Conflation of Ensemble-Learned Nuclear Mass Models for Enhanced Precision

TL;DR

This paper introduces a novel ensemble learning approach called ELMA that combines multiple nuclear mass models to significantly improve prediction accuracy, achieving an RMSE below 100 keV and validating results through decay energy evaluations.

Contribution

The paper presents a new ensemble learning framework that integrates model averaging and correction techniques to enhance nuclear mass predictions beyond existing methods.

Findings

Achieved an RMSE of approximately 65 keV in nuclear mass predictions.

Demonstrated improved accuracy in $Q$ value predictions for $ ext{α}$ decay.

Provided a publicly accessible database of nuclear masses and energies for 6,300 nuclei.

Abstract

Ensemble learning algorithms, the gradient boosting and bagging regressors, are employed to correct the residuals of nuclear mass excess for a diverse set of six nuclear mass models. The weighted average of these corrected residuals reduces due to their partial cancellation, yielding a significant improvement in nuclear mass predictions. Our conflated model, which integrates ensemble learning and model averaging (ELMA), achieves a root mean square error of approximately 65 keV, well below the critical threshold of 100 keV, for the complete data set of Atomic Mass Evaluation (AME2020). The validity of ELMA is demonstrated through the evaluation of $Q$ values for $\alpha$ decay, showing a marked decrease in deviations from experimental data relative to predictions from individual nuclear mass models. We have also compiled a table of nuclear mass excesses and binding energies for about 6,300 nuclei, which serves as a valuable resource for various nuclear physics applications and is publicly accessible via the ELMA web interface (https://ddnp.in).

Tables

Table 1. Table 1 : Root mean square errors σ \sigma for the weighted-average model obtained using raw residuals (RR) and corrected residuals (CR) for different numbers of nuclear mass models ( N m N_{m} ), obtained using Eq. 4 . Corrected residuals are obtained by using ensemble learning algorithm, GBR and BAR. Results are presented for six datasets—train, test, extpl, 2020, new, and full dataset. The values of mean absolute errors (MAE) for CR case with N m = 6 N_{m}=6 are also presented in the last row.

		$𝝈$ (MeV)
	$N_{\text{m}}$	train	test	extpl	2020	new	full
$\overline{\mathrm{𝐑𝐑}}$	2	0.1886	0.1874	0.3263	0.1938	0.2893	0.1953
	4	0.1996	0.1978	0.3299	0.2043	0.2813	0.2054
	6	0.2004	0.1976	0.3285	0.2049	0.2775	0.2059
$\overline{\mathrm{𝐂𝐑}}$	2	0.0484	0.1186	0.2013	0.0718	0.2627	0.0771
	4	0.0426	0.1195	0.1784	0.0671	0.2311	0.0715
	6	0.0412	0.1181	0.1702	0.0654	0.2223	0.0695
	MAE	0.0299	0.0835	0.1247	0.0404	0.1565	0.0419

Equations

$$\delta M_i^{\mathrm{RR}}=M_{\mathrm{Exp}}-M_i$$

$$\delta M_i^{\mathrm{CR}}$$

$$=$$

$$\delta {\bar{M}}^{\mathrm{X}}$$

$$w_i^X=\frac{{\left(\frac{1}{{\sigma }_i^{\mathrm{X}}}\right)}^2}{{\sum }_{k=1}^{N_X}{\left(\frac{1}{{\sigma }_k^{\mathrm{X}}}\right)}^2}$$

$${\sigma }_i^{\mathrm{X}}=\sqrt{\frac{1}{N_d}\sum _{j=1}^{N_d}{\left(\delta M_i^{\mathrm{X}}(j)\right)}^2}$$

