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At least 37 records · Page 2

BSM Sensitivity Analysis and Meta-Modeling Next Steps [Slides]

We performed a global sensitivity analysis of the Bioenergy Scenario Model (BSM), using Elementary Effects analysis to identify potentially influential factors, with a focus on sustainable aviation fuel (SAF) production. The process was iterative and informed key model changes and updates over the course of the study in addition to identifying the key model inputs that affect the cumulative production of SAF from the present through 2050. More work will be performed to gain deeper insight into the sensitivity of individual pathways as part of our larger efforts to develop a reduced-form version of the BSM.

09 BIOMASS FUELS↗

Physiological Controls on Carbon Fluxes and Biomass Production in Miscanthus: Insights From a Process‐Based Agroecosystem Model

Biomass crops serve as essential feedstocks for renewable energy and bioproducts and play a critical role in achieving lower emissions in the transportation sector. However, dedicated perennial biomass crops such as Miscanthus × giganteus (Miscanthus) remain underrepresented in process-based agroecosystem models, limiting robust evaluation of their economic and environmental performance. In this study, we developed a data-constrained representation of the sterile triploid Miscanthus (IL clone) within the process-based model ecosys, integrating global sensitivity analysis, ensemble simulation, and parameter calibration. Planting, harvesting, and fertilization practices consistent with field management were incorporated, and phenology was constrained using PhenoCam-derived Green Chromatic Coordinate (GCC) data. Using the Morris global sensitivity analysis method, we identified 11 key physiological parameters governing plant carbon, water, and nutrient relations, particularly processes associated with CO 2 assimilation. We then conducted ensemble simulations by perturbing these parameters and calibrated the model against eddy covariance fluxes and field-measured biomass. Building on the calibrated operating state, parameter-response analyses show that different photosynthetic processes influence productivity in different ways. Protein allocation determines whether productivity increases toward a higher level, whereas electron transport capacity controls additional gains once protein allocation approaches saturation. These findings demonstrate that parameter importance depends on physiological context and on which photosynthetic processes remain limiting. Calibration and validation against observations show that ecosys can reliably reproduce carbon and water fluxes, as well as both above- and belowground biomass, with post-calibration GPP R 2 improving from 0.67 to 0.95 during the calibration period and remaining high during validation (R 2 = 0.95). These results provide a mechanistic foundation for regional simulations and sustainable bioenergy assessments.

ecosys↗

Evaluating SWAT + model uncertainties for human and natural outcomes: Application in a Great Lakes agricultural watershed

Nutrient exports from agricultural lands in the Great Lakes Region pose significant threats to water quality and ecological health through eutrophication, hypoxia, and harmful algal blooms. Climate change and agricultural adaptation practices complicate future nutrient loading due to intensified hydrologic cycles and land use decisions. Our research focuses on evaluating the Soil and Water Assessment Tool (SWAT) plus model parametric uncertainties for human and natural outcomes across different scales. These factors are integral to ensuring a balance between productive agricultural practices and maintaining the health of watershed hydrology. However, uncertainties in modeling such complex interactions pose significant challenges, limiting our ability to precisely determine critical factors that influence crop yield and soil moisture. Our analysis employs Sobol global sensitivity analysis to evaluate first-order, second order, and total-order indices for SWAT crop growth parameter, ensuring comprehensive assessment of individual and interactive effects on model outputs. The objective is to identify the parameters that significantly affect model outputs for crop yield and soil moisture and improve our understanding of their interactions at the basin and hydrological response unit (HRU) scale. Our case study, the Portage River Watershed, which drains into Lake Erie, is chosen to better capture finer scale interactions crucial for predicting nutrient loading under future climate scenarios. This foundational work is aimed at setting the stage for the future development of an agent-based model (ABM). The ABM model would incorporate SWAT outputs to dynamically simulate decision-making processes.

Bunyon, Enock↗

Data for Physiological Controls on Carbon Fluxes and Biomass Production in Miscanthus: Insights From a Process- Based Agroecosystem Model

