Model Uncertainty Quantification Research Articles

SECRET: Statistical Emulation for Computational Reverse Engineering and Translation with applications in healthcare

There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

Unsupervised stochastic learning and reduced order modeling for global sensitivity analysis in cardiac electrophysiology models

Background and Objective:Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the cardiac cell model, domain geometry, and boundary or initial conditions used in the mathematical modeling. Conventional techniques for uncertainty quantification in modeling electrical activities of the heart encounter significant challenges, primarily due to the high computational costs associated with fine temporal and spatial scales. Additionally, the need for numerous model evaluations to quantify ubiquitous uncertainties increases the computational challenges even further. Methods:In the present study, we propose a non-intrusive surrogate model to perform uncertainty quantification and global sensitivity analysis in cardiac electrophysiology models. The proposed method combines an unsupervised machine learning technique with the polynomial chaos expansion to reconstruct a surrogate model for the propagation and quantification of uncertainties in the electrical activity of the heart. The proposed methodology not only accurately quantifies uncertainties at a very low computational cost but more importantly, it captures the targeted quantity of interest as either the whole spatial field or the whole temporal period. In order to perform sensitivity analysis, aggregated Sobol indices are estimated directly from the spectral mode of the polynomial chaos expansion. Results:We conduct Uncertainty Quantification (UQ) and global Sensitivity Analysis (SA) considering both spatial and temporal variations, rather than limiting the analysis to specific Quantities of Interest (QoIs). To assess the comprehensive performance of our methodology in simulating cardiac electrical activity, we utilize the monodomain model. Additionally, sensitivity analysis is performed on the parameters of the Mitchell-Schaeffer cell model. Conclusions:Unlike conventional techniques for uncertainty quantification in modeling electrical activities, the proposed methodology performs at a low computational cost the sensitivity analysis on the cardiac electrical activity parameters. The results are fully reproducible and easily accessible, while the proposed reduced-order model represents a significant contribution to enhancing global sensitivity analysis in cardiac electrophysiology.

Uncertainty Quantification in Radial Anisotropy Models Based on Transdimensional Bayesian Inversion of Receiver Functions and Surface-Wave Dispersion: Case Study Sri Lanka

ABSTRACT In geophysical inference problems, quantification of data uncertainties is required to balance the data-fitting ability of the model and its complexity. The transdimensional hierarchical Bayesian approach is a powerful tool to evaluate the level of uncertainty and determine the complexity of the model by treating data errors and model dimensions as unknown. In this article, we take account of the uncertainty through the whole procedure, thus developing a two-step fully Bayesian approach with coupled uncertainty propagation to estimate the crustal isotropic and radial anisotropy (RA) model based on Rayleigh and Love dispersion as well as receiver functions (RFs). First, 2D surface-wave tomography is applied to determine period-wise ambient noise phase velocity maps and their uncertainty for Rayleigh and Love waves. Probabilistic profiles of the isotropic average VS and RA as a function of depth are then derived at station sites by inverting the local surface-wave dispersion and model errors and RFs jointly. The workflow is applied to a temporary seismic broadband array covering all of Sri Lanka. The probabilistic results enable us to effectively quantify the uncertainty of the final RA model and provide robust inferences. The shear-wave velocity results show that the range of Moho depths is between 30 and 40 km, with the thickest crust (38–40 km) beneath the central Highland Complex. Positive RA (VSH>VSV) observed in the upper crust is attributed to subhorizontal alignment of metamorphic foliation and stretched layers resulting from deformation. Negative RA (VSV>VSH) in the midcrust of central Sri Lanka may indicate the existence of melt inclusions and could result from the uplift and folding process. The positive RA in the lower crust could be caused by crustal channel flow in a collision orogeny.

Machine learning techniques for predictive modelling and uncertainty quantification of the mechanical properties of woven carbon fibre composites

