scholarly journals Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models: a case study for biogenic emissions from EURAD-IM version 5

2021 ◽  
Vol 14 (9) ◽  
pp. 5583-5605
Author(s):  
Annika Vogel ◽  
Hendrik Elbern
Keyword(s):  
Forecast Model ◽  
High Dimensional ◽  
Biogenic Emissions ◽  
Model Parameters ◽  
Emission Rates ◽  
Parameter Uncertainties ◽  
Model Uncertainties ◽  
Dimensional Parameter ◽  
Correlated Parameters ◽  
Ensemble Generation

Abstract. Atmospheric chemical forecasts heavily rely on various model parameters, which are often insufficiently known, such as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties with an ensemble of forecasts is impaired by the high dimensionality of the system. This study presents a novel approach, which substitutes the problem into a low-dimensional subspace spanned by the leading uncertainties. It is based on the idea that the forecast model acts as a dynamical system inducing multivariate correlations of model uncertainties. This enables an efficient perturbation of high-dimensional model parameters according to their leading coupled uncertainties. The specific algorithm presented in this study is designed for parameters that depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen–Loéve expansion. Due to their perceived simulation challenge, the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state that highly correlated uncertainties of regional biogenic emissions can be represented by a low number of dominant components. Depending on the required level of detail, leading parameter uncertainties with dimensions of 𝒪(106) can be represented by a low number of about 10 ensemble members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

scholarly journals Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models

2021 ◽  
Author(s):  
Annika Vogel ◽  
Hendrik Elbern
Keyword(s):  
Forecast Model ◽  
High Dimensional ◽  
Biogenic Emissions ◽  
Model Parameters ◽  
Emission Rates ◽  
Model Uncertainties ◽  
Dimensional Parameter ◽  
Novel Approach ◽  
Correlated Parameters ◽  
Ensemble Generation

Abstract. Atmospheric chemical forecasts highly rely on various model parameters, which are often insufficiently known, as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties by an ensemble of forecasts is impaired by the high-dimensionality of the system. This study presents a novel approach to efficiently perturb atmospheric-chemical model parameters according to their leading coupled uncertainties. The algorithm is based on the idea that the forecast model acts as a dynamical system inducing multi-variational correlations of model uncertainties. The specific algorithm presented in this study is designed for parameters which depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen-Loéve expansion. Due to their perceived simulation challenge the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state high spatial- and cross-correlations of regional biogenic emissions, which are represented by a low number of dominating components. Consequently, leading uncertainties can be covered by low number of perturbations enabling ensemble sizes of the order of 10 members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

Towards an Efficient Validation of Dynamical Whole-brain Models

2021 ◽  
Author(s):  
Kevin J. Wischnewski ◽  
Simon B. Eickhoff ◽  
Viktor K. Jirsa ◽  
Oleksandr V. Popovych
Keyword(s):  
Structural Connectivity ◽  
Three Dimensional ◽  
Bayesian Optimization ◽  
High Dimensional ◽  
Brain Dynamics ◽  
Model Parameters ◽  
Phase Oscillators ◽  
Dimensional Parameter ◽  
Whole Brain ◽  
Brain Models

Abstract Simulating the resting-state brain dynamics via mathematical whole-brain models requires an optimal selection of parameters, which determine the model’s capability to replicate empirical data. Since the parameter optimization via a grid search (GS) becomes unfeasible for high-dimensional models, we evaluate several alternative approaches to maximize the correspondence between simulated and empirical functional connectivity. A dense GS serves as a benchmark to assess the performance of four optimization schemes: Nelder-Mead Algorithm (NMA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMAES) and Bayesian Optimization (BO). To compare them, we employ an ensemble of coupled phase oscillators built upon individual empirical structural connectivity of 105 healthy subjects. We determine optimal model parameters from two- and three-dimensional parameter spaces and show that the overall fitting quality of the tested methods can compete with the GS. There are, however, marked differences in the required computational resources and stability properties, which we also investigate before proposing CMAES and BO as efficient alternatives to a high-dimensional GS. For the three-dimensional case, these methods generated similar results as the GS, but within less than 6% of the computation time. Our results contribute to an efficient validation of models for personalized simulations of brain dynamics.

scholarly journals A sensitivity study of radiative fluxes at the top of atmosphere to cloud-microphysics and aerosol parameters in the community atmosphere model CAM5

