Reply on RC2

Evolutionary algorithms and elliptical copulas applied to continuous optimization problems

This paper presents a study for using Kriging metamodeling in combination with Covariance Matrix Adaptation Evolution Strategies (CMA-ES) to find robust solutions. A general, archive based, framework is proposed for integrating Kriging within CMA-ES, including a method to utilize the covariance matrix of the CMA-ES in a straightforward way to improve the accuracy of the Kriging predictions without introducing much additional computational cost. Moreover, it adopts an elegant way to select appropriate archive points for building a local metamodel. The study shows that this Kriging metamodeling scheme for finding robust solutions outperforms common, straightforward approaches and is very useful when there is a limited budget of function evaluations. Though using the covariance matrix can improve the prediction quality, it has no significant effect on the overall quality of the optimization results.

The problem of identification of unknown epidemiological parameters (contagiosity, the initial number of infected individuals, probability of being tested) of an agent-based model of COVID-19 spread in Novosibirsk region is solved and analyzed. The first stage of modeling involves data analysis based on the machine learning approach that allows one to determine correlated datasets of performed PCR tests and number of daily diagnoses and detect some features (seasonality, stationarity, data correlation) to be used for COVID-19 spread modeling. At the second stage, the unknown model parameters that depend on the date of introducing of containment measures are calibrated with the usage of additional measurements such as the number of daily diagnosed and tested people using PCR, their daily mortality rate and other statistical information about the disease. The calibration is based on minimization of the misfit function for daily diagnosed data. The OPTUNA optimization framework with tree-structured Parzen estimator and covariance matrix adaptation evolution strategy is used to minimize the misfit function. Due to ill-posedness of identification problem, the identifiability analysis is carried out to construct the regularization algorithm. At the third stage, the identified parameters of COVID-19 for Novosibirsk region and different scenarios of COVID-19 spread are analyzed in relation to introduced quarantine measures. This kind of modeling can be used to select effective anti-pandemic programs.

Context. Exoplanet characterization is one of the main foci of current exoplanetary science. For super-Earths and sub-Neptunes, we mostly rely on mass and radius measurements, which allow us to derive the mean density of the body and give a rough estimate of the bulk composition of the planet. However, the determination of planetary interiors is a very challenging task. In addition to the uncertainty in the observed fundamental parameters, theoretical models are limited owing to the degeneracy in determining the planetary composition. Aims. We aim to study several aspects that affect the internal characterization of super-Earths and sub-Neptunes: observational uncertainties, location on the M–R diagram, impact of additional constraints such as bulk abundances or irradiation, and model assumptions. Methods. We used a full probabilistic Bayesian inference analysis that accounts for observational and model uncertainties. We employed a nested sampling scheme to efficiently produce the posterior probability distributions for all the planetary structural parameter of interest. We included a structural model based on self-consistent thermodynamics of core, mantle, high-pressure ice, liquid water, and H–He envelope. Results. Regarding the effect of mass and radius uncertainties on the determination of the internal structure, we find three different regimes: below the Earth-like composition line and above the pure-water composition line smaller observational uncertainties lead to better determination of the core and atmosphere mass, respectively; and between these regimes internal structure characterization only weakly depends on the observational uncertainties. We also find that using the stellar Fe/Si and Mg/Si abundances as a proxy for the bulk planetary abundances does not always provide additional constraints on the internal structure. Finally we show that small variations in the temperature or entropy profiles lead to radius variations that are comparable to the observational uncertainty. This suggests that uncertainties linked to model assumptions can eventually become more relevant to determine the internal structure than observational uncertainties.

Communities are basic units of complex networks and understanding of their structure help us to understand the structure of a network. Communities are groups of nodes that have many links inside and few links outside them. Community detection in a network can be modeled as an optimization problem. We can use some measures such as Modularity and Community Score for evaluating the quality of a partition of nodes. In this paper, we present a new algorithm for detecting communities in networks based on an Estimation of Distribution Algorithm (EDA) with the assumption that the problem variables are independent. EDAs are those evolutionary algorithms that build and sample the probabilistic models of selected solutions instead of using crossover and mutation operators. In this paper, we assess our algorithm by synthetic and real data sets and compare it with other community detection algorithms.