Carbon fibre composites owe their exceptional mechanical properties to the characteristics of their constituents; fibres and resin. However, uncertainty in these individual constituent properties can introduce significant variations in the macroscale mechanical performance of composites. These variations are amplified in the presence of various plies in the composite and pose a challenge to quantify during manufacturing stages. In this study, uncertain constituent material properties are propagated to the macroscale composite through multiscale homogenisation to compute the varied resultant thin-shell stiffness matrices. An in-house-built automated simulation environment has been used to create a physics-conforming trainable database for model training, testing, validation and uncertainty quantification using Gaussian Process Regression (GPR), Artificial Neural Networks (ANNs), and Multiple Linear Regression (MLR). Through rigorous comparative analyses, the superior performance of GPR is demonstrated when compared to alternative techniques with R² ≥ 0.99 and NRMSE < 10⁻⁷. Further, the findings approve the validity of GPR for extrapolatory predictions. For instance, a randomly sampled [-5, 5] % variation of constituent material properties leads to extreme uncertainties in macroscale ± 0.067 %, for axial stiffness with excellent GPR predictive accuracy of R² = 0.99. This slightly increases to ± 0.14 % for a variation of [-10, 10] %. Moreover, the extreme uncertainties indicate that the direct axial and bending stiffnesses are more sensitive to variations in constituent properties than others. Additional investigations presented in the paper produce predictive models and uncertainty bounds for all stiffness entries that are of high importance for macroscale property control during manufacturing.

QSARtuna: An Automated QSAR Modeling Platform for Molecular Property Prediction in Drug Design.

Machine-learning (ML) and deep-learning (DL) approaches to predict the molecular properties of small molecules are increasingly deployed within the design-make-test-analyze (DMTA) drug design cycle to predict molecular properties of interest. Despite this uptake, there are only a few automated packages to aid their development and deployment that also support uncertainty estimation, model explainability, and other key aspects of model usage. This represents a key unmet need within the field, and the large number of molecular representations and algorithms (and associated parameters) means it is nontrivial to robustly optimize, evaluate, reproduce, and deploy models. Here, we present QSARtuna, a molecule property prediction modeling pipeline, written in Python and utilizing the Optuna, Scikit-learn, RDKit, and ChemProp packages, which enables the efficient and automated comparison between molecular representations and machine learning models. The platform was developed by considering the increasingly important aspect of model uncertainty quantification and explainability by design. We provide details for our framework and provide illustrative examples to demonstrate the capability of the software when applied to simple molecular property, reaction/reactivity prediction, and DNA encoded library enrichment classification. We hope that the release of QSARtuna will further spur innovation in automatic ML modeling and provide a platform for education of best practices in molecular property modeling. The code for the QSARtuna framework is made freely available via GitHub.

Opinion: Optimizing climate models with process knowledge, resolution, and artificial intelligence

Abstract. Accelerated progress in climate modeling is urgently needed for proactive and effective climate change adaptation. The central challenge lies in accurately representing processes that are small in scale yet climatically important, such as turbulence and cloud formation. These processes will not be explicitly resolvable for the foreseeable future, necessitating the use of parameterizations. We propose a balanced approach that leverages the strengths of traditional process-based parameterizations and contemporary artificial intelligence (AI)-based methods to model subgrid-scale processes. This strategy employs AI to derive data-driven closure functions from both observational and simulated data, integrated within parameterizations that encode system knowledge and conservation laws. In addition, increasing the resolution to resolve a larger fraction of small-scale processes can aid progress toward improved and interpretable climate predictions outside the observed climate distribution. However, currently feasible horizontal resolutions are limited to O(10 km) because higher resolutions would impede the creation of the ensembles that are needed for model calibration and uncertainty quantification, for sampling atmospheric and oceanic internal variability, and for broadly exploring and quantifying climate risks. By synergizing decades of scientific development with advanced AI techniques, our approach aims to significantly boost the accuracy, interpretability, and trustworthiness of climate predictions.

Approach for predicting and adjusting the pointing accuracy of opto-mechanical systems considering multi-source uncertainty.

Pointing accuracy is a critical performance indicator of opto-mechanical systems, directly affecting the systems' efficiency and application range. This study introduces what we believe to be a novel approach for predicting pointing accuracy and adjusting processes in opto-mechanical systems, considering multi-source uncertainty quantification. First, the relationship between error components and total error is quantified using homogeneous coordinate transformation theory. Second, by applying the Nataf transformation to uncertain variables, a hybrid interval-probabilistic uncertainty quantification model based on generalized polynomial chaos is constructed. Third, by selecting points from the probability distribution domain, a parameterized finite element simulation is conducted to create a pointing accuracy prediction model, obtaining the theoretical limit accuracy for the opto-mechanical system. Finally, considering multi-bolt elastic interactions, an assembly process adjustment model is developed to achieve performance-based assembly process adjustments, and tests are conducted to measure the pointing accuracy of the opto-mechanical system after calibration. Pointing accuracy measurements following calibration showed an improvement from 249" to 117", an increase of 53.01%, approaching the theoretical limit of 108". This approach requires only one adjustment to approach optimal accuracy compared to eight adjustments with traditional methods, greatly enhancing assembly efficiency. This study offers a theoretical foundation for predicting and adjusting pointing accuracy in opto-mechanical systems.

