Bayesian Inference Algorithm Research Articles

Estimating evolutionary and demographic parameters via ARG-derived IBD.

Inference of evolutionary and demographic parameters from a sample of genome sequences often proceeds by first inferring identical-by-descent (IBD) genome segments. By exploiting efficient data encoding based on the ancestral recombination graph (ARG), we obtain three major advantages over current approaches: (i) no need to impose a length threshold on IBD segments, (ii) IBD can be defined without the hard-to-verify requirement of no recombination, and (iii) computation time can be reduced with little loss of statistical efficiency using only the IBD segments from a set of sequence pairs that scales linearly with sample size. We first demonstrate powerful inferences when true IBD information is available from simulated data. For IBD inferred from real data, we propose an approximate Bayesian computation inference algorithm and use it to show that even poorly-inferred short IBD segments can improve estimation. Our mutation-rate estimator achieves precision similar to a previously-published method despite a 4 000-fold reduction in data used for inference, and we identify significant differences between human populations. Computational cost limits model complexity in our approach, but we are able to incorporate unknown nuisance parameters and model misspecification, still finding improved parameter inference.

Bayesian Regression Analysis for Dependent Data with an Elliptical Shape.

This paper proposes a parametric hierarchical model for functional data with an elliptical shape, using a Gaussian process prior to capturing the data dependencies that reflect systematic errors while modeling the underlying curved shape through a von Mises-Fisher distribution. The model definition, Bayesian inference, and MCMC algorithm are discussed. The effectiveness of the model is demonstrated through the reconstruction of curved trajectories using both simulated and real-world examples. The discussion in this paper focuses on two-dimensional problems, but the framework can be extended to higher-dimensional spaces, making it adaptable to a wide range of applications.

Neural Network Constraints on the Cosmic-Ray Ionization Rate and Other Physical Conditions in NGC 253 with ALCHEMI Measurements of HCN and HNC

We use a neural network model and Atacama Large Millimeter/submillimeter Array (ALMA) observations of HCN and HNC to constrain the physical conditions, most notably the cosmic-ray ionization rate (CRIR, ζ), in the Central Molecular Zone (CMZ) of the starburst galaxy NGC 253. Using output from the chemical code UCLCHEM, we train a neural network model to emulate UCLCHEM and derive HCN and HNC molecular abundances from a given set of physical conditions. We combine the neural network with radiative transfer modeling to generate modeled integrated intensities, which we compare to measurements of HCN and HNC from the ALMA Large Program ALCHEMI. Using a Bayesian nested sampling framework, we constrain the CRIR, molecular gas volume and column densities, kinetic temperature, and beam-filling factor across NGC 253's CMZ. The neural network model successfully recovers UCLCHEM molecular abundances with ∼3% error and, when used with our Bayesian inference algorithm, increases the parameter-inference speed tenfold. We create images of these physical parameters across NGC 253's CMZ at 50 pc resolution and find that the CRIR, in addition to the other gas parameters, is spatially variable with ζ ∼ a few ×10−14 s−1 at r ≳ 100 pc from the nucleus, increasing to ζ > 10−13 s−1 at its center. These inferred CRIRs are consistent within 1 dex with theoretical predictions based on nonthermal emission. Additionally, the high CRIRs estimated in NGC 253's CMZ can be explained by the large number of cosmic-ray-producing sources as well as a potential suppression of cosmic-ray diffusion near their injection sites.

Cost-effectiveness analysis of Chagas disease screening in pregnant women and their infants in Italy

