Forecasting End-of-Life Vehicle Generation in the EU-27: A Hybrid LSTM-Based Forecasting and Grey Systems Theory-Based Backcasting Approach

: End-of-life vehicle (ELV) forecasting constitutes a crucial aspect of sustainable waste management and resource allocation strategies. While the existing literature predominantly employs time-series forecasting and machine learning methodologies, a dearth of studies leveraging deep learning techniques, particularly Long Short-Term Memory (LSTM) networks, is evident. Moreover, the focus on localized contexts within national or municipal boundaries overlooks the imperative of addressing ELV generation dynamics at an international scale, particularly within entities such as the EU-27. Furthermore, the absence of methodologies to reconcile missing historical data presents a significant limitation in forecasting accuracy. In response to these critical gaps, this study proposes a pioneering framework that integrates grey systems theory (GST)-based backcasting with LSTM-based deep learning methodologies for forecasting ELV generation within the EU until 2040. By introducing this innovative approach, this study not only extends the methodological repertoire within the field but also enhances the applicability of findings to supranational regulatory frameworks. Moreover, the incorporation of backcasting techniques addresses data limitations, ensuring more robust and accurate forecasting outcomes. The results indicate an anticipated decline in the recovery and recycling of ELVs, underscoring the urgent need for intervention by policymakers and stakeholders in the waste management sector. Through these contributions, this study enriches our understanding of ELV generation dynamics and facilitates informed decision-making processes in environmental sustainability and resource management domains.