Sample-Based Continuous Approximate Method for Constructing Interval Neural Network.

In safety-critical engineering applications, such as robust prediction against adversarial noise, it is necessary to quantify neural networks' uncertainty. Interval neural networks (INNs) are effective models for uncertainty quantification, giving an interval of predictions instead of a single value for a corresponding input. This article formulates the problem of training an INN as a chance-constrained optimization problem. The optimal solution of the formulated chance-constrained optimization naturally forms an INN that gives the tightest interval of predictions with a required confidence level. Since the chance-constrained optimization problem is intractable, a sample-based continuous approximate method is used to obtain approximate solutions to the chance-constrained optimization problem. We prove the uniform convergence of the approximation, showing that it gives the optimal INN consistently with the original ones. Additionally, we investigate the reliability of the approximation with finite samples, giving the probability bound for violation with finite samples. Through a numerical example and an application case study of anomaly detection in wind power data, we evaluate the effectiveness of the proposed INN against existing approaches, including Bayesian neural networks, highlighting its capability to significantly improve the performance of applying INNs for regression and unsupervised anomaly detection.

Pixel-MPS: Stochastic Embedding and Density-Based Clustering of Image Patterns for Pixel-Based Multiple-Point Geostatistical Simulation

Multiple-point geostatistics (MPS) is an established tool for the uncertainty quantification of Earth systems modeling, particularly when dealing with the complexity and heterogeneity of geological data. This study presents a novel pixel-based MPS method for modeling spatial data using advanced machine-learning algorithms. Pixel-based multiple-point simulation implies the sequential modeling of individual points on the simulation grid, one at a time, by borrowing spatial information from the training image and honoring the conditioning data points. The developed methodology is based on the mapping of the training image patterns database using the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm for dimensionality reduction, and the clustering of patterns by applying the Density-based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, as an efficient unsupervised classification technique. For the automation, optimization, and input parameter tuning, multiple stages are implemented, including entropy-based determination of the template size and a k-nearest neighbors search for clustering parameter selection, to ensure the proposed method does not require the user’s interference. The proposed model is validated using synthetic two- and three-dimensional datasets, both for conditional and unconditional simulations, and runtime information is provided. Finally, the method is applied to a case study gold mine for stochastic orebody modeling. To demonstrate the computational efficiency and accuracy of the proposed method, a two-dimensional training image with 101 by 101 pixels is simulated for 100 conditional realizations in 453 s (~4.5 s per realization) using only 361 hard data points (~3.5% of the simulation grid), and the resulting average simulation has a good visual match and only an 11.8% pixel-wise mismatch with the training image.

Switching diffusions for multiscale uncertainty quantification

High-fidelity simulations are increasingly called-upon to resolve the nucleation of instabilities such as crack initiation and propagation and fluid mixing. While multiscale modeling capabilities have progressed rapidly over recent decades, associated simulations still present a computational burden, thus often preempting a systematic statistical analysis of related problems. Given the paucity of data that relate micro-structure to macroscale behavior, and the unavoidable modeling errors at both scales, the lack of a probabilistic characterization significantly limits the value of highly-resolved numerical simulators. The goal of the present research is to develop a probabilistic model that encodes pathwise relationships between micro and macro scales. Specifically, we develop a switching diffusion model to relate damage evolution, characterized at the microscale, to system performance identified with a macroscale property. Microscale behavior is modeled as a Markov switching process with a finite state space while the macroscale counterpart is modeled as a continuous-state diffusion process. The interaction between macro and micro scales is captured by coupling these two processes. Calibrated by data, the switching diffusion model can generate, with minimal computational effort, sample paths with prescribed statistics. The proposed model contributes new capabilities and perspectives at the interface of multiscale simulation, uncertainty quantification, and stochastic modeling.

Towards trustworthy cybersecurity operations using Bayesian Deep Learning to improve uncertainty quantification of anomaly detection

Uncertainty quantification of cybersecurity anomaly detection results provides critical guidance for decision makers on whether or not to accept the results. Improving the trustworthiness of anomaly predictions can reduce the amount of alert false positives that security teams have to process. In this work we investigate the use of Bayesian Autoencoder (BAE) models for uncertainty quantification in anomaly detection. A novel heteroscedastic aleatoric uncertainty modelling method is explored that jointly considers aleatoric and epistemic uncertainty. Heteroscedastic aleatoric uncertainty is modelled on the latent layer of the BAE and further explored through considering the variational lower bound. An uncertainty quantification framework for cybersecurity is designed and verified on UNSW-NB15 and CIC-IDS-2017 data sets. This research enhances the modelling of uncertainty in the BAE model and expands its application in cybersecurity.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics.

