset between model predictions and observations, which might be caused by measurement noise, model-form uncertainty, and numerical error, drives the process by which uncertainty in the models parameters is characterized. The resulting description of uncertainty along with the computational model constitute a predictor model. Two types of predictor models are studied: Interval Predictor Models (IPMs) and Random Predictor Models (RPMs). IPMs use sets to characterize uncertainty, whereas RPMs use random vectors. The propagation of a set through a model makes the response an interval valued function of the state, whereas the propagation of a random vector yields a random process. Optimization-based strategies for calculating both types of predictor models are proposed. Whereas the formulations used to calculate IPMs target solutions leading to the interval value function of minimal spread containing all observations, those for RPMs seek to maximize the models' ability to reproduce the distribution of observations. Regarding RPMs, we choose a structure for the random vector (i.e., the assignment of probability to points in the parameter space) solely dependent on the prediction error. As such, the probabilistic description of uncertainty is not a subjective assignment of belief, nor is it expected to asymptotically converge to a fixed value, but instead it casts the model's ability to reproduce the experimental data. This framework enables evaluating the spread and distribution of the predicted response of target applications depending on the same parameters beyond the validation domain.

Crespo, Luis G.↗

Distribution System State Estimation With High Penetration of Demand Response Enabled Loads

Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. Additionally, the inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Probabilistic Look-ahead Contingency Analysis Integration with Commercial Tool and Practical Data

This paper presents an initial effort of integrating a smart sampling-based probabilistic look-ahead contingency analysis algorithm with General Electric (GE) Grid Solutions’ commercial energy management system (EMS) tool as a proof-of-concept for a seamless research tool integration using real world large-scale grid data. With the increasing impact of random forces such as variable generation and load, their stochastic behaviors cannot be ignored. However, the current practices are still dominated by deterministic tools. They are becoming increasingly inadequate for the future grid. The developed look-ahead contingency analysis algorithm incorporates forecast errors of variable energy and load to address the challenges brought by the increasing uncertainty of power system. The algorithm can reveal the potential violations caused by the variance of variable energy and load that are not normally detected by traditional deterministic approaches. To test its performance under practical environments ( real data with real commercial tool), significant efforts have been made to prepare test cases, modify GE EMS tool, and adapt an extreme value distribution algorithm to analyze the GE EMS’s violation-only outputs. The test results clearly demonstrate the effectiveness of the developed algorithm as new transformer violations that were not previously detected have been identified. This performance provides better situational awareness to engineers for their decision-making process under uncertainty. Moreover, with the discussion of computational performance and future work, this paper has shown a clear path for integrating the probabilistic algorithm with commercial tools to make us better equipped for the changing power system.

Modeling and simulation of power systems, constrai↗

Uncertainty quantification in electromagnetic observables of nuclei

We present strategies to quantify theoretical uncertainties in modern ab initio calculations of electromagnetic observables in light and medium-mass nuclei. We discuss how uncertainties build up from various sources, such as the approximations introduced by the few- or many-body solver and the truncation of the chiral effective field theory expansion. We review the recent progress encompassing a broad range of electromagnetic observables in stable and unstable nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Revisiting proton–proton fusion in chiral effective field theory

We calculate the S-factor for proton–proton fusion using chiral effective field theory interactions and currents. By performing order-by-order calculations with a variety of chiral interactions that are regularized and calibrated in different ways, we assess the uncertainty in the S-factor from the truncation of the effective field theory expansion and from the sensitivity of the S-factor to the short-distance axial current determined from three- and four-nucleon observables. We find that S(0) = (4.100 ± 0.024(syst) ± 0.013(stat) ± 0.008(g$_{A}$)) × 10$^{−23}$ MeV fm$^{2}$, where the three uncertainties arise, respectively, from the truncation of the effective field theory expansion, use of the two-nucleon axial current fit to few-nucleon observables and variation of the axial coupling constant within the recommended range. The increased value of S(0) compared to previous calculations is mainly driven by an increase in the recommended value for the axial coupling constant and is in agreement with a recent analysis based on pionless effective field theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Multi-Model and Multi-Scale Global Sensitivity Analysis for Identifying Controlling Processes of Complex Systems