Biomass crops serve as essential feedstocks for renewable energy and bioproducts and play a critical role in achieving lower emissions in the transportation sector. However, dedicated perennial biomass crops such as Miscanthus × giganteus (Miscanthus) remain underrepresented in process- based agroecosystem models, limiting robust evaluation of their economic and environmental performance. In this study, we developed a data- constrained representation of the sterile triploid Miscanthus (IL clone) within the process- based model ecosys, integrating global sensitivity analysis, ensemble simulation, and parameter calibration. Planting, harvesting, and fertilization practices consistent with field management were incorporated, and phenology was constrained using PhenoCam- derived Green Chromatic Coordinate (GCC) data. Using the Morris global sensitivity analysis method, we identified 11 key physiological parameters governing plant carbon, water, and nutrient relations, particularly processes associated with CO2 assimilation. We then conducted ensemble simulations by perturbing these parameters and calibrated the model against eddy covariance fluxes and field- measured biomass. Building on the calibrated operating state, parameter- response analyses show that different photosynthetic processes influence productivity in different ways. Protein allocation determines whether productivity increases toward a higher level, whereas electron transport capacity controls additional gains once protein allocation approaches saturation. These findings demonstrate that parameter importance depends on physiological context and on which photosynthetic processes remain limiting. Calibration and validation against observations show that ecosys can reliably reproduce carbon and water fluxes, as well as both above- and belowground biomass, with post- calibration GPP R2 improving from 0.67 to 0.95 during the calibration period and remaining high during validation (R2 = 0.95). These results provide a mechanistic foundation for regional simulations and sustainable bioenergy assessments.

Carbon↗

Sensitivity analysis of generic deep geologic repository with focus on spatial heterogeneity induced by stochastic fracture network generation

Geologic Disposal Safety Assessment Framework is a state-of-the-art simulation software toolkit for probabilistic post-closure performance assessment of systems for deep geologic disposal of nuclear waste developed by the United States Department of Energy. This paper presents a generic reference case and shows how it is being used to develop and demonstrate performance assessment methods within the Geologic Disposal Safety Assessment Framework that mitigate some of the challenges posed by high uncertainty and limited computational resources. Variance-based global sensitivity analysis is applied to assess the effects of spatial heterogeneity using graph-based summary measures for scalar and time-varying quantities of interest. Behavior of the system with respect to spatial heterogeneity is further investigated using ratios of water fluxes. This analysis shows that spatial heterogeneity is a dominant uncertainty in predictions of repository performance which can be identified in global sensitivity analysis using proxy variables derived from graph descriptions of discrete fracture networks. New quantities of interest defined using water fluxes proved useful for better understanding overall system behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Sensitivity Analysis for the Component Design App: Analysis of Success Assured Data

A new tool has been developed to perform variance-based global sensitivity analysis (VBGSA) on data from a set-based concurrent engineering software called Success Assured (SA). The tool is part of a digital component design app, which is currently in production as an Accelerated Digital Engineering Pathfinder at Sandia National Laboratories. When working with complex digital models, it is important to understand relationships between inputs and outputs, i.e., how “sensitive” model outputs are to changes in model inputs. After extensive research and trials of various sensitivity analysis methods, it was determined that estimation of Sobol’ indices for VBGSA with Monte Carlo simulation, paired with simple surrogate models, produces the best results for SA data. This tool increases understanding of SA models and streamlines the creation of SA datasets. This report details the methodology and implementation of this sensitivity analysis tool so others can understand it and implement it.

97 MATHEMATICS AND COMPUTING↗

Process-informed adsorbent design guidelines for direct air capture

Direct air capture using solid adsorbents is a proven technology critical to reducing our net greenhouse gas emissions to zero and beyond. Currently, academic research into the technology mainly focuses on the development of new adsorbents. However, there is a discord between the adsorbent design and process performance. Many materials scientists focus on maximising metrics such as the CO 2 capacity of their adsorbent. Here, we combine detailed process modelling, machine learning, and extensive global sensitivity analysis, which entails varying all of the model parameters together, on a direct air capture process to show that the dry CO 2 adsorption capacity does not influence process performance for an amine-functionalised adsorbent operating in a temperature vacuum swing adsorption (TVSA) process, while it is important in a steam-assisted TVSA (S-TVSA) process. In fact, adsorption kinetics, density, and thermal conductivity are all critical attributes to obtaining a low energy penalty and reduced costs. The analysis also highlights the importance of heat transfer, directing process engineers to (alternative) adsorber designs that maximise this. By an in-depth evaluation of how process performance indicators are affected by materials properties and process operating parameters, this work provides guidance to both material scientists and process engineers towards the design of a “unicorn adsorbent” and intensified DAC processes. This will improve the performance of solid adsorbent direct air capture and help drive down the costs of this vital technology to avert the worst impacts of climate change.

