Deep Learning-based Multivariate LSTM Approach for Forecasting Export and Import Container Throughput at Busan Port

2.1 Deep learning and M-LSTM approaches in container throughput forecasting

Accurate forecasting of container throughput is fundamental to port operations, enabling proactive resource allocation, congestion mitigation, and strategic capacity planning. Traditionally, linear time-series models such as ARIMA and SARIMA have been widely adopted in maritime logistics forecasting [7][8]. While these approaches effectively model stable and recurring patterns, their reliance on linear structures and fixed seasonal assumptions limits their performance under nonlinear and structurally dynamic conditions frequently observed in port environments, where throughput levels fluctuate with trade cycles, exchange-rate variation, and macroeconomic conditions. Consequently, conventional statistical models often fail to fully capture the volatility and cyclical interdependence inherent in container flow systems [1][2].

To overcome these limitations, machine learning methods such as support vector regression and gradient-boosting frameworks have been applied to enhance nonlinear approximation capability [3]. However, these methods typically treat temporal information as static features rather than sequential signals, thereby failing to capture long-term dependencies essential for port throughput forecasting.

Deep learning methods, particularly the LSTM network [4], have demonstrated strong capacity for modeling nonlinear sequential dependencies. Empirical studies in maritime and transportation analytics consistently report superior accuracy and temporal robustness of LSTM models relative to traditional approaches. For example, S. Shankar et al. [9] applied an LSTM framework incorporating economic, environmental, and social factors and reported superior forecasting accuracy compared with ARIMAX model, while C. H. Yang and P. Y. Chang [10] demonstrated that a CNN–LSTM architecture outperforms classical machine learning approaches in port container throughput forecasting.

Despite these advances, most existing studies still rely on univariate LSTM structures that forecast export and import flows separately. Such univariate designs overlook the operational interdependence between inbound and outbound movements, which arise from shared vessel schedules, container repositioning constraints, and terminal resource coupling. Recent port-forecasting research generally models only a single throughput series, such as total container volume or aggregate port demand, and therefore does not address the challenge of learning cross-flow interactions between distinct but correlated sequences. Hybrid or multi-source approaches, including models incorporating hinterland-foreland information [11], decomposition-enhanced hybrid neural models [12], or network-based port-interaction structures [13], broaden the information environment but still stop short of implementing a unified multivariate sequence model capable of jointly predicting export and import flows.

In contrast, general M-LSTM frameworks demonstrate the benefits of explicitly modeling multiple correlated temporal inputs. The ATT-LSTM of W. Ju and J. Liu [14], although applied in non-maritime settings, shows that jointly learning interactions across correlated time series can enhance temporal representation and forecasting accuracy. Likewise, Y. Liu et al. [15] present a dual-stage attention-based multivariate recurrent network that effectively captures long-term and cross-channel dependencies, reinforcing the methodological value of multivariate sequence learning. These findings collectively motivate the use of an M-LSTM architecture in the present study, where export and import flows evolve jointly and require integrated modeling.

2.2 Mechanics of the LSTM network

LSTM networks represent an advanced class of recurrent neural networks designed to capture long-range temporal dependencies in sequential data. Conventional recurrent neural networks often face gradient vanishing or explosion during back-propagation through long sequences, limiting their ability to retain information across extended temporal horizons [4].

Fig. 1 provides a schematic representation of the internal computations within an LSTM cell, which centers around a memory cell regulated by three gating mechanisms, the forget, input, and output gates. At each time step t, the LSTM receives the current input Xₜ, the previous hidden state Hₜ₋₁, and the previous cell state Cₜ₋₁. The forget gate determines which historical information to discard, the input gate controls how much new information to store, and the output gate modulates the transformed memory that influences the next hidden state. Through this selective gating process, the LSTM preserves relevant long-term context while adapting to short-term variations, providing a flexible mechanism for modeling nonlinear and time-varying dynamics.

Fig. 1.

Schematic of the internal computations of an LSTM cell [4][18]

This architecture is particularly advantageous for port throughput forecasting, where time series exhibit volatility, seasonality, and regime shifts. Empirical work such as X. Ma et al. [16] confirms that LSTM models can effectively capture relationships across correlated temporal variables.

For multi-step or multi-horizon forecasting tasks, LSTM architectures can be extended into an encoder–decoder structure. In this configuration, the encoder compresses historical information into a latent state representation, while the decoder unfolds it across future time steps to produce coherent forecasts. This design has been successfully applied in various domains, including energy demand, financial modeling, and transportation analytics [17][18], and provides the architectural foundation for the proposed framework in this study.