Full text

††journal: Physics Letters B

\affiliation

[first]organization=Department of Mechanical Engineering, BITS-Pilani Hyderabad campus, city=Hyderabad, postcode=500078, country=India \affiliation[second]organization=Department of Physics, School of Physical and Biological Sciences, Manipal University Jaipur, city=Jaipur, postcode=303007, country=India \affiliation[third]organization=Department of Physics (H&S), Govt. Women Engineering College,city=Ajmer, postcode=305002, country=India \affiliation[fourth]organization=Department of Physics, Faculty of Science, University of Zagreb,addressline=Bijenička cesta 32, city=Zagreb, postcode=10000, country=Croatia \affiliation[fifth]organization=Saha Institute of Nuclear Physics,addressline=1/AF Bidhannagar, city=Kolkata, postcode=700064, country=India

Introduction

The mass of an atomic nucleus, or its mass excess, is one of the fundamental observables that encapsulates total binding energy, thereby serving as a direct insight to the underlying nuclear interactions and many-body quantum structure [1]. Accurate values of mass are necessary for mapping the limits of nuclear existence at the proton and neutron drip lines [1]. It also plays an important role in astrophysical reaction network calculations, determining nuclear abundances not only through rapid and slow neutron capture processes but also in other nucleosynthesis pathways. The uncertainties in nuclear masses of few hundred keV can change calculated elemental abundances by many orders of magnitude [2, 3]. Despite several technological advances in mass measurements [4, 5, 6, 7, 8], experimental determination is exceedingly challenging for nuclei far from line of stability, which are characterized by extremely short half-lives, low production rates [1], and the complicated task of separating low-energy isomeric states from the ground state [9]. Therefore, one relies heavily on theoretical calculations for unexplored territory of the nuclear chart [10].

Atomic Mass Evaluation (AME-2020) provides a comprehensive and reliable database of experimentally measured masses for over 2400 nuclei [11], however, theoretical predictions of masses of the nuclei away from the line of stability remain indispensable. Theoretical models predict the existence of over 6000 isotopes, spanning vast regions of the nuclear chart, particularly on the neutron-rich side, many of which are experimentally inaccessible [12, 13]. A multitude of models have been developed, that is broadly divided into the macroscopic-microscopic approaches and fully microscopic theories. The earliest of these is the Liquid Drop Model, whose binding energy described by the foundational Bethe-Weizsäcker semi-empirical mass formula [14, 15], its predictive accuracy is limited, with root mean square error (RMSE) of about 3 MeV from experimental data [11]. Later macroscopic-microscopic refinements led to the Finite-Range Droplet Model (FRDM) which significantly led to reduction of RMSE to 0.662 MeV [16]. An alternative approach, the Duflo-Zuker (DZ) family of models, was developed based on a shell-model Hamiltonian, achieving RMSE of around 0.3–0.6 MeV [17]. Lately, the Weizsäcker-Skyrme (WS4) model delivered one of the highest accuracies in this class with an RMSE of 0.298 MeV [18]. An improved version, the WS4+ model uses radial basis functions to correct systematic errors, obtaining a very small discrepancy of less than 0.250 MeV for most heavy nuclei [19]. Microscopic models are often based on self-consistent mean-field frameworks. Non-relativistic Hartree-Fock-Bogoliubov (HFB) theory became highly competitive with global models achieving RMSE below 0.8 MeV [20, 21]. Relativistic approaches, framed within Covariant Density Functional Theory (CDFT), have also been extensively developed [22, 23]. Early Relativistic Mean-Field (RMF) models had RMSE of more than 1 MeV [24], though later versions with corrections have improved this to  0.5 MeV [25]. These global theoretical models generally achieve an accuracy in predicting experimental data in the range of RMSE 0.2–0.8 MeV. But their predictive performance deteriorates near nuclei far from the beta-stability line, where the deviations can increase to several MeV [26]. This uncertainty poses a major challenge towards consistent extrapolation of exotic nuclear properties and is well below the sub-100 keV precision needed to perform high-fidelity r-process calculations [27].