2013 ◽  
Vol 13 (21) ◽  
pp. 10969-10987 ◽  
Author(s):  
C. Zhao ◽  
X. Liu ◽  
Y. Qian ◽  
J. Yoon ◽  
Z. Hou ◽  
...  
Keyword(s):  
Regional Scale ◽  
Cloud Microphysics ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Dimensional Parameter ◽  
Individual Parameter ◽  
Radiative Fluxes ◽  
Community Atmosphere Model ◽  
Atmosphere Model ◽  
Global Mean

Abstract. In this study, we investigated the sensitivity of net radiative fluxes (FNET) at the top of atmosphere (TOA) to 16 selected uncertain parameters mainly related to the cloud microphysics and aerosol schemes in the Community Atmosphere Model version 5 (CAM5). We adopted a quasi-Monte Carlo (QMC) sampling approach to effectively explore the high-dimensional parameter space. The output response variables (e.g., FNET) are simulated using CAM5 for each parameter set, and then evaluated using the generalized linear model analysis. In response to the perturbations of these 16 parameters, the CAM5-simulated global annual mean FNET ranges from −9.8 to 3.5 W m−2 compared to 1.9 W m−2 with the default parameter values. Variance-based sensitivity analysis is conducted to show the relative contributions of individual parameter perturbations to the global FNET variance. The results indicate that the changes in the global mean FNET are dominated by changes in net cloud forcing (CF) within the parameter ranges being investigated. The threshold size parameter related to auto-conversion of cloud ice to snow is identified as one of the most influential parameters for FNET in CAM5 simulations. The strong heterogeneous geographic distribution of FNET variance shows that parameters have a clear localized effect over regions where they are acting. However, some parameters also have non-local impacts on FNET variance. Although external factors, such as perturbations of anthropogenic and natural emissions, largely affect FNET variance at the regional scale, their impact is weaker than that of model internal parameters in terms of simulating global mean FNET. The interactions among the 16 selected parameters contribute a relatively small portion to the total FNET variance over most regions of the globe. This study helps us better understand the parameter uncertainties in the CAM5 model, and thus provides information for further calibrating uncertain model parameters with the largest sensitivity.

scholarly journals New Estimators of the Bayes Factor for Models with High-Dimensional Parameter and/or Latent Variable Spaces

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 399
Author(s):  
Anna Pajor
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Bayes Factor ◽  
High Dimensional ◽  
Model Parameters ◽  
Posterior Odds ◽  
Dimensional Parameter ◽  
Data Set ◽  
Multivariate Stochastic Volatility ◽  
Competing Models

Formal Bayesian comparison of two competing models, based on the posterior odds ratio, amounts to estimation of the Bayes factor, which is equal to the ratio of respective two marginal data density values. In models with a large number of parameters and/or latent variables, they are expressed by high-dimensional integrals, which are often computationally infeasible. Therefore, other methods of evaluation of the Bayes factor are needed. In this paper, a new method of estimation of the Bayes factor is proposed. Simulation examples confirm good performance of the proposed estimators. Finally, these new estimators are used to formally compare different hybrid Multivariate Stochastic Volatility–Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MSV-MGARCH) models which have a large number of latent variables. The empirical results show, among other things, that the validity of reduction of the hybrid MSV-MGARCH model to the MGARCH specification depends on the analyzed data set as well as on prior assumptions about model parameters.

scholarly journals A sensitivity study of radiative fluxes at the top of atmosphere to cloud-microphysics and aerosol parameters in the Community Atmosphere Model CAM5

2013 ◽  
Vol 13 (5) ◽  
pp. 12135-12176 ◽  
Author(s):  
C. Zhao ◽  
X. Liu ◽  
Y. Qian ◽  
J. Yoon ◽  
Z. Hou ◽  
...  
Keyword(s):  
Regional Scale ◽  
Cloud Microphysics ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Dimensional Parameter ◽  
Individual Parameter ◽  
Radiative Fluxes ◽  
Community Atmosphere Model ◽  
Atmosphere Model ◽  
Global Mean