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Quantification of modeling uncertainty in the Rayleigh damping model

AbstractUnderstanding and accurately characterizing energy dissipation mechanisms in civil structures during earthquakes is an important element of seismic assessment and design. The most commonly used model is attributed to Rayleigh. This paper proposes a systematic approach to quantify the uncertainty associated with Rayleigh's damping model. Bayesian calibration with embedded model error is employed to treat the coefficients of the Rayleigh model as random variables using modal damping ratios. Through a numerical example, we illustrate how this approach works and how the calibrated model can address modeling uncertainty associated with the Rayleigh damping model.

Uncertainty qualification in seismic analysis of concrete dams based on model order reduction accelerated stochastic SBFEM

A pioneering framework for uncertainty quantification in seismic analysis of concrete dams rooted in the stochastic scaled boundary finite element method (SSBFEM) is proposed. For seismic analysis of dams, octree decomposition is used for mesh generation. SSBFEM is developed to predict the structural responses with randomly distributed material properties. The script in this paper can integrate octree mesh and SSBFEM into ABAQUS user element (UEL). Implementing octree SSBFEM on commercial software provides accurate and convenient full order models for uncertainty quantification. Monte Carlo simulation (MCs) is deployed to calculate the statistical characteristics of structural responses under random variables. Additionally, singular value decomposition (SVD) and radial basis function (RBF) are leveraged to refine traditional MCs. The solution space of MCs is decomposed into lower-order subspaces. Any structural responses can be rapidly evaluated from linear combinations of subspaces. Particularly, the method has been successfully applied to seismic analysis of concrete dams with different random material properties. Finally, several illustrative examples are provided to validate the accuracy and efficacy of the algorithm.

Uncertainty quantification of mass models using ensemble Bayesian model averaging

Uncertainty quantification of mass models using ensemble Bayesian model averaging

Fuzzy Predator-Prey Systems by Extended Runge-Kutta Method with Polynomial Interpolation Technique

The growing significance of uncertainty quantification in mathematical modeling of physical phenomena is evident, with fuzzy sets emerging as an alternative approach. This paper focuses on exploring a numerical method for addressing fuzzy differential equations in two-dimensional problems like fuzzy predator-prey systems. The numerical solution employed the extended Runge-Kutta fourth-order method. To overcome challenges related to polynomial fuzzy differential equations, a combination of the polynomial interpolation technique and the extended Runge-Kutta fourth-order method was applied, mitigating the issues associated with high-degree polynomials. The proposed approach for fuzzy predator-prey systems is briefly described, accompanied by a numerical example. The obtained results underscore the efficacy of the extended Runge-Kutta fourth-order method with polynomial interpolation, showcasing its remarkable accuracy and potential as an alternative method for addressing various uncertainty-related problems.

REHEATFUNQ (REgional HEAT-Flow Uncertainty and aNomaly Quantification) 2.0.1: a model for regional aggregate heat flow distributions and anomaly quantification

Abstract. Surface heat flow is a geophysical variable that is affected by a complex combination of various heat generation and transport processes. The processes act on different lengths scales, from tens of meters to hundreds of kilometers. In general, it is not possible to resolve all processes due to a lack of data or modeling resources, and hence the heat flow data within a region is subject to residual fluctuations. We introduce the REgional HEAT-Flow Uncertainty and aNomaly Quantification (REHEATFUNQ) model, version 2.0.1. At its core, REHEATFUNQ uses a stochastic model for heat flow within a region, considering the aggregate heat flow to be generated by a gamma-distributed random variable. Based on this assumption, REHEATFUNQ uses Bayesian inference to (i) quantify the regional aggregate heat flow distribution (RAHFD) and (ii) estimate the strength of a given heat flow anomaly, for instance as generated by a tectonically active fault. The inference uses a prior distribution conjugate to the gamma distribution for the RAHFDs, and we compute parameters for a uninformed prior distribution from the global heat flow database by Lucazeau (2019). Through the Bayesian inference, our model is the first of its kind to consistently account for the variability in regional heat flow in the inference of spatial signals in heat flow data. Interpretation of these spatial signals and in particular their interpretation in terms of fault characteristics (particularly fault strength) form a long-standing debate within the geophysical community. We describe the components of REHEATFUNQ and perform a series of goodness-of-fit tests and synthetic resilience analyses of the model. While our analysis reveals to some degree a misfit of our idealized empirical model with real-world heat flow, it simultaneously confirms the robustness of REHEATFUNQ to these model simplifications. We conclude with an application of REHEATFUNQ to the San Andreas fault in California. Our analysis finds heat flow data in the Mojave section to be sufficient for an analysis and concludes that stochastic variability can allow for a surprisingly large fault-generated heat flow anomaly to be compatible with the data. This indicates that heat flow alone may not be a suitable quantity to address fault strength of the San Andreas fault.