The accuracy gap of theoretical models created a ground for the application of Machine Learning (ML), which emerged as a powerful tool for improving nuclear mass predictions. The current state-of-the-art in ML for the prediction of nuclear mass is dominated by the use of a residual learning strategy, where algorithms are trained on the difference between experimental data and theoretical predictions for nuclear mass excess [10]. A key demonstration of this approach was presented by Utama et al., who used a Bayesian Neural Network (BNN) to improve the predictions of several mass models by training it on their "residuals" [28]. The approach reduces the RMSE of the FRDM on the validation set from 0.664 MeV to 0.374 MeV. and, more importantly, offered a framework to compute the statistical uncertainty of the predictions [28]. Within this research paradigm, a diverse array of architectures has achieved high precision. Foundational kernel methods like Gaussian Process Regression (GPR) have demonstrated strong performance, achieving a RMSE as low as 0.26 MeV on test sets and an RMSE of 0.67 MeV when extrapolating to 71 newly measured nuclei in AME2020, confirming its predictive power on new data [29]. A significant improvement was achieved with a more advanced BNN model, which reached an accuracy of 84 keV [30]. Other advanced neural networks, such as a physics-informed Fully Connected Neural Network, have also shown further reduction with an RMSE of 0.122 MeV on its test set and extrapolation capability with an RMSE of 0.191 MeV for 71 newly measured nuclei in AME2020 [31]. Tree-based ensemble methods have also advanced the frontier of raw predictive accuracy; systematic studies applying algorithms like CatBoost to refine theoretical models have yielded RMSE of approximately 0.160 MeV in test data [32]. More recently, a multi-task Gaussian Process model that simultaneously predicts mass and charge radii achieved a RMSE of 0.090 MeV in complete dataset for nuclear masses, highlighting the continued improvement in kernel-based methods [33].

The pursuit of predictive accuracy is often hampered by model uncertainty, the ambiguity relies on selecting a single best model from multiple plausible candidates [34, 35]. Standard statistical practice, which typically relies on a single "best" model, often ignores this uncertainty, leading to over-confident inferences and conclusions that may be less reliable than they appear [36]. This challenge is underscored by the No Free Lunch theorem, which posits that no single algorithm is optimal for every problem [37]. To address this, model averaging has emerged as a powerful statistical tool, often implemented through what are known as ensemble methods [35]. The foundational principle of this approach is that a committee of diverse models, when combined with their predictions, can achieve greater accuracy and robustness than any individual member [36]. By aggregating the output of various models, where each captures different facets of data, ensemble techniques can effectively reduce overall error, mitigate the effects of individual bias of models, and improve generalization for new data [38]. This implementation is presented by Bentley et al., which introduces the Four Model Tree Ensemble [39]. The FMTE is the composite model created by taking weighted average of four distinct Least Squares Boosted Ensemble of Trees models. This multi-level averaging approach results in a model with an accuracy of RMSE 76 keV when evaluated against the AME 2020 experimental data. Furthermore, the model’s robust extrapolation capability validated against post predicted mass measurements after AME2020 compilation, which achieved an RMSE of 0.376 MeV lower than the individual mass models considered [39].

In the present work, we employ diverse set of six nuclear mass models which can be broadly characterized as macroscopic-microscopic model, non-relativistic and relativistic self consistent mean-field models. The RMSE for the residuals of nuclear masses for these models for full AME2020 are in the range of 0.25-1.0 MeV. The raw residuals obtained from individual nuclear mass models are corrected using gradient boosting regressor (GBR) and bootstrap aggregation (BAR) [40, 41], which are the most prominent ensemble learning methods [32, 42]. The GBR builds models sequentially, where each model is trained to correct the errors of its predecessors resulting reduced bias [43, 44]. The BAR trains multiple models on different random subsets of the data and averages their predictions to reduce variance, minimize overfitting, and improve reliability [45, 46]. We obtain a single improved nuclear mass model by performing the weighted average over all the corrected residuals. Our conflated nuclear mass model obtained by integrating ensemble learning and model averaging yields an overall RMSE $\sim$ 65keV which is well below the critical value of 100keV. We also confront our mass model with the newly measured mass excess and for the $Q$-values of $\alpha$-decay. We have compiled values of nuclear masses and binding energies for about 6000 nuclei from our improved nuclear mass-model.

