Dynamic Modeling of Bilateral Energy Synergy: A Data-Driven Adaptive Index for China–Korea Hydrogen System Coupling Assessment

Abstract

The development of cross-border hydrogen energy value chains involves complex interactions between technological, regulatory, and logistical subsystems. Static assessment models often fail to capture the dynamic response of these coupled systems to external perturbations. This study addresses this gap by proposing the Dual Carbon Cooperation Index (DCCI), a data-driven framework designed to quantify the synergy efficiency of the China–Korea hydrogen ecosystem. We construct a dynamic state estimation model integrating three coupled dimensions—Technology Synergy, Regulatory Alignment, and Supply Chain Resilience—utilizing an adaptive weighting algorithm (Triple Dynamic Response). Based on multi-source heterogeneous data (2020–2024), the model employs Natural Language Processing (NLP) for vectorizing unstructured regulatory texts and incorporates an exogenous signal detection mechanism (GPR). Empirical results reveal that the ecosystem’s composite synergy score recovered from 0.38 to 0.50, driven by robust supply chain resilience but constrained by high impedance in technological transfer protocols. Crucially, the novel dynamic weighting algorithm significantly reduces state estimation error during high-volatility periods compared to static linear models, as validated by bootstrapping analysis (1000 resamples). The study provides a quantitative engineering tool for monitoring ecosystem coupling stability and proposes a technical roadmap for reducing system constraints through secure IP data architectures and synchronized standard protocols.

1. Introduction

The transition to low-carbon energy systems involves complex cross-border interactions subject to non-linear external perturbations [1,2]. In the context of the China–Korea hydrogen energy ecosystem, complementary technical capabilities [3,4]—specifically China’s dominance in electrolyzer manufacturing (60% of global capacity) and hydrogen demand [5], coupled with South Korea’s leadership in fuel cell applications and hydrogen city operations [6]—are theoretically synergistic. Recent advancements in hybrid energy conversion technologies [7] and integrated renewable hydrogen supply systems utilizing waste heat [8] have further demonstrated the potential for enhanced system efficiency and sustainability.

Yet actual system coupling is often disrupted by non-linear external perturbations (e.g., geopolitical fluctuations like the U.S. Inflation Reduction Act, inconsistent technical standards, or intellectual property barriers). However, a critical limitation exists in current assessment methodologies. Traditional energy security and cooperation indices, such as the IEA’s Hydrogen Policy Database or the World Energy Council’s Energy Security Index, predominantly rely on static linear aggregation [9]. While suitable for stable environments, these static frameworks fail to capture system volatility under non-linear external perturbations.

A pertinent example is the global energy crisis triggered by the geopolitical turbulence of 2022. During this period, cascading supply chain disruptions forced a paradigm shift where system stability became more critical than cost efficiency. Static models, with their fixed weighting schemes, cannot reflect this real-time reordering of system priorities (e.g., the sudden need to value ‘Supply Chain Resilience’ over ‘Technology Synergy’), leading to significant estimation latency and a failure to signal emerging risks.

Beyond this lack of dynamic adaptability, existing frameworks suffer from a structural scope mismatch. For instance, the China Securities Hydrogen Index focuses primarily on market value, while the China Hydrogen Development Index assesses domestic industrial foundations. These prevailing energy security indices predominantly act as national ‘health checks’ rather than evaluating the interfacial efficiency of cross-border coupling [10,11]. They fail to quantify the specific ‘system impedance’—such as regulatory misalignment or IP friction—that occurs specifically at the bilateral interface, nor do they form a closed-loop analysis framework of “technology-policy-supply chain”. Furthermore, current methodologies often analyze subsystems in isolation, treating trade flows, technological outputs, and policy documents as separate silos. This compartmentalized approach overlooks the cross-domain cascading effects inherent to the hydrogen value chain, where a regulatory bottleneck can instantaneously paralyze technological transfer regardless of economic viability.

Consequently, a unified framework capable of ingesting and correlating these heterogeneous data streams is urgently required. To bridge these gaps, this study proposes the Dual Carbon Cooperation Index (DCCI), which advances current energy system assessment methodologies through three core innovations.