Introduction
End-of-life vehicles (ELVs) refer to vehicles that their registered owners have designated for disposal as waste [1].The reutilization of ELVs is critical not only for economic advantages but also for environmental sustainability.Economically, each component of ELVs represents a loss of value, and the optimal method for recuperating this value is through reuse.Environmentally, every reusable part that is not repurposed necessitates a substitute, and the production of these substitutes depletes environmental resources [2].The growing importance of environmental and social awareness has become a pivotal aspect of the sustainable automotive industry [3].The sustainable management of ELVs presents a multifaceted challenge for researchers, industry practitioners, and policymakers.This management encompasses the oversight of material, capital, and information flows between the final owners of the vehicles, vehicle collection/dismantling/shredding facilities (Vehicle Shredding Facilities-VSFs), re-manufacturing and recycling centres, second-hand markets, and industrial landfill sites [4].The sustainable management of ELVs thus involves a comprehensive approach that integrates environmental, economic, and logistical considerations.Effective strategies must address the entire lifecycle of vehicles, from their final use through to the recycling or disposal of their components [5].This process requires coordinated efforts across various sectors, including the development of policies that incentivize recycling, investment in advanced dismantling technologies, and the establishment of efficient supply chains for reclaimed materials.By focusing on these areas, stakeholders can enhance the sustainability of the automotive industry and mitigate the environmental impact of vehicle disposal.
The European Union (EU) stands as a vanguard in the global pursuit of sustainable development and environmental stewardship.Central to this endeavour is the effective management of ELVs, which represent a crucial segment of the automotive lifecycle with profound economic, environmental, and social implications.As the EU continues to chart a course towards a circular economy and carbon-neutral future, handling ELVs emerges as a crucial frontier in this transformative journey.The EU's approach to ELV management is anchored in a comprehensive legislative framework aimed at promoting recycling, recovering, reusing, resource efficiency, and pollution prevention.At the heart of this framework lies the ELV Directive (2000/53/EC), a landmark piece of legislation that established ambitious targets for the recovery, reuse, and recycling of ELVs, while mandating the phasing out of hazardous substances from automotive components.The evolution of the ELV Directive within the EU has been marked by a series of refinements and revisions aimed at enhancing its efficacy in addressing environmental challenges associated with end-of-life vehicles.Adopted initially in 2000, the directive has undergone iterative policy adjustments to accommodate emerging concerns, bolster recycling objectives, and improve the management of hazardous materials inherent in automotive waste streams [6].
In March 2023, the implementation of Delegated Directive 2023/544 commenced, which pertains to the modification of Directive 2000/53/EC of the European Parliament and the Council concerning exemptions related to the utilization of lead in aluminium alloys for machining purposes, copper alloys, and specific types of batteries [7].On 13 July 2023, the Commission introduced a fresh proposal for a regulation addressing ELVs after a comprehensive review process.Aligned with the objectives outlined in the European Green Deal and the Circular Economy Action Plan, this proposal aims to supersede and consolidate two prevailing Directives: Directive 2000/53/EC concerning end-of-life vehicles and Directive 2005/64/EC pertaining to the type approval of motor vehicles with respect to their reusability, recyclability, and recoverability (Figure 1) [8].Despite legislative advancements, the management of ELVs in the EU remains a complex challenge, marked by economic, logistical, social, and environmental factors.The substantial annual volume of ELVs in the EU, estimated at over 5,700,000 tonnes/year on average, poses significant logistical challenges for recycling infrastructure and endof-life treatment facilities (Figure 2).For instance, in 2021 alone, 5.7 million passenger cars, vans, and other light goods vehicles were scrapped in the EU, with 93.6% of parts and materials being reused and recovered, and 88.1% being reused and recycled [9,10].Additionally, the intricate composition of modern vehicles, characterized by a complex mix of materials and components, presents unique hurdles for effective dismantling, recycling, and disposal processes.In addition to logistical challenges, the EU faces pressing environmental imperatives in managing ELVs.The disposal and treatment of ELVs can give rise to various environmental risks, including soil and water contamination from hazardous substances such as heavy metals and fluids.Moreover, the carbon footprint associated with ELV management, encompassing transportation, processing, and energy consumption, underscores the urgency of adopting sustainable practises to minimize environmental impact.Efficient management of ELVs relies heavily on accurate forecasting of future ELV generation and the subsequent recovery and recycling amounts.This forecasting is essential for informing proactive strategies in sustainable resource management and environmental stewardship within the automotive industry.By anticipating trends in ELV generation and recycling capabilities, stakeholders can optimize resource allocation, policy interventions, and investment in recycling infrastructure, thereby advancing the agenda of circular economy principles and long-term environmental sustainability.In response to this imperative, the present study proposes a dual-method approach incorporating grey systems theory (GST) for backcasting and Long-Short Term Memory (LSTM)-based deep learning for forecasting the volumes of generated, recovered, and recycled ELVs within the EU context.
In the forthcoming sections, this study will embark on an in-depth exploration of the pertinent literature surrounding forecasting methodologies applied within the domain of ELVs.This critical literature review will provide a comprehensive overview of existing research endeavours, methodologies employed, and key findings in the realm of ELV forecasting, thereby establishing a robust foundation for our analytical framework.Subsequently, this study will elucidate the GST and LSTM methodologies, which serve as the cornerstone of our analytical approach.This methodological exposition will offer a detailed explanation of the theoretical underpinnings, computational procedures, and practical applications of GST and LSTM techniques within the context of ELV forecasting, ensuring transparency and reproducibility in the research methodology.Following the methodological exposition, this study will present the empirical findings derived from our application of GST and LSTM methodologies to forecast the generated, recovered, and recycled quantities of ELVs until 2040.Through rigorous data analysis and interpretation, the implications of our findings, drawing insights into the dynamics of ELV management and the potential pathways toward achieving a more sustainable and resilient automotive ecosystem within the EU, will be elucidated.Subsequent to the presentation of findings, we will synthesize our research outcomes to derive meaningful conclusions regarding the efficacy of GST and LSTM methodologies in ELV forecasting, as well as the broader implications for policy, practise, and research.These conclusions will be grounded in empirical evidence and theoretical insights gleaned from our study, thereby offering valuable contributions to both academic scholarship and practical decision-making within the domain of automotive waste management.Furthermore, the managerial implications arising from our research findings, providing actionable recommendations for policymakers, industry stakeholders, and environmental practitioners involved in the governance and management of ELVs within the EU, will be discussed.
The research objectives of this study are delineated into three primary components as follows: • Forecasting the quantities of generated, recovered, and recycled ELVs in the EU by 2040 to inform future scenarios for policymakers and stakeholders.

•
Examining the quantities of generated, recovered, and recycled ELVs, considering the influence of input variables such as GDP and population.

•
Utilizing backcasting techniques to impute missing values in the input variables, thereby ensuring a symmetrical dataset suitable for multivariable forecasting.

