An official website of the United States government
Abstract The degree of rate control (DRC) quantitatively identifies the kinetically relevant (sometimes known as rate‐limiting) steps of a complex reaction network. This concept relies on derivatives which are commonly implemented numerically, for example, with finite differences (FDs). Numerical derivatives are tedious to implement, and can be problematic, and unstable or unreliable. In this study, we demonstrate the use of automatic differentiation (AD) in the evaluation of the DRC. AD libraries are increasingly available through modern machine learning frameworks. Compared with the FDs, AD provides solutions with higher accuracy with lower computational cost. We demonstrate applications in steady‐state and transient kinetics. Furthermore, we illustrate a hybrid local‐global sensitivity analysis method, the distributed evaluation of local sensitivity analysis, to assess the importance of kinetic parameters over an uncertain space. This method also benefits from AD to obtain high‐quality results efficiently.
more »
« less
Computing a Global Degree of Rate Control for Catalytic Systems
In this paper, we discuss the concept and properties of variance-based global sensitivity analysis, as an expansion of local sensitivity metrics (such as the degree of rate control), for modeling and design of catalytic reaction systems. Using an illustrative example and supporting theory, we show that: (i) for small variations in the parameters, global sensitivities are similar to local derivatives; (ii) for larger variations in the parameters (i.e., a larger parameter space), the global sensitivities provide a ranking of importance of parameters and impose a rigorous bound on the errors that arise from fixing one or more parameters to nominal values; and (iii) in general, the global sensitivities can be related to the extrema of local derivatives. We argue that the square root of the total global sensitivity of a parameter, computed by summing the global sensitivity of that parameter acting independently and in combination with others, is a “global” degree of rate control for catalytic systems.
more »
« less
- Award ID(s):
- 1804104
- PAR ID:
- 10294441
- Editor(s):
- Jones, Chris
- Date Published:
- Journal Name:
- ACS catalysis
- Volume:
- 10
- Issue:
- 22
- ISSN:
- 2155-5435
- Page Range / eLocation ID:
- 13535−13542
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Almost all practical systems rely heavily on physical parameters. As a result, parameter sensitivity, or the extent to which perturbations in parameter values affect the state of a system, is intrinsically connected to system design and optimization. We present TADsens, a method for computing the parameter sensitivities of an output of a differential algebraic equation (DAE) system. Specifically, we provide rigorous, insightful theory for adjoint sensitivity computation of DAEs, along with an efficient and numerically well-posed algorithm implemented in Berkeley MAPP. Our theory and implementation advances resolve longstanding issues that have impeded adoption of adjoint transient sensitivities in circuit simulators for over 5 decades. We present results and comparisons on two nonlinear analog circuits. TADsens is numerically well posed and accurate, and faster by a factor of 300 over direct sensitivity computation on a circuit with over 150 unknowns and 600 parameters.more » « less
-
SUMMARY We report finite-frequency imaging of the global 410- and 660-km discontinuities using boundary sensitivity kernels for traveltime measurements made on SS precursors. The application of finite-frequency sensitivity kernels overcomes resolution limits in previous studies associated with large Fresnel zones of SS precursors and their interferences with other seismic phases. In this study, we calculate the finite-frequency sensitivities of SS waves and their precursors based on a single-scattering (Born) approximation in the framework of travelling-wave mode summation. The global discontinuity surface is parametrized using a set of triangular gridpoints with a lateral spacing of about 4°, and we solve the linear finite-frequency inverse problem (2-D tomography) based on singular value decomposition (SVD). The new global models start to show a number of features that were absent (or weak) in ray-theoretical back-projection models at spherical harmonic degree l > 6. The thickness of the mantle transition zone correlates well with wave speed perturbations at a global scale, suggesting dominantly thermal origins for the lateral variations in the mantle transition zone. However, an anticorrelation between the topography of the 410-km discontinuity and wave speed variations is not observed at a global scale. Overall, the mantle transition zone is about 2–3 km thicker beneath the continents than in oceanic regions. The new models of the 410- and 660-km discontinuities show better agreement with the finite-frequency study by Lawrence & Shearer than other global models obtained using SS precursors. However, significant discrepancies between the two models exist in the Pacific Ocean and major subduction zones at spherical harmonic degree >6. This indicates the importance of accounting for wave interactions in the calculations of sensitivity kernels as well as the use of finite-frequency sensitivities in data quality control.more » « less
-
Barrier island models that include marsh and lagoon processes are highly parameterized. To constrain model uncertainty, those desiring to use these models should seek a robust understanding of the parameter sensitivities. In this study, global sensitivity analysis was performed on a long-term barrier island model to yield insights into the modeled barrier-backbarrier system. Given that a variety of global sensitivity analysis methods exist, each one appearing to differ in its implementation, computational burden, and output, three methods (i.e., the Two-Level Full Factorial Method, Morris Method, and Sobol Method) were applied to the model for the purposes of comparison. Key influential parameters (e.g., sea level rise rate, equilibrium/critical barrier width, and reference wind speed) were consistently identified by all three sensitivity analysis methods. Despite the relatively low number of simulations required by the Morris Method, the Two-Level Method computationally outperformed the others, warranting further exploration of the Morris Method’s parallelization structure. These results may be used to help identify parameter constraints and characterize model uncertainty toward more confident predictions and management decisions for coastal barrier systems.more » « less
-
Abstract. Spatially distributed hydrological models are commonly employed to optimize the locations of engineering control measures across a watershed. Yet, parameter screening exercises that aim to reduce the dimensionality of the calibration search space are typically completed only for gauged locations, like the watershed outlet, and use screening metrics that are relevant to calibration instead of explicitly describing the engineering decision objectives. Identifying parameters that describe physical processes in ungauged locations that affect decision objectives should lead to a better understanding of control measure effectiveness. This paper provides guidance on evaluating model parameter uncertainty at the spatial scales and flow magnitudes of interest for such decision-making problems. We use global sensitivity analysis to screen parameters for model calibration, and to subsequently evaluate the appropriateness of using multipliers to adjust the values of spatially distributed parameters to further reduce dimensionality. We evaluate six sensitivity metrics, four of which align with decision objectives and two of which consider model residual error that would be considered in spatial optimizations of engineering designs. We compare the resulting parameter selection for the basin outlet and each hillslope. We also compare basin outlet results for four calibration-relevant metrics. These methods were applied to a RHESSys ecohydrological model of an exurban forested watershed near Baltimore, MD, USA. Results show that (1) the set of parameters selected by calibration-relevant metrics does not include parameters that control decision-relevant high and low streamflows, (2) evaluating sensitivity metrics at the basin outlet misses many parameters that control streamflows in hillslopes, and (3) for some multipliers, calibrating all parameters in the set being adjusted may be preferable to using the multiplier if parameter sensitivities are significantly different, while for others, calibrating a subset of the parameters may be preferable if they are not all influential. Thus, we recommend that parameter screening exercises use decision-relevant metrics that are evaluated at the spatial scales appropriate to decision making. While including more parameters in calibration will exacerbate equifinality, the resulting parametric uncertainty should be important to consider in discovering control measures that are robust to it.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://dx.doi.org/10.1021/acscatal.0c03150?ref=pdf