Abstract Background Currently, Chagas disease (CD) is widespread in European nations that host notable populations from Latin America. Vertical transmission is a pathway for the spread of the disease in countries where it is not endemic. Due to socio-economic disparities, CD is a public health concern in non-endemic regions, raised by migration phenomena in vulnerable population groups who face similar hindrances as those most at risk in endemic areas. The aim is to evaluate the cost-effectiveness of CD screening versus no screening in pregnant women and their infants in Italy. Methods A Bayesian Markov model was employed to compare the CD screening versus the no screening alternative. Model parameters were sourced from pertinent scientific literature. A lifetime perspective was adopted, aligning with the perspective of the Italian National Health Service. The Eurozone threshold was applied. Costs and benefits were discounted at a rate of 3%. Gibbs sampling served as the algorithm for Bayesian inference. Uncertainty was addressed through a probabilistic sensitivity analysis (PSA) and a value of information analysis (VOI), depicted via the Cost-Effectiveness Acceptability Curve (CEAC) and Expected Value of Perfect Information (EVPI). Results were presented as the Incremental Cost-Effectiveness Ratio (ICER). Results The base case results showed that CD screening was cost-effective, with an ICER of €5,112 [€1,850 - €10,043]. Furthermore, according to the CEAC, the screening option exhibited the greatest probability of being cost-effective across all thresholds. Additionally, the EVPI per mother was €818 based on a threshold of €50,000/diagnosis. Conclusions Implementing a structured CD screening program also in non-endemic countries has the potential for early detection and treatment. This contributes to SDG 3 by improving access to healthcare, preventing transmission, and reducing the disease burden as well as informing public health policies for marginalised populations. Key messages • This study proves that screening for CD in pregnant women and their infants in a non-endemic area is a cost-effective strategy and possibly cost-saving in the long term. • Study findings could support a wider implementation of CD screening in Italy by informing health policy-makers in their decision-making process.

Approximate inference on optimized quantum Bayesian networks

In recent years, there has been a significant upsurge in the interest surrounding Quantum machine learning, with researchers actively developing methods to leverage the power of quantum technology for solving highly complex problems across various domains. However, implementing gate-based quantum algorithms on noisy intermediate quantum devices (NISQ) presents notable challenges due to limited quantum resources and inherent noise. In this paper, we propose an innovative approach for representing Bayesian networks on quantum circuits, specifically designed to address these challenges and highlight the potential of combining optimized circuits with quantum hybrid algorithms for Bayesian network inference. Our aim is to minimize the required quantum resource needed to implement a Quantum Bayesian network (QBN) and implement quantum approximate inference algorithm on a quantum computer. Through simulations and experiments on IBM Quantum computers, we show that our circuit representation significantly reduces the resource requirements without decreasing the performance of the model. These findings underscore how our approach can better enable practical applications of QBN on currently available quantum hardware.

Using Early Rejection Markov Chain Monte Carlo and Gaussian Processes to Accelerate ABC Methods

Approximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets problems with intractable or unavailable likelihood functions. It uses synthetic data drawn from the simulation model to approximate the posterior distribution. However, ABC is computationally intensive for complex models in which simulating synthetic data is very expensive. In this article, we propose an early rejection Markov chain Monte Carlo (ejMCMC) sampler based on Gaussian processes to accelerate inference speed. We early reject samples in the first stage of the kernel using a discrepancy model, in which the discrepancy between the simulated and observed data is modeled by Gaussian process (GP). Hence, synthetic data is generated only if the parameter space is worth exploring. We demonstrate through theory, simulation experiments, and real data analysis that the new algorithm significantly improves inference efficiency compared to existing early-rejection MCMC algorithms. In addition, we employ our proposed method within an ABC sequential Monte Carlo (SMC) sampler. In our numerical experiments, we use examples of ordinary differential equations, stochastic differential equations, and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We develop an R package that is available at https://github.com/caofff/ejMCMC.