Ensemble Learning

Our predictive framework integrates two complementary ensemble techniques : Gradient Boosting Regressor (GBR) and Bootstrap Aggregating, or Bagging (BAR). Both models are well suited for capturing the complex, non-linear dependencies present in nuclear mass excess data, yet they address different aspects of model performance. The GBR focuses on sequentially reducing bias through iterative error correction [40, 43], while BAR targets variance reduction by aggregating predictions from multiple independently trained models [47, 41].

Figure 1 shows the pipeline implemented for both methods and the final prediction fusion step. In GBR (left panel), the model begins with the complete dataset for training and builds a sequence of 5000 decision tree estimators, each trained to correct the residual errors of its predecessors. The ensemble prediction is obtained by combining all estimators, weighted by the learning rate. In BAR (right panel), the dataset is resampled (25 times) with replacement to produce distinct bootstrap datasets. We use Support Vector Regressor (SVR) as a base estimator in the BAR algorithm for each of the datasets independently, and the outputs are averaged to produce the final prediction.

The outputs obtained from both GBR and BAR combined together, yielded a hybrid model balance the bias reduction properties of boosting with the variance-reduction properties of bagging. Complete details of hyperparameter optimization, and model configuration are provided in the Supplementary Material (SM).

Results and Discussion

We have selected six nuclear mass models such as Weizsäcker-Skyrme (WS4) [18], WS4+ [19], finite-range droplet model (FRDM) [16], Duflo Zuker model (DZ28) [17], Universal Nuclear Energy Density Functional 1 (UNEDF1) [48] and Relativistic Mean-Field (RMF) [49, 50] that represent a wide spectrum of theoretical approaches. The WS4 and its improved version WS4+ are macroscopic-microscopic models based on the Skyrme energy-density functional, with WS4+ including further empirical corrections for enhanced accuracy. The FRDM combines macroscopic finite range droplet energy and microscopic shell and pairing corrections, providing reliable predictions for masses across the nuclear chart. The DZ(28) is a parameter-rich Duflo–Zuker model that blends macroscopic and microscopic features for improved mass reproduction. The UNEDF1 is a self-consistent non-relativistic mean-field model based on an effective Skyrme energy-density functional for global modeling of nuclear properties. The variant of RMF model considered corresponds to interaction of nucleon through mesons along with the inclusion of nonlinear self- and mixed-interactions term and coupling strengths being density independent. These models collectively cover both empirical and fully microscopic theoretical frameworks, providing a broad and robust basis for our present analysis.

To improve the accuracy of nuclear mass prediction, the raw residuals (RR) are corrected using various machine learning algorithms. The RR is defined as:

[TABLE]

where $M_{\rm Exp}$ is the experimental nuclear mass excess for a given nucleus and $M_{i}$ is the corresponding value for the $i$-th nuclear mass model. The corrected residuals (CR) are:

[TABLE]

where the corrected mass excess $M_{i}^{\rm cor}=M_{i}+\delta M_{i}^{\rm ML}$, with $\delta M_{i}^{\rm ML}$ being the machine-learned value of the raw residuals. We employed ensemble learning methods, namely the GBR and BAR, to estimate the values of $\delta M_{i}^{\rm ML}$ in Eq. (2). The weighted average of residuals can be obtained as:

[TABLE]

where X is either RR or CR. $N_{RR}$ = $N_{m}$ and $N_{CR}$ = 2$N_{m}$, with $N_{m}$ the number of mass-models considered. The normalized weights, $w_{i}^{X}$ is given by,

[TABLE]

with $\sigma_{i}^{\rm X}$ is the root mean square error for a given nuclear mass model with raw or corrected residuals and can be evaluated as:

[TABLE]

where the index $j$ runs over all nuclei of a given dataset of size $N_{d}$. Thus, the models that perform better or having smaller values of $\sigma_{i}^{\rm X}$ are given higher weights, contributing more effectively to improving the accuracy of the prediction. These weights are calculated using the RMSE values from test dataset.