Literature Review and Problem Identification
The literature on ELV management presents a multifaceted approach to addressing the challenges posed by vehicle recycling and reverse logistics networks.Demirel et al. ( 2016) introduced a mixed integer linear programming model tailored to optimize the reverse logistics network for ELVs in Turkey [11].By considering factors such as facility placements, transportation costs, and revenues from recyclable materials, the model seeks to minimize environmental impact and associated expenses.Additionally, demographic factors are incorporated, with the GDP-dependent Gompertz function and Weibull distribution utilized to model the retirement rates of vehicles.Sokić et al. (2016) contributed to this discourse by employing the Weibull distribution function to analyze ELV generation dynamics in Serbia [12].Meanwhile, Ene and Ozturk (2017) expanded forecasting methodologies in Turkey by integrating grey systems theory (GST), utilizing models such as GM (1,1), OGM, and FOGM to anticipate ELV return flows [13].In the realm of ELV forecasting, studies extend beyond Turkey and Serbia.2019) investigated precious metal recovery potential from ELVs in Japan using population balance modelling [16].In a related study, Wang et al. (2019) employed scenario analysis and the Weibull distribution function to examine hybrid vehicle exports from Japan to Mongolia [17].Further diversifying the scope, Zhou et al. (2020) employed GST in China, presenting a GM (1,1) model for ELV forecasting [18].Abdelbaky et al. (2020) explored ELV recycling from the EU perspective, introducing a simulation model based on probability failure functions to forecast battery recycling potential from electric vehicles (EVs) [19].In Brazil, de Souza et al. (2022) proposed a hybrid forecasting model combining Autoregressive Integrated Moving Average (ARIMA) and ANN methodologies to predict ELV generation [20].Similarly, in Turkey, Karagoz et al. (2022) developed a reverse logistics supply chain optimization model and utilized the moving average method for ELV forecasting [21].Lastly, Kastanaki and Giannis (2023) proposed a dynamic estimation model for end-of-life EVs in the EU-27, contributing to the broader discourse on sustainable vehicle end-of-life management [22].Table 1 provides a comprehensive overview of extant studies pertaining to the forecasting of ELVs.
The extant literature reveals a predominant focus on time-series forecasting and machine learning methodologies within the domain of ELV forecasting.Nevertheless, scant attention has been directed towards leveraging deep-learning techniques in this realm.Specifically, the utilization of Long Short-Term Memory (LSTM) networks remains notably absent from scholarly inquiry in this field.The proposed study contributes to the existing literature on ELV forecasting in several notable ways, effectively addressing critical gaps identified within the scholarly discourse.Firstly, this study presents an innovative framework for forecasting ELV generation by integrating GST-based backcasting with LSTM-based deep learning methodologies.This departure from conventional forecasting techniques not only expands the methodological repertoire within the field but also presents a promising avenue for more accurate and robust predictions.Secondly, the study's focus on forecasting ELV generation specifically within the EU-27 context represents a significant departure from the predominantly localized scope of prior research endeavours.By extending the analysis to encompass an international perspective, the study provides insights crucial for policymakers and stakeholders operating at supranational levels, thereby enhancing the applicability and relevance of the findings to broader regulatory frameworks and strategic planning initiatives.Furthermore, the incorporation of backcasting methods to address missing historical data constitutes a methodological innovation that distinguishes the proposed study from previous research efforts.By leveraging backcasting techniques, the study not only mitigates the limitations imposed by data gaps but also enhances the reliability and accuracy of the forecasting model, thereby ensuring more robust and informative outcomes.In summary, this study advances the field of ELV forecasting by introducing a hybrid methodology, extending the analysis to encompass international dimensions, and innovatively addressing data limitations through the incorporation of backcasting techniques.By bridging these critical gaps in the literature, this study significantly enriches our understanding of ELV generation dynamics and facilitates more informed decision-making processes within the realm of environmental sustainability and resource management.
In this study, prognostications concerning the quantities of ELVs recovered, recycled, and generated within the EU-27 spanning the temporal domain from 2022 to 2040 are undertaken.Table 2 presents historical data about ELVs spanning the period from 2006 to 2021 [9,10].The input variables employed for forecasting the quantities of recovered, recycled, and generated ELVs encompass parameters such as population and Gross Domestic Product (GDP) measured in current US dollars.A comprehensive dataset encompassing population and GDP values spanning the timeframe from 1990 to 2022 serves as the empirical foundation for this analysis.Specifically, Table 3 depicts the temporal evolution of population and GDP metrics [24,25].Due to its augmented proficiency in preserving long-term memory, this neural network architecture facilitates comprehensive scrutiny of extended temporal correlations and patterns within datasets characterized by constrained sample sizes [26].It is imperative to underscore that, for optimal processing of sequential data by an LSTM layer, the input necessitates transformation into a three-dimensional format.In the context of a forecasting task, the configurability extends to both the quantity of inputs and neurons within the hidden layer.Conversely, the output layer is typically composed of a singular neuron supplemented by ancillary elements including weights, biases, and activation functions.The foundational architecture of a multilayer perceptron, illustrating the basic neural network structure, is depicted in Figure 3. Figure 4 depicts the fundamental LSTM network structure where x t is the current variable vector, h t−1 is the previous output, and C t−1 is the previous cell state, and they are the inputs to the LSTM network.Additionally, i t is the input gate, f t is the forget gate, o t is the output gate and C t is the memory cell [27][28][29]: the symbol ⊕ represents the element-wise matrix/vector multiplication operator.LSTM neural networks are a specialized form of RNNs characterized by a unique structure known as the LSTM cell within their hidden layers [30].As depicted in Figure 4, the LSTM cell incorporates three gates: the input gate, the forget gate, and the output gate.These gates regulate the information flow through the network, facilitating effective learning and memory retention over time [31].In practical applications, the availability of historical data for training the series prediction LSTM neural network is often constrained.This limitation necessitates the utilization of recurrent calculations to propagate historical information through the network, enabling the model to leverage both long-term and short-term memory for prediction purposes.To address the challenges posed by the limited and imbalanced nature of observational data in the input variables, this study employs a grey systems theory (GST)-based backcasting approach.GST provides a robust framework for generating predictive insights in scenarios characterized by sparse and uneven data distributions, thus enhancing the efficacy of the LSTM neural network in real-world applications.
Grey systems theory (GST), pioneered by Julong Deng in 1982, represents a novel methodology tailored to addressing challenges associated with limited sample sizes and incomplete information.This approach specializes in navigating uncertain systems characterized by partial knowledge by means of generating, excavating, and extracting valuable insights from the available data [32].It endeavours to formulate theories, methodologies, concepts, and insights aimed at elucidating and analyzing latent, complex, and uncertain systems [33].This framework proves particularly efficacious when confronted with scenarios characterized by a paucity of samples and incomplete information.By harnessing GST principles, it becomes feasible to expedite the generation of pertinent and actionable insights within systems operating under conditions of uncertainty and partial information.Consequently, GST facilitates the delineation and proficient monitoring of the functional dynamics inherent within the system [34].A diverse array of applications of GST are documented in the existing literature, a comprehensive examination of which will be presented in the subsequent section.
The grey prediction model of order 0, denoted as GM(0, n), serves as a method for forecasting the behaviour of systems characterized by limited or uncertain data.This approach entails the development of a first-order grey differential equation derived from the available data, subsequently employed to project future trends within the system.GM(1,1) represents an advancement over the GM(0, n) model within GST.By integrating one previous value from both the original data sequence and the accumulated generating sequence, GM(1,1) enhances prediction accuracy relative to the GM(0, n) model [35].The Differential Grey Model, DGM(1,1), represents an adaptation of the GM(1,1) model within GST.DGM(1,1) takes into account the rate of change exhibited by the original data sequence by introducing a first-order differential equation to characterize the system's dynamics.This incorporation leads to enhanced prediction accuracy, particularly beneficial for handling non-linear data patterns [36].The Adaptive Grey Model, AGM (1,1), is a refinement of the GM(1,1).It incorporates adaptive parameters to enhance prediction performance by adjusting them dynamically based on data characteristics, thereby improving adaptability to changing system dynamics [37].The probabilistic accumulation operator-based Grey Forecasting Model, PGM(1,1), is an enhanced version of the GM(1,1) model.Introducing an additional probabilistic accumulation operator improves flexibility and prediction accuracy, allowing for better capturing of system dynamics [38].A Fractional Grey System Model, FGM(q, 1), extends the GM(1,1) model by transforming first-order differential equations into fractional differential equations.This modification entails the decomposition of data matrix parameters during the solution process, aligning with the new information priority principle [39].The Improved Grey Model (1,1), IGM(1,1), involves a functional transformation of the original data series to generate a new sequence characterised by enhanced smoothness [40].
Figure 5 illustrates the Root Mean Squared Error (RMSE) values obtained from various GST-based approaches.Given the model's complexity and non-linearity, and considering the minimum RMSE value, the IGM(1,1) method is selected for the backcasting analysis of generated, recovered, and recycled amounts of ELVs.