Jaxspec : A fast and robust Python library for X-ray spectral fitting

Inferring spectral parameters from X-ray data is one of the cornerstones of high-energy astrophysics, and is achieved using software stacks that have been developed over the last 20 years and more. However, as models get more complex and spectra are obtained with higher resolutions, these established software solutions become more feature-heavy, difficult to maintain and less efficient. We present jaxspec a Python package for performing this task quickly and robustly in a fully Bayesian framework. Based on the JAX ecosystem jaxspec allows the generation of differentiable likelihood functions compilable on core or graphical process units (GPUs), enabling the use of robust algorithms for Bayesian inference. We demonstrate the effectiveness of jaxspec samplers, in particular the no U-turn sampler, using a composite model and comparing what we obtain with the existing frameworks. We also demonstrate its ability to process high-resolution spectroscopy data using original methods by reproducing the results of the Hitomi collaboration on the Perseus cluster, while solving the inference problem using variational inference on a GPU. We obtain identical results when compared to other software and approaches, meaning that jaxspec provides reliable results while being $ 10$ times faster than existing alternatives. In addition, we show that variational inference can produce convincing results even on high-resolution data in less than 10 minutes on a GPU. With this package, we aim to pursue the goal of opening up X-ray spectroscopy to the existing ecosystem of machine learning and Bayesian inference, enabling researchers to apply new methods to solve increasingly complex problems in the best possible way. Our long-term ambition is the scientific exploitation of the data from the newAthena X-ray Integral Field Unit (X-IFU).

The ESO SupJup Survey II. The 12C/13C isotope ratios of three young brown dwarfs with CRIRES+

Young brown dwarfs exhibit atmospheric characteristics similar to those of super-Jupiters, providing a unique opportunity to study planetary atmospheres. Atmospheric retrievals of high-resolution spectra reveal detailed properties of these objects, with elemental and isotopic ratios offering insights into their formation history. The ESO SupJup Survey, utilising CRIRES$^+$ on the Very Large Telescope, aims to assess the role of as a formation tracer. We present observations of three young brown dwarfs: 2MASS J12003792-7845082, TWA 28, and 2MASS J08561384-1342242. Our goal is to constrain their chemical compositions, thermal profiles, surface gravities, spin rotations, and Cratio. We conducted atmospheric retrievals of CRIRES$^+$ K-band spectra, coupling the radiative transfer code petitRADTRANS with the Bayesian inference algorithm MultiNest The retrievals provide a detailed characterisation of the atmospheres of the three objects. We report the volume mixing ratios of the main molecular and atomic species: HF, Na, Ca, and Ti, including the novel detection of hydrogen fluoride (HF) in the atmosphere of a brown dwarf. We determine values of $ and $79^ $ in the atmospheres of TWA 28 and J0856, respectively, with strong significance ($>3 We also report tentative evidence ($ of in J1200, at $. Additionally, we detect at moderate significance in J0856 (3.3sigma ) and TWA 28 (2.1sigma ). The retrieved thermal profiles are consistent with hot atmospheres ($2300-2600$ K) with low surface gravities and slow spins, as expected for young objects. The measured carbon isotope ratios are consistent among the three objects and show no significant deviation from that of the local interstellar medium, suggesting a fragmentation-based formation mechanism similar to star formation. The tentative detection of in two objects of our sample highlights the potential of high-resolution spectroscopy to probe additional isotope ratios, such as O in the atmospheres of brown dwarfs and super-Jupiters.

Degree distributions in networks: Beyond the power law

AbstractThe power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log‐log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf‐polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.

Reconciling shared versus context-specific information in a neural network model of latent causes

It has been proposed that, when processing a stream of events, humans divide their experiences in terms of inferred latent causes (LCs) to support context-dependent learning. However, when shared structure is present across contexts, it is still unclear how the “splitting” of LCs and learning of shared structure can be simultaneously achieved. Here, we present the Latent Cause Network (LCNet), a neural network model of LC inference. Through learning, it naturally stores structure that is shared across tasks in the network weights. Additionally, it represents context-specific structure using a context module, controlled by a Bayesian nonparametric inference algorithm, which assigns a unique context vector for each inferred LC. Across three simulations, we found that LCNet could (1) extract shared structure across LCs in a function learning task while avoiding catastrophic interference, (2) capture human data on curriculum effects in schema learning, and (3) infer the underlying event structure when processing naturalistic videos of daily events. Overall, these results demonstrate a computationally feasible approach to reconciling shared structure and context-specific structure in a model of LCs that is scalable from laboratory experiment settings to naturalistic settings.