Best estimate calculation and uncertainty quantification of sodium-cooled fast reactor using MARS-LMR code

This analysis revisits detection and attribution of free atmosphere temperatures from radiosondes, almost a decade after previous studies. Since that time, data sets have not only become longer, but understanding of observational uncertainty has vastly improved. In addition, a coordinated set of experiments exploring the effects of human and natural forcings on past climate change has been made with a new generation of climate models. These advances allow a much more thorough analysis of the effects of modeling and observational uncertainty on attribution results than previously possible. Observational uncertainty is explored using multiple radiosonde reconstructions including those with ensembles of realizations exploring the effects of processing choices. Modeling uncertainty is explored by calculating multiple fingerprints of natural influence (from changes in solar irradiance and volcanic aerosols) and of human influence (due to greenhouse gases and due to the effects of combined anthropogenic forcings including stratospheric ozone depletion). With increased confidence over previous studies, human influences (both greenhouse gas and other anthropogenic forcings) have been detected in spatiotemporal changes in free atmosphere temperature from 1961 to 2010, irrespective of whether the full atmospheric column (30–850 hPa) is examined or purely the troposphere, with stratospheric ozone depletion dominating the cooling that has been observed in the lower stratosphere. Thus the advances of the last decade yield increased confidence that anthropogenic influences have made a substantial contribution to the evolution of free atmosphere temperatures.

This report presents guidelines for evaluating uncertainty in mathematical equations and computer models applied to assess human health and environmental risk. Uncertainty analyses involve the propagation of uncertainty in model parameters and model structure to obtain confidence statements for the estimate of risk and identify the model components of dominant importance. Uncertainty analyses are required when there is no a priori knowledge about uncertainty in the risk estimate and when there is a chance that the failure to assess uncertainty may affect the selection of wrong options for risk reduction. Uncertainty analyses are effective when they are conducted in an iterative mode. When the uncertainty in the risk estimate is intolerable for decision-making, additional data are acquired for the dominant model components that contribute most to uncertainty. This process is repeated until the level of residual uncertainty can be tolerated. A analytical and numerical methods for error propagation are presented along with methods for identifying the most important contributors to uncertainty. Monte Carlo simulation with either Simple Random Sampling (SRS) or Latin Hypercube Sampling (LHS) is proposed as the most robust method for propagating uncertainty through either simple or complex models. A distinction is made between simulating a stochastically varying assessment endpoint (i.e., the distribution of individual risks in an exposed population) and quantifying uncertainty due to lack of knowledge about a fixed but unknown quantity (e.g., a specific individual, the maximally exposed individual, or the mean, median, or 95%-tile of the distribution of exposed individuals). Emphasis is placed on the need for subjective judgement to quantify uncertainty when relevant data are absent or incomplete.

Evolutionary algorithm solution and KKT based optimality verification to multi-area economic dispatch

Wind shear presents a considerable hazard to aviation safety, especially during the critical phases of takeoff and landing. Accurate forecasting of wind shear events is essential to mitigate these risks and improve both flight safety and operational efficiency. This paper introduces a hybrid Temporal Convolutional Networks and Tree-Based Models (TCNs-TBMs) framework specifically designed for time series modeling and the prediction of wind shear intensity. The framework utilizes the ability of TCNs to capture intricate temporal patterns and integrates it with the predictive strengths of TBMs, such as Extreme Gradient Boosting (XGBoost), Random Forest (RF), and Categorical Boosting (CatBoost), resulting in robust forecast. To ensure optimal performance, hyperparameter tuning was performed using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), enhancing predictive accuracy. The effectiveness of the framework is validated through comparative analyses with standalone machine learning models such as XGBoost, RF, and CatBoost. The proposed TCN-XGBoost model outperformed these alternatives, achieving a lower Root Mean Squared Error (RMSE: 1.95 for training, 1.97 for testing), Mean Absolute Error (MAE: 1.41 for training, 1.39 for testing), and Mean Absolute Percentage Error (MAPE: 7.90% for training, 7.89% for testing). Furthermore, the uncertainty analysis demonstrated the model’s reliability, with a lower mean uncertainty (7.14 × 10−8) and standard deviation of uncertainty (6.48 × 10−8) compared to other models. These results highlight the potential of the TCNs-TBMs framework to significantly enhance the accuracy of wind shear intensity predictions, emphasizing the value of advanced time series modeling techniques for risk management and decision-making in the aviation industry. This study highlights the framework’s broader applicability to other meteorological forecasting tasks, contributing to aviation safety worldwide.

