Local Model Research Articles

Assessment of digital elevation models accuracy for local geoid modeling

One of the critical factors influencing the accuracy of a local geoid model is the quality of the digital elevation model (DEM). A properly selected high-resolution DEM can significantly mitigate errors in geoid modeling, gravity anomaly processing, and topography and downward continuation correction. Purpose. Evaluating the accuracy of five global DEMs obtained from open sources to identify the most suitable model for creating a local geoid. Methodology. The vertical accuracy of the DEMs was assessed by comparing the heights between the DEM and control points across different types of terrain. The reference values are based on 344 ground benchmarks, where GNSS observations were performed with subsequent adjustment of coordinates and heights. The accuracy analysis involved calculating statistical indicators of the height differences between the GNSS data and the DEM data. Findings. The standard deviation assessment showed favorable values for the COPERNICUS and ALOS DEMs, followed by SRTM, ASTER, and ETOPO. In the mean absolute error calculations for mountainous areas, the ALOS model performed best, followed by COPERNICUS, SRTM, ASTER, and ETOPO. For other types of terrain, COPERNICUS demonstrated the best results in mean absolute error. Originality. This study distinguishes itself through the incorporation of advanced high-resolution DEMs, such as GLO30, providing a modern and thorough evaluation of DEM accuracy specifically for Kazakhstan. What is new is a detailed analysis of the impact of terrain features (plain, hilly, mountainous) on modeling accuracy. This approach advances beyond previous assessments, delivering new and significant insights into the performance of contemporary DEMs. Practice value. The practical value of the results obtained consists in issuing recommendations regarding the possibility of using the studied DEM for the regions of Kazakhstan which differ among themselves in terms of landscape characteristics. The findings indicate that COPERNICUS and ALOS DEMs are highly suitable for precise geoid modeling in southern Kazakhstan. These models can significantly improve the accuracy of local geoid models, benefiting applications in geospatial science and engineering.

Federated learning-based wavelength demodulation system for multi-point distributed multi-peak FBG sensors

Machine learning-based demodulation of multi-peak fiber Bragg grating (FBG) sensors has been extensively studied, demonstrating superior performance compared to conventional algorithms because it can neglect potential physical constraints. As the number of real-world monitoring points increases, the volume of fiber-optic sensing data grows exponentially. This necessitates aggregating data from various regions (e.g., via Wi-Fi), unlike traditional single-point monitoring, which challenges server storage capacity and communication efficiency. To address these issues, this paper proposes a federated learning (FL)-based framework for efficient wavelength demodulation of multi-peak FBGs in multipoint monitoring. Specifically, an arrayed waveguide grating (AWG) with multiplexing capability is employed at different monitoring points to convert spectral features into multi-channel transmission intensities, serving as training data for local models. Subsequently, the local model parameters, trained independently at each point, are uploaded to a central server to derive the optimal global model for demodulation across different monitoring points. The proposed demodulation framework is validated through stress demodulation experiments on multi-peak FBG sensors. Experimental results indicate strong multi-peak extraction performance with a demodulation error of ±0.64 pm. Additionally, the method demonstrates excellent applicability for generating high-precision global demodulation models through multi-node cooperative work under various scenarios.

MatSwarm: trusted swarm transfer learning driven materials computation for secure big data sharing

The rapid advancement of Industry 4.0 necessitates close collaboration among material research institutions to accelerate the development of novel materials. However, multi-institutional cooperation faces significant challenges in protecting sensitive data, leading to data silos. Additionally, the heterogeneous and non-independent and identically distributed (non-i.i.d.) nature of material data hinders model accuracy and generalization in collaborative computing. In this paper, we introduce the MatSwarm framework, built on swarm learning, which integrates federated learning with blockchain technology. MatSwarm features two key innovations: a swarm transfer learning method with a regularization term to enhance the alignment of local model parameters, and the use of Trusted Execution Environments (TEE) with Intel SGX for heightened security. These advancements significantly enhance accuracy, generalization, and ensure data confidentiality throughout the model training and aggregation processes. Implemented within the National Material Data Management and Services (NMDMS) platform, MatSwarm has successfully aggregated over 14 million material data entries from more than thirty research institutions across China. The framework has demonstrated superior accuracy and generalization compared to models trained independently by individual institutions.