Ultra-Efficient MCMC for Bayesian Longitudinal Functional Data Analysis

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only provide either scalable computing or accurate approximations to the posterior distribution, but not both. We introduce a new MCMC sampling strategy for highly efficient and fully Bayesian regression with longitudinal functional data. Using a novel blocking structure paired with an orthogonalized basis reparameterization, our algorithm jointly samples the fixed effects regression functions together with all subject- and replicate-specific random effects functions. Crucially, the joint sampler optimizes sampling efficiency for these key parameters while preserving computational scalability. Perhaps surprisingly, our new MCMC sampling algorithm even surpasses state-of-the-art algorithms for frequentist estimation and variational Bayes approximations for functional mixed models—while also providing accurate posterior uncertainty quantification—and is orders of magnitude faster than existing Gibbs samplers. Simulation studies show improved point estimation and interval coverage in nearly all simulation settings over competing approaches. We apply our method to a large physical activity dataset to study how various demographic and health factors associate with intraday activity. Supplementary materials for this article are available online.

Kernel Bayesian logistic tensor decomposition with automatic rank determination for predicting multiple types of miRNA-disease associations.

Identifying the association and corresponding types of miRNAs and diseases is crucial for studying the molecular mechanisms of disease-related miRNAs. Compared to traditional biological experiments, computational models can not only save time and reduce costs, but also discover potential associations on a large scale. Although some computational models based on tensor decomposition have been proposed, these models usually require manual specification of numerous hyperparameters, leading to a decrease in computational efficiency and generalization ability. Additionally, these linear models struggle to analyze complex, higher-order nonlinear relationships. Based on this, we propose a novel framework, KBLTDARD, to identify potential multiple types of miRNA-disease associations. Firstly, KBLTDARD extracts information from biological networks and high-order association network, and then fuses them to obtain more precise similarities of miRNAs (diseases). Secondly, we combine logistic tensor decomposition and Bayesian methods to achieve automatic hyperparameter search by introducing sparse-induced priors of multiple latent variables, and incorporate auxiliary information to improve prediction capabilities. Finally, an efficient deterministic Bayesian inference algorithm is developed to ensure computational efficiency. Experimental results on two benchmark datasets show that KBLTDARD has better Top-1 precision, Top-1 recall, and Top-1 F1 for new type predictions, and higher AUPR, AUC, and F1 values for new triplet predictions, compared to other state-of-the-art methods. Furthermore, case studies demonstrate the efficiency of KBLTDARD in predicting multiple types of miRNA-disease associations.

Bayesian estimation of group event-related potential components (BEGEP): testing a model for synthetic and real datasets

Objective. The spatial resolution of event-related potentials (ERPs) recorded on the head surface is quite low, since the sensors located on the scalp register mixtures of signals from several cortical sources. Bayesian models for multi-channel ERPs obtained from a group of subjects under multiple task conditions can aid in recovering signals from these sources. Approach. This study introduces a novel model that captures several important characteristics of ERP, including person-to-person variability in the magnitude and latency of source signals. Furthermore, the model takes into account that ERP noise, the main source of which is the background electroencephalogram, has the following properties: it is spatially correlated, spatially heterogeneous, and varies over time and from person to person. Bayesian inference algorithms have been developed to estimate the parameters of this model, and their performance has been evaluated through extensive experiments using synthetic data and real ERPs records in a large number of subjects (N = 351). Main results. The signal estimates obtained using these algorithms were compared with the results of the analysis of ERPs by conventional methods. This comparison showed that the use of this model is suitable for the analysis of ERPs and helps to reveal some features of source signals that are difficult to observe in their mixture signals recorded on the scalp. Significance. This study shown that the proposed method is a potentially useful tool for analyzing ERPs collected from groups of subjects in various cognitive neuroscience experiments.

