Model Calibration Research Articles

Creation and Calibration of Hydraulic Model for Leakage Management in Water Distribution Systems

Leaks occur at different rates in water distribution systems (WDSs). Network characteristics, high pressure, environmental factors and operational factors are effective on leaks. Field detection and monitoring activities should be implemented to reduce the volume of leaks resulting from faults in the WDS. The aim of this study is to create and calibrate the district metered area (DMA) based hydraulic model to understand the network behavior and monitor the hydraulic components. The hydraulic model is based on consumption data, network topology, characteristics and pipe roughness information. Calibration should be performed by comparing the pressures obtained from the model with the pressures measured in the field in order to apply the model in leakage management. Incomplete or incorrect network information may cause the difference between these two pressures to be large. In particular, basic data such as incomplete creation of the network topology, incomplete or incorrect acquisition of roughness and consumption information are effective in not providing model calibration. In the calibrated hydraulic model, it is possible to detect and prevent potential leaks by monitoring pressure changes at the nodes. It is thought that the results obtained in this study will constitute a reference in leakage management and hydraulic analysis.

Quantification of mineral oil contamination in corn oil by Fourier transform near-infrared spectroscopy: Comparison of linear and nonlinear multi-calibration methods

Corn oil is a popular edible oil among consumers, renowned for its flavor enhancement and essential nutrient content. Monitoring contaminants in corn oil is critical to ensuring consumer safety. Fourier Transform Near-Infrared (FT-NIR) spectroscopy combined with linear and nonlinear calibration models detected five different concentrations of mineral oil in corn oil. The results demonstrate that Partial Least Squares Regression (PLSR) effectively identifies contaminants such as diesel, white mineral oil, coal oil, and lubricating oil, with determination coefficients (RP2) of 0.99, 0.98, 0.98, and 0.97, respectively, and root mean square error of prediction (RMSEP) values of 1.0240, 1.3435, 1.4318, and 1.6797 mg/kg. The Ridge Regression method yielded optimal performance for detecting motor oil contamination (RP2 = 0.99, RMSEP = 0.64), demonstrating robust reliability. These findings indicate that FT-NIR spectroscopy, when paired with appropriate linear and nonlinear modeling, is an effective tool for ensuring the safety of corn oil.

Evaluating the impact of satellite soil moisture data as an additional component in the calibration of a conceptual hydrological model

Abstract This study proposes a new method for dividing a catchment with the aim of testing it in the calibration process of a conceptual hydrological model. The new catchment division is reflected in having different land cover zones and the input data prepared in a semi-distributed way. This study also explores the impact of satellite soil moisture data when multi-objective calibration is used with the land cover zone divisions of a catchment while assigning different weights to runoff ranging from 0% to 100% (with a 0.05 step). The results indicate that using a weight range of 60% to 80% on a runoff provides optimal results, bettering both the runoff model’s efficiency and soil moisture correlation. For further validation of the internal parameters and processes, the field capacity and evapotranspiration of the catchment were monitored. In regions with specially limited in-situ soil moisture data, satellite-derived data can contribute as an scarce additional component of the land cover division that can point out areas of the most reliable soil moisture information.

Integrating transfer learning and spectroscopy for enhanced pork spoilage assessment using correlation analysis

Accurate Total Viable Count (TVC) detection is vital for food quality monitoring. In this study, we investigated the feasibility of using visible near-infrared (VNIR) spectroscopy (400–1000 nm) combined with transfer learning (TL) to track the chemical spoilage of pork. The base models developed using the full band for pork TVC, total volatile basic nitrogen, pH, and color showed predictability; the correlation coefficient of prediction set (RP) for all models ranged from 0.821 to 0.916; and the root mean square error of prediction set (RMSEP) of the TVC model was 0.617 (lg CFU/g). A correlation analysis of the different indexes of pork was carried out to optimize the TVC calibration model. Different TL methods for TVC optimization were designed. The results showed that multiple correlation chain stacking-partial least squares performed best with RP, RMSEP, and the relative percent deviation of 0.947, 0.425 lg CFU/g, and 2.355, respectively, the RMSEP of TVC was reduced by 31.12 % as compared to the base model. This study demonstrated the possibility of combining the VNIR spectroscopy system with TL to monitor the degree of meat's chemical spoilage.