First, distinct from static linear indices, we introduce a “Triple Dynamic Response” algorithm that employs an adaptive gain-scheduling mechanism to eliminate estimation latency, capturing the evolving nature of bilateral cooperation during geopolitical fluctuations. Second, we transcend siloed analysis by synthesizing heterogeneous data streams (NLP-vectorized regulatory texts, patent decay rates, and trade flows) to quantify non-financial friction points, thereby integrating technical feasibility, institutional consistency, and material circulation. Third, this research establishes the first empirical quantification of the Sino–Korean hydrogen ecosystem’s synergy efficiency, providing a replicable engineering tool for diagnosing stability in transnational low-carbon value chains.

Our contributions concentrate on the methodological advancement of energy system assessment: first, we introduce a dynamic state estimation algorithm that integrates heterogeneous data streams (patents, trade flow, text vectors). Unlike static linear aggregation, our model employs a feedback control loop where weights dynamically adapt to detected risk signals (GPR > 0.5) and performance feedback; second, we operationalize abstract system interactions into measurable engineering metrics, applying exponential decay functions to quantify the timeliness of technological knowledge transfer; and third, we validate the model’s robustness through rigorous sensitivity analysis and Monte Carlo simulations, demonstrating its superior capability in capturing system volatility compared to traditional static metrics.

The paper is structured as follows: Section 2 reviews relevant literature; Section 3 details the DCCI methodology; Section 4 presents empirical results, including a critical sensitivity analysis; Section 5 discusses implications; and Section 6 concludes.

2. Literature Review

2.1. Quantitative Assessment Models for Energy Ecosystems

The evaluation of cross-border energy systems has transitioned from qualitative descriptions to quantitative modeling. Early approaches relied on static trade volume statistics [12]. Recent methodologies often employ multi-criteria decision analysis (MCDA) and composite indicators to model complex system interactions [13,14]. Other studies introduce rigorous multi-criteria frameworks designed to quantify the state variables of coupled bilateral systems [15,16]. Optimization models have been applied to assess energy security and environmental sustainability [17], focusing on maximizing system efficiency under constraints. However, existing linear aggregation models often lack dynamic adaptability, failing to account for the non-linear impact of exogenous shocks on system parameters [18]. Prevailing assessment models are limited by a static parameter configuration, failing to reflect the time-varying nature of system coupling priorities [19,20]. This study introduces a dynamic weighting algorithm to minimize this estimation error.

2.2. Hydrogen System Dynamics in Northeast Asia

Research on Northeast Asian energy systems has increasingly focused on the technical and logistical challenges inherent in regional decarbonization trajectories [21,22]. Studies analyzing clean energy transitions, including large-scale hydrogen infrastructure planning, often highlight persistent geopolitical constraints on cross-regional material flux and the reliance on foundational energy trading metrics [23], alongside enduring institutional barriers [21]. However, the specific quantification of system dynamics within the Sino–Korean hydrogen ecosystem remains critically underdeveloped. While research addresses broader technological and infrastructure challenges in the region [24,25,26], few models explicitly quantify the bilateral coupling efficiency. Existing quantitative work predominantly concentrates on isolated trade flows and value chain analysis [27,28], resulting in a “modeling gap” where the time-variant latency in standard synchronization and IP protocol adherence is underrepresented in overall system performance evaluations.

2.3. System Coupling and State Estimation

Global carbon-neutrality constraints have significantly modulated the boundary conditions for international energy ecosystem integration [29,30,31]. Recent studies model these interactions as coupled dynamic systems, quantifying emission reduction efficiencies through Belt and Road Initiative infrastructure projects [32,33] and analyzing the topology of cooperative innovation networks [34]. Regulatory synchronization parameters are increasingly treated as critical control variables within these system models [35,36,37]. Theoretical frameworks have evolved from foundational game-theoretic stability analysis [38,39,40] to complex adaptive system models tailored to specific energy domains [41,42,43]. However, a gap persists in the development of robust state estimation frameworks capable of quantifying the coupling efficiency of bilateral hydrogen subsystems under stochastic external perturbations. Our study builds on these by proposing a data-driven state estimation approach, treating bilateral ecosystem synergy as an observable state variable derived from multi-dimensional sensor data (patents, texts, trade flows).

3. Methodology

3.1. DCCI Framework Modeling

To operationalize the complex dynamics of the China–Korea hydrogen ecosystem, the DCCI framework adopts a multi-dimensional structure grounded in Socio-technical Transitions Theory [44,45], Systems Engineering principles [46] and established empirical index construction protocols [12,13,14,17]. These frameworks collectively emphasize that successful energy transitions require not only quantitative aggregation but also a collaborative configuration of technological diffusion, institutional adaptation, and material resource flows.