Analysis of the Findings
The present case study was conducted utilizing computational resources hosted on a 13th Generation Intel Core (TM) i5-1345U processor with a base clock speed of 1.60 GHz, coupled with 16.0 GB of Random Access Memory (RAM), operating within a 64-bit architecture.The analysis was implemented using Python version 3.11.5 within the JupyterLab version 3.6.3interactive development environment (IDE), leveraging various packages including TensorFlow, Keras, scikit-learn, pandas, NumPy, and SciPy to instantiate and evaluate GST and LSTM models.Furthermore, the visualization and interpretation of results were conducted utilizing Microsoft Power BI version 2404.2.18827-train, ensuring a comprehensive and intuitive presentation of the analytical findings.
The LSTM neural network model delineated in this study comprises four LSTM layers, each with 128 memory units.Each LSTM layer is followed by a dropout layer with a rate of 0.3 to mitigate overfitting, and L2 regularization with a strength of 0.01 is employed to enhance model generalization.The network is trained with a learning rate of 0.01.An early stopping mechanism is utilized to monitor the validation loss, halting training if no improvement is observed for 10 consecutive epochs, and restoring the optimal model weights.The training process uses a batch size of 32 and spans up to 100 epochs, with 20% of the data reserved for validation.
Compared to traditional neural networks, LSTM models offer a more robust framework for capturing the complexities of time-series data such as the yearly data in this case study.The inclusion of dropout, L2 regularization, and early stopping further strengthens the model by reducing overfitting and improving generalization.While traditional neural networks remain valuable in various real-life applications, they often require significant adjustments to manage sequential data as effectively as LSTMs, thereby making LSTMs a more suitable choice for tasks involving temporal dependencies.
The delineated examination underscores the discernment of forecasting outcomes pertaining to the annual aggregate of ELVs, as delineated in Figure 6, leveraging both Stacked and MV-LSTM models employing the IGM(1,1) backcasting methodology.The observed trajectory suggests a notable prospective decrement in the volume of ELVs anticipated in the forthcoming years.Moreover, Figure 7 offers a nuanced elucidation of the temporal vista spanning from 2023 to 2040.Herein, it emerges that both Stacked (with RMSE Train = 0.0859 and RMSE Test = 0.2429) and MV-LSTM (with RMSE Train = 0.8624 and RMSE Test = 2.1651) architectures manifest a downward trend.However, the outcomes yielded by the IGM(1,1) Stacked LSTM model (with RMSE Train = 0.2038 and RMSE Test = 0.4118) evince a contrary ascending trajectory.This incongruity ostensibly emanates from the inadvertent disregard of the salient backcasting attributes inherent within the dataset.In essence, the outcomes underscore the imperative of methodological prudence in incorporating backcasting features within forecasting paradigms.The neglect thereof may precipitate inaccuracies in predictive analytics, as evinced by the discordant results observed in the IGM(1,1) Stacked LSTM model, thereby accentuating the exigency for meticulous consideration of such foundational elements in empirical modelling endeavours.
Figure 8 presents an analysis of the annual recovery of ELVs in metric tonnes, covering the period from 1990 to 2005 through backcasting with IGM(1,1), and projecting from 2022 to 2040 using Stacked LSTM and MV-LSTM models.While both the Stacked LSTM (with RMSE Train = 0.0386 and RMSE Test = 0.0415) and MV-LSTM (with RMSE Train = 0.8841 and RMSE Test = 1.5913) models exhibit declining trends in ELV recovery, the nature of this decline differs significantly between the two.The Stacked LSTM model displays a relatively stable pattern, suggesting a gradual decrease over time with more stationary behaviour.In contrast, the MV-LSTM model showcases a fluctuating trajectory, indicating periodic variations in ELV recovery amounts amidst an overall declining trend.Secondly, when comparing the forecasted trends beyond 2022, the MV-LSTM model stands out as the only one projecting a statistically significant decreasing trend in ELV recovery up to 2040.This finding raises concerns about the sustainability of current recovery efforts and suggests a potential worsening of the ELV management situation in the future.