Calibrating Bayesian generative machine learning for Bayesiamplification

Abstract Recently, combinations of generative and Bayesian deep learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribution originating from limited training statistics. The interpretation of a distribution-wide uncertainty however remains ill-defined. We show a clear scheme for quantifying the calibration of Bayesian generative machine learning models. For a Continuous Normalizing Flow applied to a low-dimensional toy example, we evaluate the calibration of Bayesian uncertainties from either a mean-field Gaussian weight posterior, or Monte Carlo sampling network weights, to gauge their behaviour on unsteady distribution edges. Well calibrated uncertainties can then be used to roughly estimate the number of uncorrelated truth samples that are equivalent to the generated sample and clearly indicate data amplification for smooth features of the distribution.

NIRSpredict: a platform for predicting plant traits from near infra-red spectroscopy

SummaryNear-infrared spectroscopy (NIRS) has become a popular tool for investigating phenotypic variability in plants. We developed the Shiny NIRSpredict application to get predictions of 81 Arabidopsis thaliana phenotypic traits, including classical functional traits as well as a large variety of commonly measured chemical compounds, based from near-infrared spectroscopy values based on deep learning. It is freely accessible at the following URL: https://shiny.cefe.cnrs.fr/NirsPredict/.NIRSpredict has three main functionalities. First, it allows users to submit their spectrum values to get the predictions of plant traits from models built with the hosted A. thaliana database. Second, users have access to the database of traits used for model calibration. Data can be filtered and extracted on user’s choice and visualized in a global context. Third, a user can submit his own dataset to extend the database and get part of the application development.NIRSpredict provides an easy-to-use and efficient method for trait prediction and an access to a large dataset of A. thaliana trait values. In addition to covering many of functional traits it also allows to predict a large variety of commonly measured chemical compounds. As a reliable way of characterizing plant populations across geographical ranges, NIRSpredict can facilitate the adoption of phenomics in functional and evolutionary ecology.

Combination of near infrared spectroscopy with characteristic interval selection for rapid detection of rice protein content

Protein level significantly influences the nutritional quality of rice. For this reason, this study introduced a method to rapidly measure the rice protein content through a combination of near infrared spectroscopy (NIRS) with characteristic spectral interval (CSI) selection. Using the interval partial least squares (iPLS) concept as a basis, this study integrated genetic simulated annealing algorithm (GSA) with partial least squares (PLS) and support vector machine (SVM) to develop two CSI selection algorithms, namely GSA-iPLS and GSA-iSVM, respectively. The CSI selected by the above algorithms were compared with synergy iPLS and backward iPLS, and quantitative calibration models were established for PLS and SVM, respectively. The study revealed that the PLS calibration model for rice protein content, developed using CSI selected by GSA-iPLS, exhibited the highest regression accuracy. The optimal model achieved determination coefficients of 0.945 and 0.964, relative root mean square errors of 2.598 % and 2.796 %, and residual predictive deviations of 4.265 and 5.023 for the validation and the external test sets, respectively, which met practical detection requirements. The results indicate that the combination NIRS with GSA CSI intelligent search is a reliable approach for the rapid and accurate detection of rice protein content.

Navigating Complexity: GPT-4's Performance in Predicting Earnings and Stock Returns in China's A-Share Market

This study investigates the application of GPT-4, a large language model, in predicting earnings changes and stock returns within China's A-share market from 2000 to 2023. We evaluate the model's performance using various metrics, including prediction accuracy, F1 score, stock returns, Sharpe ratio, and alpha. Our findings reveal significant fluctuations in the model's predictive accuracy, ranging from 10.62% to 48.67%, with an average F1 score of 0.30. Despite inconsistent accuracy, the model maintained high prediction confidence levels between 75% and 90%. Stock returns associated with the model's predictions varied widely, from -4.86% to 13.59%, showing no consistent correlation with prediction accuracy. The study highlights the challenges of applying AI models to financial analysis in emerging markets, particularly given the unique characteristics of China's A-share market, such as frequent policy interventions and a high proportion of retail investors. We discuss the implications of these findings for the future of AI-driven financial analysis, emphasizing the need for improved model calibration, ethical considerations, and regulatory frameworks.