3.1 Rationale for an M-LSTM design

Building on the theoretical foundation described in Section 2, this study employs an M-LSTM framework to jointly learn intra-series temporal dependencies and inter-series relationships between export and import throughput. The gating mechanisms, forget, input, and output gates, enable the model to retain long-term contextual memory while updating short-term information, a property particularly effective in modeling cyclical and nonlinear throughput patterns driven by synchronized port operations and macroeconomic conditions.

Although M-LSTM architectures have been successfully applied in domains such as general multivariate time-series forecasting [15] and industrial process prediction [14], their use for simultaneous export–import forecasting at the port level remains limited. The proposed framework extends these applications through a dual-channel M-LSTM that encodes two correlated series within a unified temporal learning structure. By incorporating exogenous variables such as exchange rates, industrial production indices, and sinusoidal seasonality encodings, the model captures macroeconomic and calendar-driven demand conditions affecting port container throughput. These variables primarily enhance forecast stability and medium-term trend representation, rather than serving a causal interpretive role, which is consistent with the predictive focus of this study.

The proposed M-LSTM framework is particularly well suited for port container throughput forecasting, as port operations exhibit strong temporal dependencies, pronounced seasonality, and intrinsic interdependence between export and import flows arising from shared vessel schedules, container repositioning, and terminal resource constraints.

3.2 Model structure and learning configuration

The model adopts a sequence-to-sequence formulation in which 12 months of export and import observations jointly serve as the input window. Each time step is represented as a paired vector [Export_t, Import_t], constructing an input tensor X ∈ ℝ^T×2, where T denotes the length of the input window. The network learns the nonlinear mapping

f([Export_t-T+1, Import_t-T+1], . . ., [Export_t, Import_t]) → [Export_t+1, Import_t+1]), and optimizes its parameters by minimizing the mean squared error (MSE):

where N represents the number of training samples.

To support multi-horizon forecasting, an encoder–decoder configuration is implemented. The encoder extracts shared and flow-specific temporal representations, while the decoder unfolds these across future horizons to generate synchronized 12-month-ahead predictions for both export and import series. This design enforces temporal consistency and prevents unrealistic outcomes, such as simultaneous unconstrained growth in both flows, by implicitly reflecting operational capacity constraints of vessels and terminals.

The architecture remains intentionally streamlined, avoiding unnecessary hybridization with convolutional or decomposition-based components that characterize many recent complex forecasting models (e.g., Y. Tan and L. Huang [12], G. Liang et al. [13]). This simplified design enhances computational efficiency, facilitates periodic retraining as new data become available, and supports reliable, interpretable forecasting for berth scheduling, yard-capacity planning, and long-term port management.

4.1 Data description and preprocessing

This study employs a monthly time-series dataset covering August 2011 to July 2025, comprising 168 observations for Busan Port’s export and import throughput. Export and import TEU volumes serve as the primary endogenous variables, representing South Korea’s external trade and global logistics linkages. Monthly export and import container throughput data for Busan Port were obtained from the Maritime and Fisheries Statistics published by the Ministry of Oceans and Fisheries of Korea. Exogenous variables were collected from official national statistical databases.

To reflect macroeconomic and operational influences, three indicators are incorporated: exchange rate, industrial production index, and monthly public holiday counts. The exchange rate captures international trade cost fluctuations, the industrial production index represents domestic production-driven export cycles, and holiday counts approximate effective working days and seasonal rhythms.

Seasonality is encoded using sinusoidal sine and cosine functions to maintain the cyclical continuity between December and January, avoiding artificial breaks common in categorical representations. All continuous variables are normalized using Min–Max scaling (based on the training set only) to prevent data leakage, and throughput values are log-transformed to stabilize variance. The dataset is temporally partitioned into training, validation, and testing subsets, with the final 12 months (August 2024–July 2025) designated as the holdout test period. This fixed-block approach mimics real-world forecasting, where future data are unavailable during model estimation.

4.2 Forecasting configuration and training strategy

The forecasting problem is defined as a direct multi-horizon prediction, using the previous 12 months to forecast the next 12 months of throughput. The non-test segment is divided chronologically (80:20) into training and validation sets, with samples generated through a rolling-window mechanism that preserves causality. This setup exposes the model to diverse economic and operational conditions while preventing look-ahead bias.