Consistent with the ESG (Environmental, Social, and Governance) application logic in energy systems, our dimension classification answers three fundamental engineering questions: “whether it can be done” (Technical Feasibility), “whether it is allowed to be done” (Institutional Legitimacy), and “whether there are conditions to do it” (Material Foundation). Based on this theoretical logic, the DCCI constructs a closed-loop evaluation system comprising three coupled subsystems:

• Technology Synergy (TS): Represents the technical feasibility dimension. It encompasses the efficiency of knowledge transfer and technical interoperability (e.g., electrolyzers, fuel cells), quantifying the system’s innovation capability.
• Regulatory Alignment (RA): Represents the institutional guarantee dimension (formerly Policy Coupling). It captures the synchronization of technical standards, safety protocols, and subsidy mechanisms to reduce system impedance and ensure regulatory legitimacy.
• Supply Chain Resilience (SCR): Represents the material foundation dimension. It quantifies the robustness of material flows, redundancy, and emergency response capabilities, ensuring the physical continuity of cooperation.

This tripartite structure forms a dynamic feedback loop: technology drives policy development, policy enables supply chain resilience, and supply chain performance provides feedback for technological and policy improvements. The composite index is calculated as a dynamically weighted sum:

$$DCC{I}_t={\alpha }_t\times T{S}_t+{\beta }_t\times R{A}_t+{\gamma }_t\times SC{R}_t$$

where ${\alpha }_t,{\beta }_t,{\gamma }_t$ are time-variant parameters determined by the adaptive algorithm ($\sum =1$).

3.2. Model Assumptions

To ensure the validity of the DCCI framework and justify the parameter calibration detailed in Section 3, this study is grounded in the following five core assumptions:

• Patent-Based Innovation Proxy: It is assumed that joint patents containing specific keywords (e.g., “hydrogen energy”, “fuel cell”) and bilateral country codes (CN/KR) serve as a valid proxy for cross-border technology transfer. An exponential decay function ($\lambda =0.05$) is applied based on the premise that the relevance of technological knowledge diminishes over a 2–3-year cycle in high-velocity industries.
• Semantic Policy Alignment: The cosine similarity of policy documents, calculated via Natural Language Processing (NLP), is assumed to quantitatively reflect regulatory consistency. We assume that high-dimensional vector proximity correlates with reduced institutional barriers, provided that linguistic biases (e.g., Korean honorifics) are corrected.
• Trade-Based Resilience Proxy: Cross-border trade volumes of specific HS codes (280440, 731100, 850164) act as a proxy for supply chain material foundations. The operational resilience of this chain is assumed to be captured by transport safety metrics (e.g., accident-free days), reflecting the system’s physical stability.
• Validity of Geopolitical Signals: The Geopolitical Risk Index (GPR), developed by Caldara and Iacoviello (Federal Reserve Board), is assumed to be a reliable exogenous indicator of the macro-environment. To ensure compatibility with the DCCI framework, the raw GPR values are min–max normalized to a [0, 1] range. The critical threshold of 0.5 is premised on historical volatility analysis during the 2020–2024 period (normalized range: 0.42–0.58), where values above this relative mean indicate structural instability and trigger the model’s adaptive weighting mechanism.
• Algorithmic Stability: It is assumed that a rolling adjustment step of $\delta =0.05$ provides an optimal balance between system responsiveness and stability, preventing the dynamic weighting algorithm from overreacting to minor data noise.

3.3. Data Sources and Preprocessing

3.3.1. Data Sources

To construct the index, we integrated multi-source heterogeneous data spanning the period 2020–2024. The specific data categories, indicators, and sources are detailed in

Table 1. Data Sources and Acquisition Protocols.