Opponent Exploitation Based on Bayesian Strategy Inference and Policy Tracking

In a multi-agent competitive environment, it is important for an agent to detect the opponent's policy and adopt a suitable policy to exploit the opponent. Conventionally, most methods, e.g., Bayesian Policy Reuse (BPR) variants, assume the opponent adopts a fixed policy or a randomly changing policy. In this paper, we make a more realistic and reasonable assumption that the opponent may select its policy based on the previous observation. Here, we define the term “strategy” as the mapping from the previous observation to the opponent's selected policy, and we propose the Bayesian Strategy Inference (BSI) framework to infer the opponent's strategy. Furthermore, to deal with opponents who may randomly select their policies, the BSI framework is combined with an intra-episode policy tracking mechanism to construct the Bayesian Strategy Inference plus Policy Tracking (BSI-PT) algorithm. In our experiments, we design an extended batter vs. pitcher game (EBvPG) for the evaluation of the proposed BSI-PT framework. The experimental results demonstrate that BSI-PT obtains higher policy prediction accuracy and winning percentage than three other BPR variants against the opponents with a specific policy selection strategy, with a random selection strategy, or with a partially random strategy.

Species Delimitation of Some Melanargia Species (Lepidoptera, Nymphalidae, Satyrinae) in The Southeastern Anatolia Region Based On The mtCOI Gene

Among the Palearctic species, butterflies of the genus Melanargia are known for their black and white wing patterns. The morphological character polarization of this genus is full of varying combinations of subgenus, species complex, and subspecies status. Its taxonomy is open to debate, especially in species and subspecies categories, with definitions mostly based on wing color. In recent years, cryptic species, phenotypically masked species, and species with intense intraspecific variation have been identified through the determination of lineages under the leadership of molecular systematics. The mtCOI gene, which is especially described as a species signature, is an important DNA barcode used for Lepidoptera. In the presented study, the mtCOI gene sequence of the populations of Melanargia larissa, M.grumi, M.hylata, M.syriaca, and M.russiae species in the southeastern Anatolia region was determined for the first time. To determine the boundaries of these species, gene characterization and genetic distances were carried out according to the Kimura-2 Parameter, and putative species analyses were carried out by the ABGD method. Trees were constructed with Maximum likelihood and Bayesian inference algorithms to determine the phylogenetic relationships between species of the genus. In light of these analyses, it has been shown that the genetic distance of morphological species M. larissa, M. grumi, M.hylata, and M. syriaca is not at the species level and that M.larissa maintains its species status according to the principle of priority. In addition, the M.russiae population presented in this study forms a monophyletic clade with other populations of the same species in the phylogenetic tree, proving that this taxon is a stable species.

System identifiability in a time-evolving agent-based model.

Mathematical models are a valuable tool for studying and predicting the spread of infectious agents. The accuracy of model simulations and predictions invariably depends on the specification of model parameters. Estimation of these parameters is therefore extremely important; however, while some parameters can be derived from observational studies, the values of others are difficult to measure. Instead, models can be coupled with inference algorithms (i.e., data assimilation methods, or statistical filters), which fit model simulations to existing observations and estimate unobserved model state variables and parameters. Ideally, these inference algorithms should find the best fitting solution for a given model and set of observations; however, as those estimated quantities are unobserved, it is typically uncertain whether the correct parameters have been identified. Further, it is unclear what 'correct' really means for abstract parameters defined based on specific model forms. In this work, we explored the problem of non-identifiability in a stochastic system which, when overlooked, can significantly impede model prediction. We used a network, agent-based model to simulate the transmission of Methicillin-resistant staphylococcus aureus (MRSA) within hospital settings and attempted to infer key model parameters using the Ensemble Adjustment Kalman Filter, an efficient Bayesian inference algorithm. We show that even though the inference method converged and that simulations using the estimated parameters produced an agreement with observations, the true parameters are not fully identifiable. While the model-inference system can exclude a substantial area of parameter space that is unlikely to contain the true parameters, the estimated parameter range still included multiple parameter combinations that can fit observations equally well. We show that analyzing synthetic trajectories can support or contradict claims of identifiability. While we perform this on a specific model system, this approach can be generalized for a variety of stochastic representations of partially observable systems. We also suggest data manipulations intended to improve identifiability that might be applicable in many systems of interest.