The predictive system follows an encoder–decoder LSTM architecture in which the encoder summarizes historical dependencies into a latent context vector propagated across the forecast horizon via a RepeatVector layer. The decoder LSTM reconstructs sequential forecasts, refined through a TimeDistributed dense layer to adjust horizon-specific outputs. Dropout regularization mitigates overfitting, and parameters are optimized using the Adam algorithm with MSE loss. Early stopping based on validation loss ensures generalization and computational efficiency.

Model hyperparameters were selected through empirical tuning based on validation performance. Both the encoder and decoder LSTM layers were configured with 64 hidden units, providing a balance between representational capacity and overfitting risk given the monthly data frequency and sample size. Dropout regularization with a rate of 0.2 was applied to the LSTM layers to improve generalization. The model was trained for a maximum of 300 epochs using the Adam optimizer with an initial learning rate of 0.001, while early stopping with a patience of 20 epochs was implemented to terminate training once validation loss ceased to improve. The batch size was set to 16, reflecting a trade-off between training stability and computational efficiency.

These hyperparameter values were determined through preliminary experiments comparing alternative configurations, and the selected setup consistently exhibited stable convergence behavior and robust multi-horizon forecasting performance on the validation set, supporting effective learning of medium-term trade and logistics dynamics.

5.1 Comparative evaluation of overall and temporal forecast accuracy

The predictive performance of the proposed M-LSTM model was benchmarked against two widely adopted forecasting approaches. The first benchmark, SARIMA, is a classical seasonal autoregressive integrated moving-average model that captures linear temporal patterns and stable annual seasonality. The second benchmark, NeuralProphet, is a hybrid decomposition-based neural model that integrates additive trend components, Fourier-based seasonality terms, autoregressive lags, and holiday effects within a unified neural regression framework. These baselines represent three distinct methodological families, parametric statistical modeling (SARIMA), hybrid neural decomposition (NeuralProphet), and deep sequence learning (LSTM), allowing a balanced comparison of forecasting capabilities for maritime container dynamics. Forecast accuracy was primarily evaluated using MAE, supported by RMSE and MAPE, following established time-series evaluation practices.

Table 1 presents the comparative results for export throughput forecasting. SARIMA and NeuralProphet achieved MAEs of 59,198 TEU and 55,772 TEU, respectively, whereas the proposed M-LSTM markedly reduced the error to 42,180 TEU, corresponding to improvements of 28.7% and 24.4% relative to SARIMA and NeuralProphet. Similar performance gains were observed for RMSE, where M-LSTM achieved 45,875 TEU compared to 60,655 TEU and 58,307 TEU. In terms of proportional accuracy, M-LSTM attained a MAPE of 4.07%, outperforming SARIMA (5.71%) and NeuralProphet (5.40%). These results highlight the strength of deep sequence learning in capturing nonlinear market fluctuations and temporal dependencies inherent in container trade flows.

Table 1.

Comparative forecast accuracy of models (export throughput)

For import throughput (Table 2), the M-LSTM model again demonstrated superior accuracy. The proposed model achieved a MAE of 43,093 TEU, improving upon SARIMA (58,695 TEU) and NeuralProphet (56,654 TEU) by 26.6% and 23.9%, respectively. RMSE and MAPE results followed consistent trends, with M-LSTM achieving lower errors across all metrics: RMSE of 48,940 TEU (compared with 61,931 TEU and 62,589 TEU) and MAPE of 4.18% (versus 5.65% and 5.45%). These results confirm that the multivariate temporal modeling capability of M-LSTM leads to systematic accuracy gains in both outbound and inbound port flows.

Table 2.

Comparative forecast accuracy of models (import throughput)

Fig. 2 and Fig. 3 further illustrate the monthly MAE trajectories over the 12-month forecast horizon for export and import throughput. In both cases, the M-LSTM exhibited consistently lower and more stable errors than the benchmark models. For export throughput (Fig. 2), SARIMA and NeuralProphet displayed noticeable volatility, with pronounced spikes during high-variance months such as September 2024 and February 2025, whereas M-LSTM maintained lower and stable error margins. A similar pattern is evident in import throughput (Fig. 3), where M-LSTM avoided sharp error surges observed in the benchmark methods, particularly during late-2024 and early-2025 when import flow variability was heightened by seasonal and macroeconomic factors.