Data Category	Indicators and Keywords/Codes	Source Database
Patent Data	Keywords: “hydrogen energy”, “fuel cell”, “electrolyzer”	WIPO PATENTSCOPE [47]; IncoPat Global Database
	Filter: Joint Filing (CN/KR), Patent Cooperation Treaty (PCT)
Policy Texts	42 Core Documents (e.g., “Hydrogen Economy Roadmap”)	State Council (CN) [48]; MOTIE (KR) [6] Gov Portals
	Coverage: National & Regional Plans (2020–2024)
Trade Data	HS Codes: 280440 (Hydrogen), 731100 (Storage), 850164 (Fuel Cells)	UN Comtrade [49]; China NBS [50]; Korea KESIS [51]
	Metrics: Production, consumption, and reserve data
Geopolitical Risk (GPR)	Annual GPR values (2020–2024)	Caldara and Iacoviello (Federal Reserve Board) [52]
	Range: 0.42–0.58
Text Analysis Tool	Cosine similarity calculation; validated via bilingual keyword counts	Sentence-Transformers (open-source NLP) [53]

.

3.3.2. Gap Filling and Standardization

To ensure temporal consistency across all years (2020–2024), we implemented a standardized data collection protocol. For patent data, the same keywords and exclusion criteria were applied to the 2024 WIPO database. For policy texts, the Sentence-Transformers model (all-MiniLM-L6-v2) was used consistently, with manual correction of Korean honorific bias applied to reduce semantic error. For trade data, HS codes and a fixed exchange rate (1 USD ≈ 7.2 CNY) were used for all currency conversions. Missing high-frequency data points (<5%) were imputed using linear interpolation constrained by seasonal adjustment factors. Given that the raw GPR is an absolute index, we applied Min-Max normalization based on its historical variance from 2020 to 2024. The 0.5 threshold represents the 80th percentile of observed risks during this period, signifying a transition from ‘latent’ to ‘active’ systemic threat, as supported by the threat perception framework in [54].

3.3.3. Quantification of External Geopolitical Risk

To capture the non-linear impact of the macro-environment on bilateral cooperation, this study incorporates the Geopolitical Risk Index (GPR) sourced from the Federal Reserve Board [52]. Unlike internal system variables, the GPR serves as an exogenous stress signal.

• Data Authority and Applicability: The GPR is a text-based index that captures geopolitical tensions by monitoring newspaper coverage. We focus on sub-indices related to Geopolitical Threats (GPT) and Geopolitical Acts (GPA), which are particularly relevant to the China–Korea energy corridor.
• Threshold Calibration: A critical risk threshold of 0.5 was established to trigger the model’s adaptive mechanism. This value is empirically grounded in the Federal Reserve Board’s guidance, which classifies values above 0.5 as “moderate to high risk” necessitating policy adjustments. Furthermore, Bueno de Mesquita and Smith (2022) demonstrate that risk indices exceeding 0.5 typically mark the tipping point where decision-makers perceive significant threats to political survival, thereby triggering adaptive responses in cooperation strategies [54].

3.3.4. Data Engineering and Preprocessing Pipeline

The empirical validation on the China–Korea hydrogen ecosystem (2020–2024) utilizes a multi-source data ingestion pipeline designed for traceability and reliability. The data acquisition and preprocessing workflow is structured as follows:

• Patent Data Mining: Intellectual property data were extracted quarterly via Python 3.13.0 scripts (crawler/patent_spider.py) from WIPO PATENTSCOPE [47], utilizing specific keywords and country codes (CN/KR). API rate limits (429) were managed through an exponential backoff algorithm to ensure data completeness.
• Unstructured Text Vectorization: Regulatory documents were batch-downloaded from official government portals, including China’s State Council [48] and Korea’s MOTIE [6]. Scanned PDF documents underwent optical character recognition (OCR) processing using pytesseract. To mitigate linguistic bias (e.g., Korean honorifics), we applied a human-in-the-loop validation protocol, manually correcting 42 documents to reduce the error rate to 2–3% [53]. Subsequently, the Sentence-BERT model was employed to generate high-dimensional vectors for text documents. The cosine similarity between vector pairs (A, B) was calculated to quantify Regulatory Alignment: $\mathrm{S}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}={\displaystyle \frac{\mathrm{A}\cdot \mathrm{B}}{\left|\right|\mathrm{A}\left|\right|\times \left|\right|\mathrm{B}\left|\right|}}$
• Trade Flow Analysis: Material flux data were extracted monthly from UN Comtrade [49] and the IEA Hydrogen Equipment Trade Database [55] for relevant HS codes: 280440 (hydrogen), 731100 (storage vessels), and 850164 (fuel cells).
• Exogenous Signal Detection: The Geopolitical Risk Index (GPR), sourced from the Federal Reserve Board [52], served as the external perturbation signal input, with annual values ranging from 0.42 to 0.58 during the observation period.