42 ENGINEERING↗

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗

Data and scripts associated with the manuscript "A Hydrogeophysical Framework to Assess Infiltration During a Simulated Ecosystem-Scale Flooding Experiment”

This package contains the data and scripts used in "A hydrogeophysical framework to assess infiltration during a simulated ecosystem-scale flooding experiment" (Adebayo et al., 2023). The Geophysics folder contains two subfolders containing Ground Penetrating Radar (GPR) and Electrical Resistivity Imaging (ERI) datasets acquired between August 23 and August 26, 2021. The GPR subfolder contains raw data (Tempest_Project.GPZ) and processed results using the Sensors and Software EKKO Project software. The ERI subfolder contains two additional subfolders named Static and Timelapse. The Static subfolder contains background resistivity datasets acquired before infiltration, both raw and inverted results using the ResIpy code. The Timelapse subfolder contains repeated resistivity datasets acquired during infiltration on two profiles, along with raw and inverted results using the ResIpy code. The Flow model folder contains ATS model simulation files. The Geophysics-informed subfolder contains simulation datasets for two profiles generated using information from the geophysics data. The National_database-informed subfolder contains simulation datasets for two profiles generated using information from a national soil database. Each subfolder contains initial simulation results, multiple ensembles, and final simulation files. The Sensitivity_analysis folder contains the observation files exported from the flow model, notebooks used in running the code, and sensitivity analysis results showing the sensitivity of different parameters over a 48-hour period. We used mutual information-based global sensitivity analysis for the sensitivity analysis, following Jiang et al., 2022. This study shows a novel approach that integrates geophysical data with hydrological modeling to understand subsurface flow during coastal flooding.

54 ENVIRONMENTAL SCIENCES↗

Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification

Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗

Fuel performance uncertainty quantification and sensitivity analysis in the presence of epistemic and aleatoric sources of uncertainties

Fuel performance modeling and simulation includes many uncertain parameters from models to boundary conditions, manufacturing parameters and material properties. These parameters exhibit large uncertainties and can have an epistemic or aleatoric nature, something that renders fuel performance code-to-code and code-to-measurements comparisons for complex phenomena such as the pellet cladding mechanical interaction (PCMI) very challenging. Additionally, PCMI and other complex phenomena found in fuel performance modeling and simulation induce strong discontinuities and non-linearities that can render difficult to extract meaningful conclusions form uncertainty quantification (UQ) and sensitivity analysis (SA) studies. In this work, we develop and apply a consistent treatment of epistemic and aleatoric uncertainties for both UQ and SA in fuel performance calculations and use historical benchmark-quality measurement data to demonstrate it. More specifically, the developed methodology is applied to the OECD/NEA Multi-physics Pellet Cladding Mechanical Interaction Validation benchmark. A cold ramp test leading to PCMI is modeled. Two measured quantities of interest are considered: the cladding axial elongation during the irradiations and the cladding outer diameter after the cold ramp. The fuel performance code used to perform the simulation is FAST. The developed methodology involves various steps including a Morris screening to decrease the number of uncertain inputs, a nested loop approach for propagating the epistemic and aleatoric sources of uncertainties, and a global SA using Sobol indices. The obtained results indicate that the fuel and cladding thermal conductivities as well as the cladding outer diameter uncertainties are the three inputs having the largest impact on the measured quantities. More importantly, it was found that the epistemic uncertainties can have a significant impact on the measured quantities and can affect the outcome of the global sensitivity analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Investigating uncertainties in human adaptation and their impacts on water scarcity in the Colorado river Basin, United States

The Colorado River Basin (CRB) supports the water supply for seven states and forty million people in the Western United States (US) and has been suffering an extensive drought for more than two decades. As climate change continues to reshape water resources distribution in the CRB, its impact can differ in intensity and location, resulting in variations in human adaptation behaviors. The feedback from human systems in response to the environmental changes and the associated uncertainty is critical to water resources management, especially for water-stressed basins. This paper investigates how human adaptation affects water scarcity uncertainty in the CRB and highlights the uncertainties in human behavior modeling. Our focus is on agricultural water consumption, as approximately 80% of the water consumption in the CRB is used in agriculture. We adopted a coupled agent-based and water resources modeling approach for exploring human-water system dynamics, in which an agent is a human behavior model that simulates a farmer’s water consumption decisions. We examined uncertainties at the system, agent, and parameter levels through uncertainty, clustering, and sensitivity analyses. The uncertainty analysis results suggest that the CRB water system may experience 13 to 30 years of water shortage during the 2019–2060 simulation period, depending on the paths of farmers’ adaptation. The clustering analysis identified three decision-making classes: bold, prudent, and forward-looking, and quantified the probabilities of an agent belonging to each class. The sensitivity analysis results indicated agents whose decision-making models require further investigation and the parameters with the higher uncertainty reduction potentials. Here, by conducting numerical experiments with the coupled model, this paper presents quantitative and qualitative information about farmers’ adaptation, water scarcity uncertainties, and future research directions for improving human behavior modeling.