Integrated Navigation Method for Orchard-Dosing Robot Based on LiDAR/IMU/GNSS

To enhance the localization reliability and obstacle avoidance performance of the dosing robot in complex orchards, this study proposed an integrated navigation method using LiDAR, IMU, and GNSS. Firstly, the tightly coupled LIO-SAM algorithm was used to construct an orchard grid map for path planning and obstacle avoidance. Then, a global localization model based on RTK-GNSS was developed to achieve accurate and efficient initial localization of the robot’s coordinates and heading, and a Kalman filter was applied to integrate GNSS and IMU to improve robustness. Next, an improved A* algorithm was introduced to ensure the global operational path maintained a safe distance from obstacles, while the DWA algorithm handled dynamic obstacle avoidance. Field tests showed that the global localization model achieved an accuracy of 2.215 cm, with a standard deviation of 1 cm, demonstrating stable positioning performance. Moreover, the global path maintained an average safe distance of 50.75 cm from the obstacle map. And the robot exhibited a maximum absolute lateral deviation of 9.82 cm, with an average of 4.16 cm, while maintaining a safe distance of 1 m from dynamic obstacles. Overall, the robot demonstrated smooth and reliable autonomous navigation, successfully completing its tasks.

An analysis of decipherable red blood cell abnormality detection under federated environment leveraging XAI incorporated deep learning

In recent times, automated detection of diseases from pathological images leveraging Machine Learning (ML) models has become fairly common, where the ML models learn detecting the disease by identifying biomarkers from the images. However, such an approach requires the models to be trained on a vast amount of data, and healthcare organizations often tend to limit access due to privacy concerns. Consequently, collecting data for traditional centralized training becomes challenging. These privacy concerns can be handled by Federation Learning (FL), which builds an unbiased global model from local models trained with client data while maintaining the confidentiality of local data. Using FL, this study solves the problem of centralized data collection by detecting deformations in images of Red Blood Cells (RBC) in a decentralized way. To achieve this, RBC data is used to train multiple Deep Learning (DL) models, and among the various DL models, the most efficient one is considered to be used as the global model inside the FL framework. The FL framework works by copying the global model’s weight to the client’s local models and then training the local models in client-specific devices to average the weights of the local model back to the global model. In the averaging process, direct averaging is performed and alongside, weighted averaging is also done to weigh the individual local model’s contribution according to their performance, keeping the FL framework immune to the effects of bad clients and attacks. In the process, the data of the client remains confidential during training, while the global model learns necessary information. The results of the experiments indicate that there is no significant difference in the performance of the FL method and the best-performing DL model, as the best-performing DL model reaches an accuracy of 96% and the FL environment reaches 94%-95%. This study shows that the FL technique, in comparison to the classic DL methodology, can accomplish confidentiality secured RBC deformation classification from RBC images without substantially diminishing the accuracy of the categorization. Finally, the overall validity of the classification results has been verified by employing GradCam driven Explainable AI techniques.

Preoperative chemo-CIRT in Re/BRe pancreatic cancer: Insights from a multicenter prospective phase II clinical study (NCT03822936).