Variational inference: uncertainty quantification in additive models

Markov chain Monte Carlo (MCMC)-based simulation approaches are by far the most common method in Bayesian inference to access the posterior distribution. Recently, motivated by successes in machine learning, variational inference (VI) has gained in interest in statistics since it promises a computationally efficient alternative to MCMC enabling approximate access to the posterior. Classical approaches such as mean-field VI (MFVI), however, are based on the strong mean-field assumption for the approximate posterior where parameters or parameter blocks are assumed to be mutually independent. As a consequence, parameter uncertainties are often underestimated and alternatives such as semi-implicit VI (SIVI) have been suggested to avoid the mean-field assumption and to improve uncertainty estimates. SIVI uses a hierarchical construction of the variational parameters to restore parameter dependencies and relies on a highly flexible implicit mixing distribution whose probability density function is not analytic but samples can be taken via a stochastic procedure. With this paper, we investigate how different forms of VI perform in semiparametric additive regression models as one of the most important fields of application of Bayesian inference in statistics. A particular focus is on the ability of the rivalling approaches to quantify uncertainty, especially with correlated covariates that are likely to aggravate the difficulties of simplifying VI assumptions. Moreover, we propose a method, where we combine both advantages of MFVI and SIVI and compare its performance. The different VI approaches are studied in comparison with MCMC in simulations and an application to tree height models of douglas fir based on a large-scale forestry data set.

Developing climate services for vulnerable islands in the Southwest Indian Ocean: A combined statistical and dynamical CMIP6 downscaling approach for climate change assessment

Climate change is a global challenge necessitating adaptation at the local level. Small island developing states (SIDS) in the southwest Indian Ocean (SWIO) basin are particularly vulnerable and already facing significant challenges due to climate variability and extreme weather events like tropical cyclones (TCs). Tailored climate services, catering to their specific needs and contexts, are crucial for formulating appropriate adaptation strategies. This study aims to fill the gap of localized and reliable information for climate services in the SWIO region. A 12-km resolution regional climate model is dynamically downscaled from a CMIP6 model to capture the climatology of tropical cyclones. Outputs are bias-corrected at kilometer-scale resolution over multiple islands. A subset of CMIP6 simulations is also statistically downscaled over La Réunion to quantify model uncertainties at the local scale and compare statistical and dynamical downscaling methods.CMIP6 models project an average increase in daily mean temperatures over small islands ranging from 1.2 °C (SSP1-2.6) to 3.7 °C (SSP5-8.5) by the end of the century compared to the reference period of 1981–2010, and up to 4.4 °C on Madagascar (SSP5-8.5). The dry season in the SWIO region is anticipated to become significantly drier, with precipitation deficits ranging from 10 % to 40 %, primarily due to a delayed onset of the rainy season. The cyclonic risk is expected to increase due to stronger cyclone intensities, a higher proportion of strong TCs, and the poleward migration of very intense TCs by one to two degrees latitude, further amplifying the risk faced by the Mascarene islands.

Quantification of Uncertainty Cost Functions for Controllable Solar Power Modeling

Navigating the secheduling of generation resources of energy in power systems marked by a significant presence of renewable generation involves intricate optimization challenges. The conventional tools for resolving such challenges include programming techniques and heuristic approaches, both contingent upon a precisely articulated target function for optimization. Traditional optimization tools rely on precisely defined target functions, but the evolving landscape of power systems introduces complexity, especially with unpredictable behaviors of renewable sources. The research specifically quantifies penalty costs associated with photovoltaic (PV) generators, employing probabilistic methods for a robust mathematical analysis. The developed analytical model enhances adaptability in economic dispatch problems, considering uncertainty in decision-making. Validation using Monte Carlo simulation emphasizes uncertainty in PV generation and highlights the advantages of the proposed analytic model. The quadratic form of the model aligns coherently with simulation outcomes, contributing significantly to understanding uncertainty quantification in solar power modeling. The research aims to refine controllable solar power models, establish robust uncertainty cost functions, and improve the accuracy of economic dispatch strategies. Ultimately, this work promotes the seamless integration of solar energy into diverse and dynamic energy grids.