ELMO: Enhanced Real-time LiDAR Motion Capture through Upsampling

This paper introduces ELMO, a real-time upsampling motion capture framework designed for a single LiDAR sensor. Modeled as a conditional autoregressive transformer-based upsampling motion generator, ELMO achieves 60 fps motion capture from a 20 fps LiDAR point cloud sequence. The key feature of ELMO is the coupling of the self-attention mechanism with thoughtfully designed embedding modules for motion and point clouds, significantly elevating the motion quality. To facilitate accurate motion capture, we develop a one-time skeleton calibration model capable of predicting user skeleton off-sets from a single-frame point cloud. Additionally, we introduce a novel data augmentation technique utilizing a LiDAR simulator, which enhances global root tracking to improve environmental understanding. To demonstrate the effectiveness of our method, we compare ELMO with state-of-the-art methods in both image-based and point cloud-based motion capture. We further conduct an ablation study to validate our design principles. ELMO's fast inference time makes it well-suited for real-time applications, exemplified in our demo video featuring live streaming and interactive gaming scenarios. Furthermore, we contribute a high-quality LiDAR-mocap synchronized dataset comprising 20 different subjects performing a range of motions, which can serve as a valuable resource for future research. The dataset and evaluation code are available at https://movin3d.github.io/ELMO_SIGASIA2024/

A modeling study on SARS-CoV-2 transmissions in primary and middle schools in Illinois

BackgroundThe global pandemic caused by the SARS-CoV-2 virus led to a statewide lockdown in Illinois starting in March 2020. To ensure students’ and employees’ safety for school reopening, protective measures, such as a statewide mask mandate and weekly testing, were in place in Illinois from Spring 2021 to Spring 2022. The study objective is to 1) estimate the in-school and external transmission of SARS-CoV-2 in elementary and middle schools under mask mandate and weekly surveillance and 2) estimate the impacts of protective measures such as testing and mask proportion and testing frequency on SARS-CoV-2 transmission.MethodsA stochastic compartmental model was built to simulate the SARS-CoV-2 transmission within and between the student and employee groups in primary and middle schools participating in the weekly testing program and to evaluate the effectiveness of these protective measures. This stochastic model was modified from a susceptible–infected–recovered framework and calibrated to SARS-CoV-2 surveillance data in 116 primary and middle school districts from Spring 2021 to March 2022. This model calibration was assessed using the surveillance data from the rest of the spring semester in 2022.ResultsOverall, the external transmission rates in students and employees were significantly greater than those within schools, and the external transmission rates in middle school students and school employees were greater than those in primary school students. Our sensitivity analysis showed that transmission rates within student groups could significantly influence overall infection rates in vaccinated and unvaccinated students in large school districts. Under the protective measures implemented in the studied period in Illinois, an increased proportion of students and employees participating in the weekly testing can decrease infections. However, community-level measures of self-reported mask adherence among adults were not significantly associated with the infections during the study period, when a universal mask policy was in place for the state.ConclusionsAlthough increased testing proportion and/or frequency can reduce the SARS-CoV-2 infections, the costs of testing can increase with the testing volume. Further studies on the cost-effectiveness between the testing volume and cases reduction or learning disturbance can aid in policy development to reduce transmission effectively.

Improving relative humidity measurements on Mars: new laboratory calibration measurements

Abstract. In this paper we present new calibration measurements that have been performed with the ground reference models of the relative humidity instruments of the Mars Science Laboratory (MSL), Mars 2020 and ExoMars missions. All instruments are based on capacitive sensor head technology, and they are developed, manufactured and tested by the Finnish Meteorological Institute (FMI). Calibration of capacitive humidity sensors for the Martian environment has been a challenging task and special facilities are needed in order to create Martian conditions including all relevant environmental parameters that can be accurately controlled and measured: low pressure, low temperature, carbon dioxide environment and especially humidity. A measurement campaign was performed at the German Aerospace Center (DLR) PASLAB (Planetary Analog Simulation Laboratory) to determine relative humidity calibration datasets for REMS-H, MEDA HS and METEO-H instruments in temperatures from −30 °C down to −70 °C in low-pressure CO2. In addition to the stable point humidity calibration measurements in CO2, the instrument performance was tested with the actual Martian atmosphere composition and during long continuous measurements. The new calibration dataset has already been used in the flight calibration of the MEDA HS instrument, resulting in successful calibration and excellent accuracy. The results from this campaign will further improve relative humidity measurements on Mars by providing the means to reanalyze the current calibration of the REMS-H flight model and by allowing more accurate comparison between the two instruments currently on the Martian surface.