There is debate about the optimal management of borderline resectable (bRe) and resectable (Re) pancreatic ductal adenocarcinoma (PDAC). Both preclinical and clinical evidence showed that carbon ion radiotherapy (CIRT) produces superior control on radioresistant histologies compared to conventional photon beam radiotherapy (RT). However, so far there is a lack of data concerning the integration of CIRT in a multimodal approach with chemotherapy and surgery for bRe/Re. We recently presented the first analysis of a multicenter prospective phase II clinical study aimed at assessing the feasibility and effectiveness of a neoadjuvant chemotherapy + short course of CIRT followed by surgery and adjuvant chemotherapy in the management of bRe/Re PDAC. The study was terminated early due to low patient enrollment.Herein, we reported a post-hoc analysis focusing on toxicity, dosimetry and translational assessment. In our experience, CIRT can be integrated into a multimodal treatment strategy for bRe/Re PDAC, alongside chemotherapy and surgery. A case of fatal liver failure occurring three months post-surgery has been documented, likely related to the combination approach. Although the treatment plans were satisfactory according to the Local Effect Model (LEM) model, recalculations using the modified Microdosimetric Kinetic Model (mMKM) revealed suboptimal target coverage. Additionally, we observed an increased expression of PD-L1 following CIRT. This multimodal approach was well tolerated; however, clinicians should carefully monitor for vascular disorders during follow-up and further investigate surgical techniques after CIRT. The increased PD-L1 expression supports the immunogenic effects of particle therapy and lays the groundwork for future studies. To enhance the therapeutic ratio of CIRT treatments, integrating dose-averaged LETd (LETd-based objectives into the plan optimization process should be considered. ClinicalTrials.gov Identifier: NCT03822936.

Federated Learning-Based Traffic Flow Prediction Model in Intelligent Transportation Systems

The existing Intelligent Transportation System (ITS) achieves high success. As an essential component of ITS, Traffic Flow Prediction (TFP) has attracted tremendous attention. It is a critical but challenging task to improve the robust convergence and high accuracy of TFP in real-world scenarios. This study presents an optimized Federated Learning (FL)-based ChebNet model, FedproxChebNet, to realize the highly effective and accurate TFP. By selecting the best penalty constant in the proximal term to optimize the objective function, this model can achieve fast and stable convergence. Using the ChebNet model to aggregate neighbor nodes’ characteristics, more hidden information underlying the spatio-temporal traffic data can be taken into consideration for training the global and local models. All the superiority of the FedproxChebNet model makes it outperform other FL models with the Graph Convolutional Network (GCN), Graph Attention Network (GAT) and Spatio-Temporal Graph Convolutional Network (STGCN). We designed a series of experiments on various FL-based GNN model comparisons, parameter sensitivity tests, and on verifying the performance of FedproxChebNet with different heterogeneous systems with [Formula: see text], [Formula: see text] and [Formula: see text]. Based on four real-world data sets from the cognitive network, the experimental results demonstrate that the presented FedproxChebNet provides the best convergence and the highest accuracy in TFP, and achieves the best performance in a highly heterogeneous system ([Formula: see text]). Specifically, the accuracy of FedproxChebNet is at least improved by [Formula: see text] on PeMS07 than other FL-based GNN models. This proposed FedproxChebNet model may be preferable for different scenarios in ITS such as route planning, traffic congestion control and reversible lanes.

Comparison of ANN and XGBoost surrogate models trained on small numbers of building energy simulations.

Surrogate optimisation holds a big promise for building energy optimisation studies due to its goal to replace the use of lengthy building energy simulations within an optimisation step with expendable local surrogate models that can quickly predict simulation results. To be useful for such purpose, it should be possible to quickly train precise surrogate models from a small number of simulation results (10-100) obtained from appropriately sampled points in the desired part of the design space. Two sampling methods and two machine learning models are compared here. Latin hypercube sampling (LHS), widely accepted in building energy community, is compared to an exploratory Monte Carlo-based sequential design method mc-intersite-proj-th (MIPT). Artificial neural networks (ANN), also widely accepted in building energy community, are compared to gradient-boosted tree ensembles (XGBoost), model of choice in many machine learning competitions. In order to get a better understanding of the behaviour of these two sampling methods and two machine learning models, we compare their predictions against a large set of generated synthetic data. For this purpose, a simple case study of an office cell model with a single window and a fixed overhang, whose main input parameters are overhang depth and height, while climate type, presence of obstacles, orientation and heating and cooling set points are additional input parameters, was extensively simulated with EnergyPlus, to form a large underlying dataset of 729,000 simulation results. Expendable local surrogate models for predicting simulated heating, cooling and lighting loads and equivalent primary energy needs of the office cell were trained using both LHS and MIPT and both ANN and XGBoost for several main hyperparameter choices. Results show that XGBoost models are more precise than ANN models, and that for both machine learning models, the use of MIPT sampling leads to more precise surrogates than LHS.