Conclusions and Future Directions
In conclusion, the utilization of advanced modelling techniques, such as LSTM networks, undeniably contributes to our understanding of future trends in ELV generation, recycling, and recovery.However, a critical examination of the limitations and uncertainties inherent in these predictive methodologies is indispensable.The discrepancies and divergent projections observed in the outcomes of such models underscore the need for a nuanced approach to their interpretation and application in environmental management decision-making.It is crucial to acknowledge that predictive models, no matter how sophisticated, are subject to inherent biases, uncertainties, and limitations.The reliance on historical data and assumptions about future conditions introduce significant sources of error in the forecasts.Moreover, the complex interplay of socioeconomic factors, technological advancements, and regulatory frameworks further complicates the accuracy of these projections.
The results predict a significant decline in the amount of recovery and recycling of ELVs in the EU by 2040.The projected decline in the recovery of ELVs, as indicated by certain models, necessitates urgent attention from policymakers and stakeholders within the waste management sector.Rather than passively accepting these forecasts as inevitable, proactive measures must be taken to address the underlying causes and mitigate their adverse impacts.This necessitates a holistic approach that encompasses not only technological innovation but also policy interventions, stakeholder engagement, and public awareness campaigns.Furthermore, the emphasis on sustainable waste management practises should not be limited to ELVs alone but should extend to the broader context of circular economy principles.This entails rethinking our consumption patterns, product design, and resource allocation to minimize waste generation and maximize resource efficiency.
In light of these considerations, it is evident that while predictive modelling can provide valuable insights, it should not be regarded as a panacea for the complexities of environmental management.Rather, it should be complemented by a robust framework of evidence-based decision-making, adaptive governance mechanisms, and stakeholder collaboration to navigate the uncertainties and challenges ahead.Failure to do so risks exacerbating existing environmental problems and undermining efforts towards a more sustainable future.
Funding: This research received no external funding.