Fig. 2.

Monthly MAE comparison of models (export throughput)

Fig. 3.

Monthly MAE comparison of models (import throughput)

Taken together, the tabular and graphical evidence demonstrates that the M-LSTM consistently outperforms SARIMA and NeuralProphet in both aggregate and month-to-month accuracy. The model’s ability to jointly learn export and import dynamics and accommodate nonlinear temporal dependencies results in smoother forecast trajectories and enhanced robustness under volatile trade conditions. These findings support the practical feasibility of deep learning architectures for accurate, operationally relevant port throughput forecasting.

5.2 Visual assessment of forecasting trajectories

Fig. 4 and Fig. 5 compare the actual observations and M-LSTM forecasts for export and import container throughput across the 12-month evaluation period. Overall, the forecast trajectories align closely with the observed monthly movements, indicating that the model effectively reproduces seasonal fluctuations and evolving trade dynamics.

Fig. 4.

Actual and forecasted monthly export throughput

Fig. 5.

Actual and forecasted monthly import throughput

For the export series (Fig 4), the M-LSTM successfully captures the gradual increase in throughput from late 2024 into early 2025 and follows most short-term month-to-month variations. Although the model shows slight over- or under-estimations in a few months, the overall directional movement and structural pattern remain consistent with the actual data.

For the import series (Fig. 5), the model demonstrates strong responsiveness to rapid short-term fluctuations. In particular, it reproduces the pronounced dip in early 2025 followed by an immediate rebound, a characteristic feature of the actual import flow during that period. Minor discrepancies in isolated months do not alter the overall alignment with observed market behavior.

Overall, these visual comparisons show that the M-LSTM produces forecasts that are both smooth and adaptive, preserving the essential temporal structures of the real series. This confirms the model’s operational relevance, complementing the quantitative evaluation presented in Section 5.1.

6.1 Summary of contributions

This study proposed a M-LSTM forecasting framework designed to predict monthly export and import container throughput at Busan Port, the largest gateway hub for South Korea’s maritime trade. Unlike conventional univariate or single-target forecasting approaches that model export and import flows independently, the present framework jointly learns both series within a unified architecture, allowing the model to exploit shared trade dynamics, macroeconomic drivers, and synchronized operational rhythms across inbound and outbound cargo flows. Through this design, the model captures the inherent interdependence between export and import activity, a structural characteristic shaped by global trade cycles, vessel rotation schedules, and container repositioning patterns.

The empirical analysis demonstrated that the proposed model consistently outperformed benchmark approaches including SARIMA and NeuralProphet, achieving lower error metrics across MAE, RMSE, and MAPE for both export and import throughput. Monthly error trajectories further confirmed the model’s advantage, particularly in periods marked by heightened operational volatility or seasonal fluctuations. The results underscore the importance of jointly modeling correlated logistics flows and incorporating exogenous economic indicators when forecasting port-level throughput.

Beyond predictive accuracy, this study advances methodological clarity for maritime forecasting by applying a structured encoder-decoder LSTM with multi-horizon output generation. The model integrates log-transformation, seasonal encodings, and exogenous indicators such as exchange rates and industrial production indices, enabling it to capture macroeconomic and seasonal signals that govern container throughput. From an applied perspective, the findings highlight the value of data-driven forecasting tools for strategic port planning and operational decision support, offering a scalable and update-ready forecasting foundation that adapts to changing macroeconomic and logistics conditions. In sum, this research highlights the practical and theoretical importance of jointly modeling bilateral trade throughput using advanced recurrent architectures, contributing a reliable forecasting baseline for data-driven port operations and maritime policy analysis.

6.2 Limitations and future research directions

While the proposed M-LSTM model demonstrated strong forecasting performance for container throughput at Busan Port, several limitations remain. First, the empirical analysis was limited to a single case study. Because operational characteristics and cargo flow dynamics vary across ports, future work should extend the analysis to additional domestic and international ports to assess generalizability.

Second, this study highlights the structural advantages of M-LSTM modeling but does not provide a direct comparison with univariate LSTM models. Future work should conduct such comparisons to quantitatively assess the effect of interdependence learning.

Third, this study evaluated the model mainly in terms of predictive accuracy, without directly linking forecasts to operational decision-making. Future research could integrate the framework with decision support or digital-twin systems to enable real-time planning and policy evaluation, thereby enhancing its practical utility for data-driven port management.