RNEP: Random Node Entropy Pairing for Efficient Decentralized Training with Non-IID Local Data

The proliferation of edge devices and advancements in Internet of Things technology have created a vast array of distributed data sources, necessitating machine learning models that can operate closer to the point of data generation. Traditional centralized machine learning approaches often struggle with real-time big data applications, such as climate prediction and traffic simulation, owing to high communication costs. In this study, we introduce random node entropy pairing, a novel distributed learning method for artificial neural networks tailored to distributed computing environments. This method reduces communication overhead and addresses data imbalance by enabling nodes to exchange only the weights of their local models with randomly selected peers during each communication round, rather than sharing the entire dataset. Our findings indicate that this approach significantly reduces communication costs while maintaining accuracy, even when learning from non-IID local data. Furthermore, we explored additional learning strategies that enhance system accuracy by leveraging the characteristics of this method. The results demonstrate that random node entropy pairing is an effective and efficient solution for distributed learning in environments where communication costs and data distribution present significant challenges.

Large-eddy simulation of tip clearance cavitating flow around a hydrofoil

Large-eddy simulations of tip clearance cavitating flow between a National Advisory Committee for Aeronautics 0012 hydrofoil and the endwall have been performed to investigate the effects of cavitation on vortical structures, turbulence statistics and hydrofoil performance within the tip clearance region. The wall-adapting local eddy-viscosity model is employed to compute the subgrid-scale stress, and the Zwart-Gerber-Belamri cavitation model is used to predict the cavitating flow. The simulation results show that cavitation has insignificant effects on the tip clearance flow structures and the wandering motion of the tip leakage vortex (TLV). Detailed analysis of turbulence statistics indicates that the turbulent kinetic energy and pressure fluctuation inside the TLV core are significantly increased under the effect of cavitation. In addition, it is found that cavitation enhances the unstable wall-normal motion of the TLV, leading to the enhancement of turbulence near the TLV core. The hydrofoil performance affected by cavitation is also investigated, showing that the lift and drag forces acting on the hydrofoil is substantially reduced due to the cavitation.

Redefining “expansion” in congressional communication: Homestyles for a digital constituency

AbstractSelf‐presentation in Congress is more nationalized, with digital constituencies on platforms such as Twitter offering new reputation‐building opportunities. Digital constituencies transform traditional expectations of constituent communication, challenging Richard Fenno's theory that representatives adopt an “expansionist” style with constituents during early, vulnerable phases of their tenure. In a digital era that encourages a more national approach, we question how Fenno's distinction between expansionist and protectionist phases of connecting with constituents applies to reputation‐building with digital constituencies. While electorally vulnerable senators still seek to expand their presentation among geographic constituents, digital platforms, such as Twitter, incentivize them to protect their reputation among a digital constituency. We analyzed senators' Twitter communications from 2013 to 2023. We find the electoral vulnerabilities of Fenno's expansionist local model are associated with a protectionist model of engagement with digital constituencies on Twitter. Our study sheds light on the significance of online reputation management and its implications for representing a media‐influenced, modern Congress.

Leveraging Machine Learning for Photometric Redshift Estimation of JWST Galaxies

With the launch of JWST, the volume and complexity of astronomical data are increasing, a trend that will continue with future instruments such as SKA and Euclid. It is inevitable that data-driven methods will become more prominent alongside model-driven analysis. This research utilises machine learning, specifically a kernelised local linear regression model, in photometric redshift predictions of galaxies observed with JWST. With a spectroscopic dataset of 4605 galaxies, we trained the model and achieved a deviation of σdz = 0.018 and a catastrophic outlier rate of foutlier = 3.5%. These results demonstrate high accuracy and computational efficiency, highlighting the potential of machine learning for astronomical data analysis, in particular for large-scale surveys.