The models were trained using 12 features, as detailed in Table 2 of the SM, with the target variable being $\delta M_{i}^{\rm RR}$ as given by Eq. (1). The training dataset is constructed from the Atomic Mass Evaluation (AME2020) by excluding the nuclear mass excess values of 71 nuclei measured for the first time, as described in the SM. After training, the model’s performance for the corrected residuals is evaluated on various datasets-labeled by test, extpl, 2020, new, and full as described in Table 3 of the SM.

The weighted-average nuclear mass excess is calculated using Eq. (4) for $N_{m}=2,4,$ and $6$, considering both the raw and corrected residuals. The $N_{m}=2$ case uses the WS4 and WS4+ models; for $N_{m}=4$, residuals from FRDM and DZ(28) are further included; and for $N_{m}=6$, the average is taken over all six models considered. The RMSE values for WS4 and WS4+ are smaller than those of the other models (see Table 4 of SM). Table 1 presents the RMSE values ($\sigma$) obtained using the weighted average of residuals for $N_{m}=2,4,$ and 6. For $N_{m}=6$, the mean absolute error of the corrected residuals are also listed in the last row. Each nuclear mass model yields two sets of corrected residuals, corresponding to the GBR and BAR ensemble approaches. For RR, the values of $\sigma$ increase slightly with $N_{m}$ for most datasets, except for the ’new’ dataset, which contains nuclei measured after AME2020. This behavior arises because the weights are heavily skewed: WS4 and WS4+ together account for nearly 82% of the total weight, leaving only ~18% distributed among the other models (Table 4, SM). In contrast, for CR, the values of $\sigma$ generally decrease with increasing $N_{m}$. Here, the weights are more evenly distributed, with WS4 and WS4+ contributing about 60% and the remaining models collectively contributing  40%. This redistribution demonstrates how the GBR and BAR ensembles effectively integrate contributions from a wider range of models, mitigating the dominance of any single one. For the ’extpl’ and ’new’ datasets, $\sigma$ decreases by 20–25% as $N_{m}$ increases from 2 to 6. To further substantiate this observation, we analyzed all 15 possible combinations of four models out of the six mass models considered and evaluated the corresponding RMSE reductions for both the extpl and new datasets. In every case, the conflated model achieved RMSE values lower by 30–70 keV compared to the best-performing individual model. This demonstrates that the improvement is not an artifact of choosing a particular subset of models but rather a robust statistical feature of the averaging approach. This marked reduction—especially for nuclei far from the $\beta$-stability line, underscores the superior predictive capability of the CR method compared to RR. Further, across all datasets (except ’new’), the $\sigma$ values from CR are reduced by more than 40%; for the ’new’ dataset, the reduction is about 20%.

Figure 2 shows the probability density distributions for the weighted averages of both raw and corrected residuals, incorporating contributions from all six nuclear mass models. The upper panel corresponds to the weighted-average residuals for the 358 nuclei in the test dataset, the middle panel for the 71 nuclei in the extpl dataset, and the lower panel for the 31 nuclei in the new dataset measured after AME2020. For the comparison, we have also plotted the distributions corresponding to the raw residual for the different nuclear mass models considered. For the raw residuals, the weighted-average distributions closely resemble those of WS4+, which accounts for more than 60% of the total weight. In contrast, the distributions for the corrected residuals are more sharply peaked around zero for all the different datasets, owing to the redistribution of weights that allows contributions from the other mass models as well (see Tables 3 and 4 of SM). In the case of RR, the residual distributions for individual models are generally broad, which is associated with the higher values of $\sigma$, in particular for UNEDF1 and RMF. The peak heights of the probability density distribution corresponding to the test and extrapolated datasets obtained from the corrected residuals are nearly twice those of the raw residuals. For the dataset labeled ’new’, however, this increase is only marginal. This is also evident from Table 1 that the overall performance is better for the weighted average values of nuclear masses in comparison to the corrected residuals for the individual model across the test, extrapolation, and newly measured data sets.