Abstract. In this study, we investigated the sensitivity of net radiative fluxes (FNET) at the top of atmosphere (TOA) to 16 selected uncertain parameters mainly related to the cloud microphysics and aerosol schemes in the Community Atmosphere Model version 5 (CAM5). We adopted a quasi-Monte Carlo (QMC) sampling approach to effectively explore the high dimensional parameter space. The output response variables (e.g., FNET) were simulated using CAM5 for each parameter set, and then evaluated using the generalized linear model analysis. In response to the perturbations of these 16 parameters, the CAM5-simulated global annual mean FNET ranges from −9.8 to 3.5 W m−2 compared to the CAM5-simulated FNET of 1.9 W m−2 with the default parameter values. Variance-based sensitivity analysis was conducted to show the relative contributions of individual parameter perturbation to the global FNET variance. The results indicate that the changes in the global mean FNET are dominated by those of net cloud forcing (CF) within the parameter ranges being investigated. The threshold size parameter related to auto-conversion of cloud ice to snow is identified as one of the most influential parameters for FNET in CAM5 simulations. The strong heterogeneous geographic distribution of FNET variance shows parameters have a clear localized effect over regions where they are acting. However, some parameters also have non-local impacts on FNET variance. Although external factors, such as perturbations of anthropogenic and natural emissions, largely affect FNET variance at the regional scale, their impact is weaker than that of model internal parameters in terms of simulating global mean FNET. The interactions among the 16 selected parameters contribute a relatively small portion to the total FNET variance over most regions of the globe. This study helps us better understand the parameter uncertainties in the CAM5 model, and thus provides information for further calibrating uncertain model parameters with the largest sensitivity.

scholarly journals Constraining the parameters of high-dimensional models with active learning

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Sascha Caron ◽  
Tom Heskes ◽  
Sydney Otten ◽  
Bob Stienen
Keyword(s):  
Active Learning ◽  
Particle Physics ◽  
High Energy Physics ◽  
High Energy ◽  
Physical Models ◽  
High Dimensional ◽  
Physical Parameters ◽  
Model Parameters ◽  
Dimensional Parameter ◽  
Parameter Spaces

AbstractConstraining the parameters of physical models with $$>5-10$$>5-10 parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of computational resources. The commonly used solution of reducing the number of relevant physical parameters hampers the generality of the results. In this paper we show that this problem can be alleviated by the use of active learning. We illustrate this with examples from high energy physics, a field where simulations are often expensive and parameter spaces are high-dimensional. We show that the active learning techniques query-by-committee and query-by-dropout-committee allow for the identification of model points in interesting regions of high-dimensional parameter spaces (e.g. around decision boundaries). This makes it possible to constrain model parameters more efficiently than is currently done with the most common sampling algorithms and to train better performing machine learning models on the same amount of data. Code implementing the experiments in this paper can be found on GitHub "Image missing"

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

PSV-14 Using Bayesian Hamiltonian Monte Carlo and a nonlinear model for the estimation of genetic parameters for lactation curves in goats

2021 ◽  
Vol 99 (Supplement_3) ◽  
pp. 305-307
Author(s):  
Andre C Araujo ◽  
Leonardo Gloria ◽  
Paulo Abreu ◽  
Fabyano Silva ◽  
Marcelo Rodrigues ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Milk Yield ◽  
Nonlinear Model ◽  
Genetic Parameters ◽  
Model Parameters ◽  
Promising Alternative ◽  
Hamiltonian Monte Carlo ◽  
Heritability Estimates ◽  
Correlated Parameters ◽  
Wood Model

Abstract Hamiltonian Monte Carlo (HMC) is an algorithm of the Markov Chain Monte Carlo (MCMC) method that uses dynamics to propose samples that follow a target distribution. This algorithm enables more effective and consistent exploration of the probability interval and is more sensitive to correlated parameters. Therefore, Bayesian-HMC is a promising alternative to estimate individual parameters of complex functions such as nonlinear models, especially when using small datasets. Our objective was to estimate genetic parameters for milk traits defined based on nonlinear model parameters predicted using the Bayesian-HMC algorithm. A total of 64,680 milk yield test-day records from 2,624 first, second, and third lactations of Saanen and Alpine goats were used. First, the Wood model was fitted to the data. Second, lactation persistency (LP), peak time (PT), peak yield (PY), and total milk yield [estimated from zero to 50 (TMY50), 100(TMY100), 150(TMY150), 200(TMY200), 250(TMY250), and 300(TMY300) days-in-milk] were predicted for each animal and parity based on the output of the first step (the individual phenotypic parameters of the Wood model). Thereafter, these predicted phenotypes were used for estimating genetic parameters for each trait. In general, the heritability estimates across lactations ranged from 0.10 to 0.20 for LP, 0.04 to 0.07 for PT, 0.26 to 0.27 for PY, and 0.21 to 0.28 for TMY (considering the different intervals). Lower heritabilities were obtained for the nonlinear function parameters (A, b and l) compared to its predicted traits (except PT), especially for the first and second lactations (range: 0.09 to 0.18). Higher heritability estimates were obtained for the third lactation traits. To our best knowledge, this study is the first attempt to use the HMC algorithm to fit a nonlinear model in animal breeding. The two-step method proposed here allowed us to estimate genetic parameters for all traits evaluated.

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