Seasonal Variations of PM2.5 Pollution in the Chengdu–Chongqing Urban Agglomeration, China

During the development of the Chengdu–Chongqing Urban Agglomeration (CCUA) in China, PM2.5 pollution severely threatened public health, presenting a significant environmental challenge. This study employs a novel spatial interpolation method known as High Accuracy Surface Modeling (HASM), along with the geographical detector method, local and regional contributions calculation model, and the Hybrid Single–Particle Lagrangian Integrated Trajectory model to analyze the seasonal spatial distribution of PM2.5 concentrations and their anthropogenic driving factors from 2014 to 2023. The transport pathway and potential sources of seasonal PM2.5 concentrations were also examined. The results showed the following: (1) HASM was identified as the most suitable interpolation method for monitoring PM2.5 concentrations in the CCUA; (2) The PM2.5 concentrations exhibited a decreasing trend across all seasons, with the highest values in winter and the lowest in summer. Spatially, the concentrations showed a pattern of being higher in the southwest and lower in the southeast; (3) Industrial soot (dust) emissions (ISEs) and industry structure (IS) were the most important anthropogenic driving factors influencing PM2.5 pollution; (4) The border area between the eastern part of the Tibet Autonomous Region and western Sichuan province in China significantly contribute to PM2.5 pollution in the CCUA, especially during winter.

Understanding Relaxation in the Kob-Andersen Liquid Based on Entropy, String, Shoving, Localization, and Parabolic Models.

We assess the validity of a range of models of glass formation based on molecular dynamics simulation results of the Kob-Andersen (KA) model system under a wide range of constant volume and constant pressure conditions. These models include the Adam-Gibbs model emphasizing configurational entropy, the string model emphasizing collective particle exchange motion, the shoving model emphasizing material elasticity, the localization model emphasizing dynamical free volume, and parabolic models based on the ideas of dynamic facilitation and, alternatively, the hypothesis that glass formation involves an avoided critical point. We demonstrate that these seemingly disparate models all provide a reasonable description of structural relaxation and diffusion data for the KA model system under all simulation conditions considered. Hence, the present study points to some unity in our understanding of the relationship between leading models of glass formation, supporting inferences drawn from previous studies of polymeric glass-forming liquids.

Analysis and evaluation of suitability of high-pressure dynamic constitutive model for concrete under blast and impact loading

Concrete demonstrates complex dynamic mechanical behaviors under the influence of blast or impact loads, and there are inherent limitations in experimental and theoretical methods when dealing with highly nonlinear problems. As computational technologies and mechanics continue to evolve, it is possible to conduct high-fidelity simulations of the transient response of concrete structures subjected to intense dynamic loads. Such simulations play a crucial role in revealing the propagation laws of stress waves, the progression of damage, the mechanisms of structural failure, and in conducting protective engineering design. An accurate concrete material model is essential for conducting numerical studies. This article reviews the development of high-pressure dynamic constitutive models for concrete in recent years from both experimental research and theoretical modeling perspectives, focusing on the analysis and evaluation of the modeling methods and main shortcomings of the equation of state(EOS), strength model, and damage model. Using single-element numerical simulations under a single loading path and numerical calculations of engineering cases under complex loading paths, a systematic analysis and comparison were conducted on the predictive capabilities of the HJC, RHT, KCC, and CSC models, as well as the newly developed Kong-Fang and Yan-Chen models. It pointed out the impact of high-pressure mechanical behavior of concrete and the cumulative effect of damage under hydrostatic pressure on the calculation results. Finally, a discussion was conducted on the inherent flaws, applicability, and research difficulties of local constitutive models of concrete in the finite element method. This provides a reference for the selection and research of constitutive models when conducting numerical analysis of the blast and impact resistance of concrete structures.

Joint calibration of local volatility models with stochastic interest rates using semimartingale optimal transport

We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results established in Joseph et al. (Calibration of local volatility models with stochastic interest rates using optimal transport, 2023). and jointly calibrates the whole equity-rate dynamics. It uses an iterative approach which starts with a parametric model and tries to stay close to it, until a perfect calibration is obtained. We demonstrate the performance of our approach on market data using European SPX options and European cap interest rate options. Finally, we compare the joint calibration approach with the sequential calibration, in which the short rate model is calibrated first and frozen.