Long-term reproducibility improvement of LIBS quantitative analysis based on multi-period data fusion calibration method

Long-term reproducibility is one of the important problems that urgently need to be solved in the quantitative analysis of laser-induced breakdown spectroscopy (LIBS). In this work, a new calibration method based on multi-period data fusion was proposed. Under the same experimental equipment and parameters, LIBS data collected at different times were fused together to establish calibration models. The spectra of the same set of standard samples were collected once a day for 20 days, the spectral data from the first 10 days were used as the training set for the calibration model, and the data from the last 10 days were used as the test set. As a comparison, three types of calibration models of four elements (Mn, Ni, Cr, and V) were established, including the internal calibration model (IS-1) based on the data from first day, multi-period data fusion internal calibration model established using internal calibration (IS-10) and genetic algorithm based back-propagation artificial neural network (GA-BP-ANN) based on the data from first 10 days. The test set spectral data were used to verify the prediction effect of the above three models. It was found that the GA-BP-ANN models have the lowest average relative errors (ARE) and the average standard deviations (ASD). Therefore, the proposed multi-period data fusion GA-BP-ANN model provides a novel method for improving the reproducibility of LIBS long-term repeated measurement.

Evaluating Performance and Agreement of Coronary Heart Disease Polygenic Risk Scores

Polygenic risk scores (PRSs) for coronary heart disease (CHD) are a growing clinical and commercial reality. Whether existing scores provide similar individual-level assessments of disease susceptibility remains incompletely characterized. To characterize the individual-level agreement of CHD PRSs that perform similarly at the population level. Cross-sectional study of participants from diverse backgrounds enrolled in the All of Us Research Program (AOU), Penn Medicine BioBank (PMBB), and University of California, Los Angeles (UCLA) ATLAS Precision Health Biobank with electronic health record and genotyping data. Polygenic risk for CHD from published PRSs and new PRSs developed separately from testing samples. PRSs that performed population-level prediction similarly were identified by comparing calibration and discrimination of models of prevalent CHD. Individual-level agreement was tested with intraclass correlation coefficient (ICC) and Light κ. A total of 48 PRSs were calculated for 171 095 AOU participants. The mean (SD) age was 56.4 (16.8) years. A total of 104 947 participants (61.3%) were female. A total of 35 590 participants (20.8%) were most genetically similar to an African reference population, 29 801 (17.4%) to an admixed American reference population, 100 493 (58.7%) to a European reference population, and the remaining to Central/South Asian, East Asian, and Middle Eastern reference populations. There were 17 589 participants (10.3%) with and 153 506 participants without (89.7%) CHD. When included in a model of prevalent CHD, 46 scores had practically equivalent Brier scores and area under the receiver operator curves (region of practical equivalence ±0.02). Twenty percent of participants had at least 1 score in both the top and bottom 5% of risk. Continuous agreement of individual predictions was poor (ICC, 0.373 [95% CI, 0.372-0.375]). Light κ, used to evaluate consistency of risk assignment, did not exceed 0.56. Analysis among 41 193 PMBB and 53 092 ATLAS participants yielded different sets of equivalent scores, which also lacked individual-level agreement. CHD PRSs that performed similarly at the population level demonstrated highly variable individual-level estimates of risk. Recognizing that CHD PRSs may generate incongruent individual-level risk estimates, effective clinical implementation will require refined statistical methods to quantify uncertainty and new strategies to communicate this uncertainty to patients and clinicians.

Dynamic characteristics of commercial Adaptive Cruise Control across driving situations: Response time, string stability, and asymmetric behavior

Adaptive Cruise Control (ACC) is a popular feature for long-distance highway driving due to its convenience. Research has been conducted on the driving characteristics of commercial ACC vehicles that could impact road capacity and congestion. While response time and string stability are major characteristics, previous studies have often overlooked their variations across driving situations. This study analyzes the dynamic characteristics of commercial ACC, including response time, string stability, and asymmetric behavior across different driving situations. A method is proposed to extract the response time of commercial ACC vehicles during cruising, decelerating, and accelerating situations, using cross-correlation and acceleration threshold methods. Phenomena that influence string stability are categorized based on driving situations focusing on their origin and features. This study identifies patterns in asymmetric behavior and presents a car-following model calibration process that incorporates observed features using the OpenACC dataset. The findings reveal distinct variations in response time across different driving situations, escalating in the sequence of deceleration, cruising, and acceleration. String instability during deceleration is influenced by the vehicle’s response time, while during acceleration, it stems from an expanded gap reduction process. ACC vehicles exhibit asymmetric behavior, with a reduced tolerance for gap changes. The Helly model, which integrates response times, asymmetric behavior, and maximum acceleration, accurately simulates vehicle movement and string instability. The observed variations in response time and asymmetric behavior across driving situations provide an understanding of the traffic hysteresis of commercial ACC vehicles. Furthermore, our analysis suggests that achieving string stability requires diverse approaches for each driving situation.