Figure 1 .
Figure 1.Temporal evolution of the ELV Directive policy in the EU.

Figure 2 .
Figure 2. The number of generated ELVs in the EU from 2006 to 2021.
where b f , b i , b o and b C are bias vectors; U f , U i , U o and U c are the weight matrices linking the preceding output to the three gates and the memory cell.W f , W i , W o and W c are the weight matrices, σg() stands for the gate activation function (a sigmoid function), and tanh() stands for the hyperbolic tangent function.The computation of the cell output state C t and the layer output h t can be established according to the following equations:

Figure 4 .
Figure 4.The fundamental architecture of LSTM models.

Figure 6 .
Figure 6.The forecasting and backcasting results of the generated ELVs.

Figure 7 .
Figure 7.The forecasting results of the generated ELVs.Moreover, as depicted in Figure 9, the discrepancy between the forecasts of the IGM(1,1) model and the LSTM-based models warrants scrutiny.While the Stacked LSTM model forecasts a steady increase in ELV recovery, both the IGM(1,1) Stacked LSTM (with RMSE Train = 0.2044 and RMSE Test = 0.2775) and MV-LSTM models project a decline.This disparity underscores the limitations of traditional statistical methods in capturing the complex dynamics of ELV recovery, especially in light of changing socio-economic and environmental factors.

Figure 8 .
Figure 8.The forecasting and backcasting results of the recovered ELVs.

Figure 9 .
Figure 9.The forecasting results of the recovered ELVs.The discerned downward trajectory in both backcasting and forecasting methodologies regarding the recycling volume of annually generated ELVs runs parallel to observed recovery amounts.Notably, this trend exhibits a nuanced differentiation between forecasting techniques, wherein the MV-LSTM model (with RMSE Train = 0.8615 and RMSE Test = 1.8430) demonstrates a fluctuating pattern.Conversely, the Stacked LSTM model (with RMSE Train = 0.0620 and RMSE Test = 0.0125) portrays a more consistent decline over time.Such fluctuation in the MV-LSTM model underscores the sensitivity of the forecasted outcomes to macroeconomic variables such as GDP and population dynamics.Figure 10 elucidates this phenomenon, illustrating the discernible impact of GDP and population shifts on the predictive performance of the MV-LSTM model.
Figure 10  elucidates this phenomenon, illustrating the discernible impact of GDP and population shifts on the predictive performance of the MV-LSTM model.

Figure 10 .
Figure 10.The forecasting and backcasting results of the recycled ELVs.Moreover, Figure 11 elucidates the comparable behaviour of the IGM(1,1) Stacked LSTM model (with RMSE Train = 0.2359 and RMSE Test = 0.2771), aligning closely with the results obtained from the standard Stacked LSTM model.This congruence contrasts starkly with the divergent projections produced by the MV-LSTM model, further highlighting the robustness and stability of the Stacked LSTM approach in forecasting recycling volumes of ELVs up to 2040.

Figure 11 .
Figure 11.The forecasting results of the recycled ELVs.

Table 1 .
The overview of the existing literature regarding the forecasting of ELVs.

Table 2 .
Recovered, recycled, and generated amounts of ELVs in the EU-27 between 2006 and 2021.