Agent-based modeling↗

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Towards operational atmospheric correction of airborne hyperspectral imaging spectroscopy: Algorithm evaluation, key parameter analysis, and machine learning emulators

Atmospheric correction of airborne hyperspectral imaging spectroscopy (AHIS) to obtain high-quality surface reflectance is the prerequisite for remote sensing applications. Over the last decades, different atmospheric correction methods have been developed based on radiative transfer models (RTMs), however, the relative performances of different algorithms are unclear. Automated operational atmospheric correction methods to process large-volume AHIS data in a high-accurate and high-throughput manner are still lacking. Therefore, this study proposed an operational atmospheric correction pipeline for deriving surface reflectance from AHIS data. To ensure the accuracy and efficiency of the pipeline, we focused on three specific aspects: (1) selecting a suitable RTM for the development of atmospheric lookup tables (LUTs) by comparing the commercial MODerate resolution atmospheric TRANsmission (MODTRAN) and open-sourced Library for Radiative TRANsfer (LibRadTRAN) models, where the widely-used software, Atmospheric/Topographic Correction for Airborne Imagery (ATCOR), was used as benchmarks; (2) identifying key atmospheric correction parameters and determining suitable sources for parameter retrievals including AHIS, Moderate Resolution Imaging Spectroradiometer (MODIS), and AErosol RObotic NETwork (AERONET); and (3) testing the performance of using machine learning emulators to speed up the RTM-based atmospheric correction. Results indicate that (1) atmospheric correction based on MODTRAN LUTs can produce surface reflectance accurately with mean absolute errors < 0.05 and cosine similarities > 0.98 compared to field measurements, which is comparable to the software ATCOR and slightly outperforms the LibRadTRAN LUTs; (2) sobol global sensitivity analysis demonstrates that in the atmospheric correction, visibility and water vapor are two key parameters that can be accurately derived from AHIS in contrast to MODIS or AERONET data; and (3) Random Forest emulators can produce accurate estimations of surface reflectance with mean absolute errors < 0.03 and cosine similarities > 0.98 for higher processing efficiency and determine a suitable set of wavelengths for retrieving atmospheric visibility and water vapor. In conclusion, the proposed atmospheric correction pipeline also improved the four-stream radiative transfer theory for airborne applications by considering adjacent effects from airborne surrounding pixels and can also be applied for atmospheric correction of hyperspectral data from spaceborne missions.

47 OTHER INSTRUMENTATION↗

Near-Surface Hydrology and Soil Properties Drive Heterogeneity in Permafrost Distribution, Vegetation Dynamics, and Carbon Cycling in a Sub-Arctic Watershed: Modeling Archive

This Modeling Archive is in support of a NGEE-Arctic publication: Shirley et al. (2022) “Near-Surface Hydrology and Soil Properties Drive Heterogeneity in Permafrost Distribution, Vegetation Dynamics, and Carbon Cycling in a Sub-Arctic Watershed". [DOI].The dataset contains outputs from the global sensitivity analysis (GSA) of the “ecosys” model as reported in Shirley et al. (2022). The study showed that discontinuous permafrost environments are characterized by complex feedback loops and strong spatial heterogeneity which is created by variability in near-surface hydrology and soil properties. Additionally, the study demonstrated that missing representation of sub-grid heterogeneity in terrestrial ecosystem models can lead to biased estimates of the high-latitude carbon budget. Included in this dataset are the factor values for each run in the GSA and the model outputs used in this study. Included are two *.csv data files and one *.pdf.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Bayesian Adaptive Polynomial Chaos Expansions

Polynomial chaos expansions (PCEs) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare—especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that the Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis and ordinal regression tasks.

97 MATHEMATICS AND COMPUTING↗

Catalytic resonance theory for parametric uncertainty of programmable catalysis

Microkinetic models are useful tools for screening catalytic materials; however, errors in their input parameters can lead to significant uncertainty in model predictions of catalyst performance. Here, in this work, we investigate the impact of linear scaling and Brønsted-Evans-Polanyi relation parametric uncertainty on microkinetic predictions of programmable-catalyst performance. Two case studies are considered: a generic A-to-B prototype reaction and the oxygen evolution reaction (OER). The results show that error-unaware models can accurately predict trends and, for the prototype reaction, values of optimal waveform parameters. The specific model parameters driving output uncertainty are identified via variance-based global sensitivity analysis. However, predictions of dynamic rate enhancement can decrease when uncertainty is propagated into the models. In both cases, we identify operating conditions where the programmable catalyst achieves a rate enhancement of at least one order of magnitude despite parametric uncertainty in the model, supporting programmable catalysis as a viable strategy for exceeding the Sabatier limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