Structural health assessment of existing dams based on non-destructive testing, physics-based models and machine learning tools

The safe operation of dams is ensured by monitoring systems that collect periodic information on environmental conditions (for example, temperature and water level) and on the structural response to external actions. In newly built or retrofitted facilities, large networks of sensors can take daily measurements that are automatically transferred to servers. In other cases, additional information can be acquired, occasionally or systematically, through emerging drone-based non-contact full-field techniques.The measurements are processed by various analytical and machine learning tools trained on historical data sets, capable of highlighting any anomalous recordings. Monitoring data can also support the accurate calibration of a physics-based model of the structure, usually built in the finite element framework. The analyses carried out by the digital twin allow the experimental database to be expanded with the displacements evaluated in the event of extreme environmental conditions, damage or collapse mechanisms never occurred before.This contribution illustrates an integrated approach to the safety assessment of existing dams that combines experimental, computational and data processing methodologies. Attention is particularly focused on model calibration procedures and on the uncertainties that influence the characteristics of the joints. The presented results of the validation studies performed by the Authors on benchmark and real-scale problems highlight the merits and limitations of alternative approaches to data exploitation and remote measurement.

Development and validation of a risk prediction model for cognitive impairment in breast cancer patients

BackgroundBreast cancer patients often experience cognitive impairment as a complication during treatment, which seriously affects their quality of life. This study aimed to assess the risk factors associated with cognitive impairment in breast cancer patients and to construct and validate a nomogram model to predict cognitive impairment in this population.MethodsIn this study, we used a convenience sampling method to select 423 breast cancer patients who attended the Department of Breast Surgery at the First Hospital of Jinzhou Medical University from September 2023 to March 2024. We analyzed these patients’ cognitive impairment risk factors through LASSO regression and logistic regression analysis to develop a predictive model. The model was evaluated using the area under the curve (AUC) from the receiver operating characteristic (ROC) curve and the calibration curve and decision curve analysis.ResultsThis study found a prevalence of cognitive impairment of 19.62% among breast cancer patients. A nomogram model was developed based on six influencing factors: age, educational level, pathological type, treatment program, emotional state, and fatigue. The area under the curve (AUC) for the model’s training and validation groups was 0.944 and 0.931, respectively. The model calibration curves showed a high degree of consistency, and the decision curve analysis (DCA) indicated good clinical applicability of the model.ConclusionsThis nomogram demonstrates good discrimination, calibration, and clinical applicability, making it a more intuitive predictor of the risk of cognitive impairment in breast cancer patients.

Investigation of coupling DSSAT with SCOPE-RTMo via sensitivity analysis and use of this coupled crop-radiative transfer model for sensitivity-based data assimilation

The increasing availability of remote sensing (RS) data and the advancement of computation abilities, combined with the demands for enhancing crop production, encourages the creation of a framework in which crop growth simulation can be updated sequentially to serve as a yield predictor and be part of a decision support system. However, crop model outputs and RS data must be linked via a radiative transfer model (RTM), which simulates the interaction between the crop and the intercepted radiation. In this study, a comprehensive coupling scheme between a crop model (DSSAT-CROPGRO-tomato) and an RTM (SCOPE-RTMo) was formulated and investigated through global sensitivity analysis (SA) and by testing the coupled model in a synthetic data assimilation (DA) experiment. The DA experiment utilized a sensitivity-based particle filter (PF) in which the SA results were used to enhance the PF convergence rate and accuracy. The SA results provide the sensitivity of simulated reflectance at different wavelengths to DSSAT-CROPGRO parameters throughout the season. This information can help guide future data assimilation experiments by choosing imaging instruments with appropriate spectral bands and timing the measurements to enhance model calibration. The results of the synthetic DA experiment showed a good convergence of the particle filter towards the ground truth. The results also demonstrated the strong relation between LAI and reflectance, as several model runs with different initial values of DSSAT-CROPGRO parameters all converged and predicted the synthetic LAI observations very well. The convergence of DSSAT-CROPGRO parameters to their ground truth values was only partial, and phenology-related parameters tended to converge better than growth-related parameters.