Sparse species interactions reproduce abundance correlation patterns in microbial communities

During the last decades, macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations of different species are found to be correlated, both across time and across communities in metagenomic samples. Reproducing such correlations through appropriate population models remains an open challenge. The present paper tackles this problem and points to sparse species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka-Volterra constants as a successful ansatz. For this, we design a Bayesian inference algorithm to extract sets of interaction constants able to reproduce empirical probability distributions of pairwise correlations for diverse biomes. Importantly, the inferred models still reproduce well-known single-species macroecological patterns concerning abundance fluctuations across both species and communities. Endorsed by the agreement with the empirically observed phenomenology, our analyses provide insights into the properties of the networks of microbial interactions, revealing that sparsity is a crucial feature.

Promoting the transformation of agricultural supply chain management under the development of digital economy in the Internet era

Abstract Agricultural products, as the necessities of people’s daily consumption, are related to the national economy and people’s livelihood, and the development of information technology provides a new direction and ideas for the transformation of agricultural products supply chain management. The article proposes the risk assessment method for the agricultural products supply chain based on the Bayesian network inference algorithm and OWA algorithm, firstly constructs the Bayesian network model for risk assessment of agricultural products supply chain, elaborates on the belief updating algorithm and the belief-free updating algorithm in the Bayesian network, then combines with the OWA operator, proposes the method of risk diagnosis of agricultural products supply chain based on the Bayes-OWA hybrid operator, and with this The algorithm is the core of the proposed agricultural supply chain management strategy. Through empirical tests, it can be obtained that the average supply time of enterprise 4 in agricultural products is 22.3 days, and the reliability of supply is 92.3%, which is highly efficient. In the agricultural products supply program, the average value of quality qualification rate has been improved by 2.67%, the average number of days for supplier delivery has been shortened by 13 days, and the supplier’s ability to respond quickly to demand has been improved by 3.61%. Therefore, actively constructing the informationization construction of the agricultural supply chain, building a logistics information platform, improving rural communication facilities, and providing timely market information to farmers can better ensure the efficient operation of the agricultural supply chain.

Bayesian Calibration to Address the Challenge of Antimicrobial Resistance: A Review.

Antimicrobial resistance (AMR) emerges when disease-causing microorganisms develop the ability to withstand the effects of antimicrobial therapy. This phenomenon is often fueled by the human-to-human transmission of pathogens and the overuse of antibiotics. Over the past 50 years, increased computational power has facilitated the application of Bayesian inference algorithms. In this comprehensive review, the basic theory of Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods are explained. These inference algorithms are instrumental in calibrating complex statistical models to the vast amounts of AMR-related data. Popular statistical models include hierarchical and mixture models as well as discrete and stochastic epidemiological compartmental and agent based models. Studies encompassed multi-drug resistance, economic implications of vaccines, and modeling AMR in vitro as well as within specific populations. We describe how combining these topics in a coherent framework can result in an effective antimicrobial stewardship. We also outline recent advancements in the methodology of Bayesian inference algorithms and provide insights into their prospective applicability for modeling AMR in the future.

Airborne Pollutant Removal Effectiveness and Hidden Pollutant Source Identification of Bionic Ventilation Systems: Direct and Inverse CFD Demonstrations

A healthy and efficient ventilation system is essential for establishing a comfortable indoor environment and significantly reducing a building’s energy demand simultaneously. This paper proposed a novel ventilation system and applied it to the IEA Annex 20 mixing ventilation enclosure to verify its feasibility through mathematical modeling and CFD simulations. First, two bionic ventilation systems, single-side and dual-side ventilations, were compared to a conventional constant-volume supply system using CFD simulations, with the results demonstrating that the bionic ventilation system could provide higher ventilation efficiency and more effective pollutant removal from stagnant regions. Furthermore, the present work exercised these two bionic ventilation systems with different temporal periods of sine and rectangular wave functions, identifying a turning point at a period of 0.06 τ n , which could contribute to further enhancement of these bionic ventilation systems. Finally, a methodology depending on the Bayesian inference algorithm was developed for identifying pollution sources in the bionic ventilation system with unstable flow fields, and factors influencing source identification accuracy were discussed. The results show that the peaks of the KDE distributions and the sampling average values of both the source location and intensity are all consistent with the actual source parameters. The potential of the proposed bionic ventilation systems has been well demonstrated by direct and inverse CFD models, paving the way for further engineering applications.