An environmental model consists of multiple process level sub-models, and each sub-model represents a process that is key to the operation of the simulated system. Global sensitivity analysis methods have been widely used to identify important processes for system model development and improvement. The existing methods of global sensitivity analysis only consider parametric uncertainty, and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes. To address this problem, this project develops a new method to probe model output sensitivity to competing process models by integrating model averaging methods with variance-based global sensitivity analysis to address uncertainty in process models and parameters. The new method yields three process sensitivity indices. The first one is called first-order process sensitivity index, and it is derived as a single summary measure of relative process importance. Evaluating the index is computationally expensive, because it relies in a Monte Carlo scheme that requires thousands and even millions of model executions. To reduce computational cost, this project develops a computationally efficient, quasi Monte Carlo method, and this method is presented in Chapter 2 of this report with and a numerical example for demonstration. The numerical example shows that the results of the quasi Monte Carlo method are substantially close to those of the full Monte Carlo method, but the computational cost of the quasi Monte Carlo method is only 0.7% of that of the full Monte Carlo method. The second index is called total-effect process sensitivity index, and it measures interactions between different processes. Therefore, this sensitivity index includes the first-order process sensitivity index, and can be used to identify influential processes. On the other hand, the total-effect process sensitivity index can also be used to screen non-influential processes. This is demonstrated by two numerical examples using the Sobol-G* functions and groundwater flow models that consider recharge process, geological process, and snowmelt process. The numerical examples shows that the total-effect process sensitivity index is more informative than the first-order process sensitivity. The derivation of the process sensitivity index and the numerical examples are discussed in Chapter 3. Chapter 4 presents two computationally efficient methods for screening non-influential processes to exclude them from further investigation. The two methods are the multi-model difference-based sensitivity (MMDS) analysis method, which can be implemented using the Latin Hypercube Sampling. The second one is the implementation of MMDS method using a binning method. The numerical example for the Sobol-G* function indicates the two methods are capable of identifying non-influential models, and the numerical examples for the groundwater flow and reactive transport show that the two methods are effective for groundwater problems. However, it should be noted that the two methods are numerical approximations, and they can only be used for screening non-influential processes, not for ranking importance of system processes. All the sensitivity analysis methods are implemented by developing python codes, and the codes are in a software called SAMMPY: a python package for process sensitivity analysis under multiple models. The SAMMPY design and structure are discussed in Chapter 5, and the package is released to the public for free download.

54 ENVIRONMENTAL SCIENCES↗

Robust Scheduling of Microgrids Considering Unintentional Islanding Conditions

This paper proposes a robust scheduling model for microgrids considering the stochastic unintentional islanding conditions. The proposed model minimizes the total operating cost of the microgrid by efficiently coordinating the supply of power from local distributed energy resources and the main grid. To capture the prevailing uncertainties in renewable generation and demand as well as unintentional islanding conditions, a two-stage adaptive robust optimization model is formulated to minimize the total operating cost under the worst realization of the modeled uncertainties. The column and constraint generation (C&CG) method is used to solve the problem in an iterative manner. The solution of the proposed scheduling model ensures robust microgrid operation in consideration of all possible realization of renewable generation, demand and unintentional islanding condition. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, two micro-turbines, a diesel generator and a battery demonstrate the effectiveness of the proposed approach.

Liu, Guodong↗

Simultaneous inference of equation of state parameters and unknown data errors with uncertainty quantification via hierarchical Bayesian posterior maximization

Equations of state (EOSs) are a key component in running hydrodynamic simulations as they relate the thermodynamic states for the material. The Davis reactants EOS is commonly used for modeling high explosives (HEs), and the EOS model parameters are calibrated using material specific data. The calibrations are often performed with uncertainty quantification via Bayesian inference to account for uncertainty in the data and generate ensembles of likely parameters. However, there are relatively few HE data sets to use for calibration and many are historical and lack error information. In this work, we simultaneously calibrate the Davis reactants EOS model parameters and unknown data error terms for the high explosive PBX 9501. To quantify the uncertainty in the models and the data, we use a Bayesian framework for the calibration and compute the hierarchical Bayesian posterior distribution with both a posteriori maximization approach and Markov Chain Monte Carlo. In general, we find that, given our assumptions, the two approaches result in similar calibrated parameters, posterior covariance matrices, and insights about the parameters but that the posterior maximization requires far less computational resources.

97 MATHEMATICS AND COMPUTING↗

Climate Change and Drought: From Past to Future

Drought is a complex and multivariate phenomenon influenced by diverse physical and biological processes. Such complexity precludes simplistic explanations of cause and effect, making investigations of climate change and drought a challenging task. Here, we review important recent advances in our understanding of drought dynamics, drawing from studies of paleoclimate, the historical record, and model simulations of the past and future. Paleoclimate studies of drought variability over the last two millennia have progressed considerably through the development of new reconstructions and analyses combining reconstructions with process-based models. This work has generated new evidence for tropical Pacific forcing of megadroughts in Southwest North America, provided additional constraints for interpreting climate change projections in poorly characterized regions like East Africa, and demonstrated the exceptional magnitude of many modern era droughts. Development of high resolution proxy networks has lagged in many regions (e.g., South America, Africa), however, and quantitative comparisons between the paleoclimate record, models, and observations remain challenging. Fingerprints of anthropogenic climate change consistent with long-term warming projections have been identified for droughts in California, the Pacific Northwest, Western North America, and the Mediterranean. In other regions (e.g., Southwest North America, Australia, Africa), however, the degree to which climate change has affected recent droughts is more uncertain. While climate change-forced declines in precipitation have been detected for the Mediterranean, in most regions, the climate change signal has manifested through warmer temperatures that have increased evaporative losses and reduced snowfall and snowpack levels, amplifying deficits in soil moisture and runoff despite uncertain precipitation changes. Over the next century, projections indicate that warming will increase drought risk and severity across much of the subtropics and mid-latitudes in both hemispheres, a consequence of regional precipitation declines and widespread warming. For many regions, however, the magnitude, robustness, and even direction of climate change-forced trends in drought depends on how drought is defined, with often large differences across indicators of precipitation, soil moisture, runoff, and vegetation health. Increasing confidence in climate change projections of drought and the associated impacts will likely depend on resolving uncertainties in processes that are currently poorly constrained (e.g., land-atmosphere interactions, terrestrial vegetation) and improved consideration of the role for human policies and management in ameliorating and adapting to changes in drought risk.