Causality-Driven Feature Selection for Calibrating Low-Cost Airborne Particulate Sensors Using Machine Learning.

With escalating global environmental challenges and worsening air quality, there is an urgent need for enhanced environmental monitoring capabilities. Low-cost sensor networks are emerging as a vital solution, enabling widespread and affordable deployment at fine spatial resolutions. In this context, machine learning for the calibration of low-cost sensors is particularly valuable. However, traditional machine learning models often lack interpretability and generalizability when applied to complex, dynamic environmental data. To address this, we propose a causal feature selection approach based on convergent cross mapping within the machine learning pipeline to build more robustly calibrated sensor networks. This approach is applied in the calibration of a low-cost optical particle counter OPC-N3, effectively reproducing the measurements of PM1 and PM2.5 as recorded by research-grade spectrometers. We evaluated the predictive performance and generalizability of these causally optimized models, observing improvements in both while reducing the number of input features, thus adhering to the Occam's razor principle. For the PM1 calibration model, the proposed feature selection reduced the mean squared error on the test set by 43.2% compared to the model with all input features, while the SHAP value-based selection only achieved a reduction of 29.6%. Similarly, for the PM2.5 model, the proposed feature selection led to a 33.2% reduction in the mean squared error, outperforming the 30.2% reduction achieved by the SHAP value-based selection. By integrating sensors with advanced machine learning techniques, this approach advances urban air quality monitoring, fostering a deeper scientific understanding of microenvironments. Beyond the current test cases, this feature selection method holds potential for broader applications in other environmental monitoring applications, contributing to the development of interpretable and robust environmental models.

Hydrological Modeling of Krishna Upper Catchment Area of India Using Multisite Calibration and Validation of SWAT Model

Multisite calibration & validation of model reduces the uncertainty present in the model parameters and improve the SWAT model output. In the present study, an effort was made to set up SWAT model along with multisite calibration and validation for Kishna upper basin of India. A total of six gauging stations maintained by Central water commission across the area were selected for SWAT model calibration and validation. Sequential Uncertainty Fitting (SUFI-2) programme of SWAT-CUP (Calibration and Uncertainty Programme) was employed to calibrate the SWAT model. During sensitivity analysis of SWAT model, parameters which are highly sensitive that influences flow characteristics of different gauging station were identified. These parameters along with parameter range were used to calibration and validation of SWAT model each of the sub basins. Observed flow and predicted stream flows were compared with certain model performance indices. These indices indicated that for all six gauging stations, the SWAT model found to be very good. The performance indices like R2, NSE, RSR and PBIAS were ranged from 0.70 to 0.84, 0.67 to 0.76, 0.49 to 0.57 and -11.7 to 24.0% respectively during model calibration period and 0.70 to 0.93, 0.67 to 0.83, 0.41 to 0.58 and 8.5 to 22.9% respectively during model validation period. A good agreement between observed and simulated flows at all the gauging stations were observed. It can be concluded that SWAT model output was improved with multisite calibration and validation of the model.

Predictions for the abundance and clustering of H α emitting galaxies

ABSTRACT We predict the surface density and clustering bias of H $\alpha$ emitting galaxies for the Euclid and Nancy Grace Roman Space Telescope redshift surveys using a new calibration of the galform galaxy formation model. We generate 3000 galform models to train an ensemble of deep learning algorithms to create an emulator. We then use this emulator in a Markov Chain Monte Carlo (MCMC) parameter search of an eleven-dimensional parameter space, to find a best-fitting model to a calibration data set that includes local luminosity function data, and, for the first time, higher redshift data, namely the number counts of H $\alpha$ emitters. We discover tensions when exploring fits for the observational data when applying a heuristic weighting scheme in the MCMC framework. We find improved fits to the H $\alpha$ number counts while maintaining appropriate predictions for the local universe luminosity function. For a flux limited Euclid-like survey to a depth of $2\times 10^{-16}~\textrm {erg}^{-1}~\textrm {s}^{-1}~\textrm {cm}^{-2}$ for sources in the redshift range $0.9< z< 1.8$, we estimate 2962–4331 H $\alpha$ emission-line sources deg$^{-2}$. For a Nancy Grace Roman survey, with a flux limit of $1\times 10^{-16}~\textrm {erg}^{-1}~\textrm {s}^{-1}~\textrm {cm}^{-2}$ and a redshift range $1.0< z< 2.0$, we predict 6786–10 322 H $\alpha$ emission-line sources deg$^{-2}$.