Figure 3 shows the weighted average values of the raw residuals, $\delta\bar{M}^{\rm RR}$(lower panel), and the corrected residuals, $\delta\bar{M}^{\rm CR}$ (upper panel), for all nuclei in the complete data set. The green colour symbols indicates the nuclei whose absolute value of residuals lie within 100 keV, total number of such nuclei is denoted by $N^{+0.1}_{-0.1}$. The value of $N^{+0.1}_{-0.1}$ increases significantly for the case of corrected residuals. In the data set comprising 2,386 nuclei, most have turned green in the upper panel, indicating improved agreement as compared to the case of RR. Several nuclei from the extrapolated (extpl) data set as seen in the upper panel have also changed to green as compared with the lower panel. The values of the $\sigma_{full}$= 0.070 MeV and the mean absolute error (MAE) = 0.042 MeV for the complete set obtained with weighted average corrected residuals are nearly three times smaller than those for the raw residuals. The maximum spread in the values of $\delta\bar{M}^{\rm CR}$ is almost 1 MeV smaller than $\delta\bar{M}^{\rm RR}$.

The advantage of the weighted-averaging approach in improving nuclear mass-excess predictions is evident from Table 1 and Figures 2 and 3. These effects are further illustrated in Figure 4, which compares the weighted-average of corrected residuals for a representative set of 15 nuclei, selected over a wide mass range, with those from individual nuclear mass models obtained using the GBR and BAR ensemble methods. It is evident that the weighted-average residual values lie very close to zero, demonstrating the cancellation effect and importance of the averaging procedure. Residuals, by definition, exhibit both positive and negative deviations and, under unbiased model assumptions, follow a distribution centered at zero with finite variance [51]. This statistical symmetry implies that averaging residuals leads to partial cancellation of deviations, thereby reducing the net error. Consistent with this, the corrected residuals from individual models are randomly scattered around zero, often with opposite signs for the GBR and BAR approaches within the same model. It may also be noted that out of 12 different values of corrected residuals, for each of the 15 nuclei considered, we have roughly equal number of points on either side of zero line leading to partial cancellation of the residuals while performing the weighed average. This partial cancellation brings the weighted-average residuals, shown as black diamonds, consistently closer to zero than those of any single model. Models that overestimate the mass excess ($\delta\bar{M}^{\rm CR}$<0) for certain isotopes are balanced by others that underestimate them ($\delta\bar{M}^{\rm CR}$>0), reducing systematic bias. Because weights are assigned according to each model’s predictive accuracy on the test set, better-performing models exert greater influence on the final estimate, enhancing the stability of ensemble predictions. This mutual error balancing not only lowers RMSE values (Table 1) but also yields more robust and reliable predictions across the nuclear chart, including extrapolative and data-sparse regions where individual models typically underperform as seen in Table 1 and Figure 4.

Application of refined nuclear masses

We name our refined nuclear mass model as ELMA which denotes ensemble learning and model averaging. The refinement of nuclear mass predictions through the use of ELMA may provide a foundation for broader applications in nuclear physics and astrophysics. Having minimized the deviations and enhanced predictability across the nuclear chart, the resulting mass table becomes more reliable resource for theoretical and experimental studies alike. In nuclear structure and decay studies, accurate nuclear masses serves as a cornerstone for calculating separation energies, decay energies and reaction thresholds. Even small improvements in mass prediction accuracy can lead to substantial gains in the reliability of theoretical models and experimental planning.

One of the most direct and critical applications of an improved mass table is in the determination of the $Q_{\alpha}$ values. These values are required for determining the properties of alpha decay, assessing the boundaries of nuclear stability and interpreting decay chains of newly synthesized heavy and superheavy elements. For superheavy nuclei in particular, where experimental mass measurements are scarce or absent, the precision of predicted values of $Q_{\alpha}$ is often considered as deciding factor in confirming the discovery of new isotope.