The reconstruction of acoustic attenuation maps for transmission Ultrasound Computed Tomography (USCT) based on the standard least-squares full wave inversion method requires the accurate knowledge of the sound speed map in the region under study. Any deviation in the reconstructed speed maps creates a very significant bias in the attenuation map, as the standard least-squares misfit function is more sensitive to time misalignments than to amplitude differences of the signals. In this work, we propose a generalized misfit function which includes an additional term that accounts for the amplitude differences between the measured and the estimated signals. The functional gradients used to minimize the proposed misfit function were obtained using an adjoint field formulation and the fractional Laplacian wave equation. The forward and backward wave propagation was obtained with the parallelized GPU version of the software k-Wave and the optimization was performed with a line search method. A numerical phantom simulating breast tissue and synthetic noisy data were used to test the performance of the proposed misfit function. The attenuation was reconstructed based on a converged speed map. An edge-preserving regularization method based on total variation was also implemented. To quantify the quality of the results, the mean values and their standard deviations in several regions of interest were analyzed and compared to the reference values. The proposed generalized misfit function decreases considerably the bias in the attenuation map caused by the deviations in the speed map in all the regions of interest analyzed.

Gridded datasets of precipitation are of great importance to evaluate recent climate models and are frequently applied to select a subset of available models. As climate models are still prone to biases on the regional scale, gridded datasets are also essential to correct or adjust these biases. Various studies revealed considerable differences, that is, observational uncertainty, in the available gridded datasets of precipitation, especially over complex terrain. This study focuses on the impacts of observational uncertainty on the evaluation, selection, and bias correction of 15 regional climate model (RCM) simulations provided through the EURO-CORDEX initiative over the alpine Adige catchment located in northern Italy. Nine reference datasets originating from observations, reanalysis, and remote sensing are applied to evaluate the performance of RCMs and select a subset based on validity. These reference datasets are then applied to bias correct the RCM ensemble using a standard quantile mapping method, and the resulting changes in the projections are assessed. The presented results show a selection of similar RCMs, indicating that observational uncertainty is lower than model uncertainty. The influence of the choice of the reference dataset on bias correction is negligible for the climate change signals. Small differences in projected change signals can be attributed to model selection. As expected, the choice of the reference dataset strongly influences future projections of precipitation even more pronounced for the extremes. The findings of this study highlight the need to account for observational uncertainty for bias correction of RCM simulations for impact modeling studies.

Sensitivity analysis in the context of uncertainty analysis for computationally intensive models

Management decisions and policy development are oftentimes limited by the incomplete knowledge of the phenomena under study and by the inability to quantify the effective reliability of the system to be managed. It is possible to circumvent these limitations by including in the management decision process, an analysis of the variability and uncertainty of the model results. One regulatory process that can benefit from coupling the traditional deterministic modeling with the uncertainty analysis is the computation of the total maximum daily load (TMDL). By definition, in the TMDL, the margin of safety (MOS) is added to account for the inherent variability of the natural phenomena and for the limitations of their mathematical representation. In practice selection of the MOS, rarely reflects the data variability or the model uncertainty. This paper suggests a scientific method to incorporate variability and uncertainty in the computation of the TMDL by estimating a MOS based on the risk of the system of exceeding a critical concentration. The work presented here reports the results of the uncertainty and risk analyses conducted using the modified Rosenblueth Point Estimate Method to estimate the variability of lead concentrations in the Niagara River. A TMDL for lead is also computed for the first time by choosing a MOS based on the uncertainty analysis results and a selected risk of exceeding the most stringent water quality criteria

Large structure in tomographic images of the core‐mantle boundary (CMB) found by fitting low‐degree spherical harmonic models to International Seismological Centre (ISC) travel time data by linear least squares may be artifacts of the fitting procedure, rather than necessary features of Earth. Two numerical experiments show that gaps in the data coverage and the use of low‐degree models tend to yield spurious topography. We fit a large set of summary PKP and PcP rays for 23 years of ISC arrival times (for events relocated with the iasp91 model) to obtain least squares CMB “reference models” of maximum degree 4, 8, and 12. Least squares CMB models derived from subsets of the data with new artificial gaps comparable in size to the gaps in the original data set can have significantly different structure than the reference models, both globally and within the artificial gaps. In spite of these differences, the correlation of models with different sized gaps is high: correlation is not a good measure of model similarity nor of reliability of the fitted models in this problem. We generated synthetic data from the degree 12 reference model rotated relative to the source‐receiver frame. Least squares fits of low‐degree models to the synthetic data show significant features not present in the reference model, in approximately the same place relative to the gaps in the original observations. The spurious features of the models with new gaps and with rotated synthetic data are qualitatively indistinguishable from large features in the reference models.