Beam Local Stress Prediction Model for Incremental Launching Construction Based on SSA-SVR Algorithm

In the multi-point incremental launching construction process, without setting temporary piers at the mid-span, it is difficult to ensure the synchronization of the launching equipment at the same pier, which can easily cause the beam to deviate from the design axis, leading to changes in the stress of the beam. Calculating the local maximum stress of the beam when lateral deviation occurs is beneficial for establishing a reasonable and reliable threshold for controlling beam deviations. To address this issue, this paper utilizes a finite element model of the bridge under typical adverse conditions, simulating the lateral deviation and asynchronous jacking of the beam to explore stress variation patterns. The results show that the beam stress increases as the lateral deviation and jacking differences increase, severely affecting the structural safety. To overcome the inefficiency of the finite element modeling method when dealing with multiple working conditions and to establish a reasonable deviation control threshold, this study proposes a beam local stress prediction model under the combined influence of lateral deviation and jacking height differences based on the SSA-SVR algorithm. The model calculates the local maximum stress of the beam for 2500 sets of parameters. An engineering case analysis shows that the prediction model has high calculation accuracy, reliable results, fast computational speed, and high efficiency. Based on the stress prediction results, it is recommended to set the jacking height difference control threshold at 20 mm. When the jacking height difference is less than 20 mm, the local maximum stress value under the combined influence of both parameters should be less than the standard limit. The corresponding lateral deviation control threshold can be dynamically adjusted according to the actual travel difference recorded by the jacking equipment, with the control precision improved to 1 mm.

End-to-end underwater acoustic source separation model based on EDBG-GALR

In practical work scenarios, it is common for multiple vessels to be present in close proximity within the same water area. In such cases, the acoustic signals emitted by these vessels often overlap, causing interference and reducing the accuracy of vessel identification. This paper proposes an improved GALR end-to-end underwater acoustic source separation algorithm, with ECA-DE (Efficient Channel Attention-Deep Encoder) and Bi-GRU (Bidirectional Gated Recurrent Unit), which consists of an encoder, separation blocks, and a decoder (EDBG-GALR). Addressing the issue of GALR encoder’s limited expressiveness due to its single-layer one-dimensional convolutional layer, we introduce a new deep encoder, ECA-DE, to enhance the encoder’s capability to process temporal signals and improve the efficiency of the separator’s input. Additionally, we integrate Bi-GRU into the GALR separation block’s local modeling module to enhance the local modeling ability of sequence features, thereby reducing the model’s computational and parameter requirements. Experimental results demonstrate that the proposed EDBG-GALR method can effectively separate mixed multi-target signals into multiple single-target signals, achieving a maximum scale-invariant signal-to-noise ratio (SI-SNR) improvement of 3.32 dB and a signal distortion ratio (SDR) improvement of 3.38 dB over baseline methods. These results highlight the practical applicability of EDBG-GALR in complex underwater environments.

Numerical simulation of phase transition with the hyperbolic Godunov-Peshkov-Romenski model

In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.

Modelling nonlinear moderation effects with local structural equation modelling (LSEM): A non-technical introduction.

Understanding the differential strength of effects in the presence of a third variable, known as a moderation effect, is a common research goal in many psychological and behavioural science fields. If structural equation modelling is applied to test effects of interest, the investigation of differential strength of effects will typically ask how parameters of a latent variable model are influenced by categorical or continuous moderators, such as age, socio-economic status, personality traits, etc. Traditional approaches to continuous moderators in SEMs predominantly address linear moderation effects, risking the oversight of nonlinear effects. Moreover, some approaches have methodological limitations, for example, the need to categorise moderators or to pre-specify parametric forms of moderation. This tutorial introduces local structural equation modelling (LSEM) in a non-technical way. LSEM is a nonparametric approach that allows the analysis of nonlinear moderation effects without the above-mentioned limitations. Using an empirical dataset, we demonstrate the implementation of LSEM through the R-sirt package, emphasising its versatility in both exploratory analysis of nonlinear moderation without prior knowledge and confirmatory testing of hypothesised moderation functions. The tutorial also addresses common modelling issues and extends the discussion to different application scenarios, demonstrating its flexibility.