Detection and attribution↗

Development of a Liner Design Methodology and Relevant Results of Acoustic Suppression in the Farfield for Mixer-Ejector Nozzles

We have developed a process to predict noise field interior to the ejector and in the farfield for any liner design for a mixer-ejector of arbitrary scale factor. However, a number of assumptions, not verified for the current application, utilized in this process, introduce uncertainties in the final result, especially, on a quantitative basis. The normal impedance model for bulk with perforated facesheet is based on homogeneous foam materials of low resistivity. The impact of flow conditions for HSCT application as well as the impact of perforated facesheet on predicted impedance is not properly accounted. Based on the measured normal impedance for deeper bulk samples (i.e., 2.0 in.) the predicted reactance is much higher compared to the data at frequencies above 2 kHz for T-foam and 200 ppi SiC. The resistance is under predicted at lower frequencies (below 4 kHz) for these samples. Thus, the use of such predicted data in acoustic suppression is likely to introduce inaccuracies. It should be noted that the impedance prediction methods developed recently under liner technology program are not utilized in the studies described in this report due to the program closeout. Acoustic suppression prediction is based on the uniform flow and temperature conditions in a two-sided treated constant area rectangular duct. In addition, assumptions of equal energy per mode noise field and interaction of all frequencies with the treated surface for the entire ejector length may not be accurate. While, the use of acoustic transfer factor minimizes the inaccuracies associated with the prediction for a known test case, the assumption of the same factor for other liner designs and with different linear scale factor ejectors seems to be very optimistic. As illustrated in appendix D that the predicted noise suppression for LSM-1 is lower compared to the measured data is an indication of the above argument. However, the process seems to be more reliable when used for the same scale models for different liner designs as demonstrated for Gen. 1 mixer-ejectors.

Salikuddin, M.↗

KGML-ag: a modeling framework of knowledge-guided machine learning to simulate agroecosystems: a case study of estimating N<sub>2</sub>O emission using data from mesocosm experiments

Abstract. Agricultural nitrous oxide (N2O) emission accounts for a non-trivial fraction of global greenhouse gas (GHG) budget. To date, estimating N2O fluxes from cropland remains a challenging task because the related microbial processes (e.g., nitrification and denitrification) are controlled by complex interactions among climate, soil, plant and human activities. Existing approaches such as process-based (PB) models have well-known limitations due to insufficient representations of the processes or uncertainties of model parameters, and due to leverage recent advances in machine learning (ML) a new method is needed to unlock the “black box” to overcome its limitations such as low interpretability, out-of-sample failure and massive data demand. In this study, we developed a first-of-its-kind knowledge-guided machine learning model for agroecosystems (KGML-ag) by incorporating biogeophysical and chemical domain knowledge from an advanced PB model, ecosys, and tested it by comparing simulating daily N2O fluxes with real observed data from mesocosm experiments. The gated recurrent unit (GRU) was used as the basis to build the model structure. To optimize the model performance, we have investigated a range of ideas, including (1) using initial values of intermediate variables (IMVs) instead of time series as model input to reduce data demand; (2) building hierarchical structures to explicitly estimate IMVs for further N2O prediction; (3) using multi-task learning to balance the simultaneous training on multiple variables; and (4) pre-training with millions of synthetic data generated from ecosys and fine-tuning with mesocosm observations. Six other pure ML models were developed using the same mesocosm data to serve as the benchmark for the KGML-ag model. Results show that KGML-ag did an excellent job in reproducing the mesocosm N2O fluxes (overall r2=0.81, and RMSE=3.6 mgNm-2d-1 from cross validation). Importantly, KGML-ag always outperforms the PB model and ML models in predicting N2O fluxes, especially for complex temporal dynamics and emission peaks. Besides, KGML-ag goes beyond the pure ML models by providing more interpretable predictions as well as pinpointing desired new knowledge and data to further empower the current KGML-ag. We believe the KGML-ag development in this study will stimulate a new body of research on interpretable ML for biogeochemistry and other related geoscience processes.

54 ENVIRONMENTAL SCIENCES↗

On‐site surrogates for large‐scale calibration

Abstract Motivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on‐site design and surrogate modeling for a computer simulator acting on a high‐dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data‐faithful modeling and computational tractability in a calibration framework—tailoring the computer model to a limited field experiment. Situating our on‐site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example.

Huang, Jiangeng↗