In Figure 5 we plot residuals of the $Q_{\alpha}$ values calculated with weighted averaged values of RR and CR for nuclear mass excess. The refinement in nuclear mass prediction is evident, since, the residual distribution of $Q_{\alpha}$ is narrower as can be visualized from figure by enhancement in the number of green symbols (upper panel). The RMSE reduces to 0.058 MeV (upper panel) which is factor of two smaller than those for the RR (lower panel). In addition, the number of nuclei for which $\left\lvert\delta Q_{\alpha}\right\rvert<0.05$ MeV increases from 1064 to 1609, reflecting a substantial enhancement in predictive accuracy of the $Q_{\alpha}$ values across a wide range of periodic chart. This enhancement in predictive accuracy is particularly critical, as an uncertainty of just $\pm$0.05 MeV in $Q_{\alpha}$ demonstrates a profound sensitivity of decay rates, where an increase of that magnitude may result in a predicted half-life changed by $\sim 40\%$ of its original value.

Nuclear Mass Table for ELMA

The values of mass excess and binding energies obtained using nuclear mass model ELMA are calculated for 6303 nuclei. This mass table is made available as supplementary material (masstable_ELMA.txt). By providing, more accurate mass predictions, this table can be used to integrate into variety of research workflows, including r-process nucleosynthesis, $\beta$ decay energy calculations, and the evaluation of reaction Q-values in astrophysical environments. Furthermore, its enhanced precision in $Q_{\alpha}$ estimation makes it as valuable method for guiding experimental results in the synthesis and identification of isotopes at the limits of nuclear chart. We have also deployed ELMA on a web interface, accessible via the provided link (https://ddnp.in. In the future, we plan to continuously update ELMA by incorporating new experimental measurements as well as theoretical advancements, thereby enhancing its predictive accuracy.

Conclusions

We employed ensemble learning and model averaging to improve the predictability of nuclear mass models. Our study uses a diverse set of six models: WS4, WS4+, FRDM, DZ(28), UNEDF1, and RMF. The raw residuals for each of these nuclear mass models were employed to train two ensemble learning algorithms: GBR and BAR. The GBR iteratively reduces bias through sequential error correction, whereas the BAR reduces variance by aggregating predictions from multiple independently trained models. The ensemble learned residuals were then used to correct the raw residuals, thereby incorporating effects not captured by the original nuclear mass models. Hence, there are two different types of corrected residuals for each of the raw residuals for a given nuclear mass model. An improved mass model was obtained by conflating all twelve sets of corrected residuals through a weighted average.

Our nuclear mass model, constructed from a weighted average of corrected residuals, demonstrates a substantial enhancement in predictive accuracy compared with the individual mass models across the validation datasets considered. The resulting conflated mass model achieves an RMSE of approximately 0.0654 MeV for the AME2020 dataset. It is found that the weights assigned to the corrected residuals are substantially redistributed compared to those for the raw residuals. Consequently, the nuclear mass predictions obtained from the weighted average of the corrected residuals exhibit a marked improvement, primarily due to partial cancellation of the residuals. This improvement becomes more pronounced with the increases in the number of nuclear mass models included in the averaging procedure (see Table 1).

We have applied our mass model to evaluate the $Q$ values for $\alpha$ decay and compared them with experimental data. The deviations from the measured values are found to be significantly reduced. We designate our mass model as ELMA (Ensemble Learning and Model Averaging). Using ELMA, we have compiled a table of nuclear mass excess and binding energies for approximately 6,300 nuclei. The ELMA has been deployed on a web interface, accessible via the following URL: https://ddnp.in.

The authors gratefully acknowledge Jatin Fulwani for his valuable assistance in developing the ELMA web interface. B.K.A. acknowledges with gratitude the support received under the Raja Ramanna Chair scheme of the Department of Atomic Energy (DAE), Government of India. T.G. and N.P. acknowledge support from the Croatian Science Foundation under the project Relativistic Nuclear Many-Body Theory in the Multimessenger Observation Era (HRZZ-IP-2022-10-7773). N.C. and G.S. expresses gratitude for the support received from the Department of Science & Technology (DST), Government of Rajasthan, Jaipur, India under F24(1)DST/R&D/2024-EAC-00378-6549873/819.