Data cleaning and alignment were performed using pandas, involving deduplication, unit standardization (to million USD), and monthly-to-annual aggregation. A three-layer validation protocol was implemented: (a) internal consistency checks (>20% deviation from historical data flagged for review), (b) external benchmarking against national statistical yearbooks [50,51], and (c) OCR quality verification. Missing data points in high-frequency supply chain time series were imputed using linear interpolation with a constraint of <5% fluctuation. The full raw dataset and processing code are archived at the China-Korea Hydrogen Industry Alliance Data Repository, and key code snippets are provided in Appendix A to ensure reproducibility.

To visualize the integration logic of these heterogeneous data streams, the overall methodological architecture is presented in Figure 1. This flowchart delineates the end-to-end processing pipeline, capturing the transformation from raw data acquisition (Left: Patents, Policy Texts, Trade Flows) to core processing (Middle: NLP Vectorization, Adaptive Weighting) and final system state assessment (Right). Crucially, the diagram explicitly illustrates the ‘Triple Dynamic Response’ feedback mechanism, where performance outputs and external risk signals (GPR) actively recalibrate the system parameters, ensuring the model remains responsive to real-time perturbations.

3.4. Mathematical Modeling of System Dimensions

The system state is defined by 12 normalized indicators (

Table 2. System Indicator Definitions and Calculation Logic.

Subsystem	Indicator Variable	Initial Weight	Mathematical Model/Calculation Logic
Technology Synergy (Tech)	1. Patent Sharing Rate	0.12	Exponentially decayed ratio of joint patents to total patents
	2. Tech Transfer Efficiency	0.10	Ratio of licensing events to joint R&D projects
	3. Standard Synchronization	0.08	Cosine similarity of technical standard document vectors (NLP) [53]
	4. R&D Intensity	0.10	Normalized joint funding volume
Regulatory Alignment (Policy)	5. Regulatory Vector Similarity	0.09	Cosine similarity of policy document vectors (NLP) [53]
	6. Safety Protocol Overlap	0.07	Z-score standardized overlapping clauses in safety codes
	7. Subsidy Correlation	0.08	Inverse difference of subsidy ratios: $-1\times (R_{cn}-R_{kr})$
	8. Institutional Compatibility	0.06	Normalized score of bilateral technical mechanisms
Supply Chain Resilience (Chain)	9. Node Diversity	0.08	Ratio of cross-border nodes to total nodes
	10. Transport Reliability	0.07	Composite score: $(\mathrm{D}\mathrm{r}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{s}\times 0.3+\mathrm{S}\mathrm{a}\mathrm{f}\mathrm{e}\mathrm{D}\mathrm{a}\mathrm{y}\mathrm{s}\times 0.4+\mathrm{C}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}\times 0.3)/\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}.\mathrm{C}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}.$[56]
	11. Buffer Adequacy	0.07	Strategic reserve volume/90-day consumption rate
	12. Response Latency	0.08	Emergency drill frequency/Disruption events

Note 1: The normalization coefficient is defined as the sum of the theoretical maximum scores of the three weighted components ($0.3\times 1.0+0.4\times 1.0+0.3\times 1.0=1.0$), ensuring the final index falls within the 0–1 range.

), selected based on empirical frameworks for energy cooperation evaluation [17]. To capture the time-sensitivity of technological innovation, we applied an exponential decay function to the Patent Sharing Rate:

$$P_{adjusted}=P_{raw}\times e^{-\lambda t}$$

where $\lambda =0.05$ (calibrated via cross-validation) and $t$ is the age of the patent in years.

3.5. DCCI Architecture and Adaptive Weighting Algorithm

3.5.1. Core Logic: The Three-Stage Closed Loop

To address the latency inherent in static indices, the DCCI operates on a “Three-Stage Closed Loop” mechanism:

• Dimension Integration: Converting unstructured policy texts into computable vectors via NLP, combined with patent citation intensity (Tech) and trade flow intensity (Chain) to form the basic indicator system.
• Dynamic Feedback: Utilizing the adaptive weighting algorithm to adjust dimension weights (${\alpha }_t,{\beta }_t,{\gamma }_t$) in real-time.
• Collaborative Evaluation: Generating a composite score (0–100) that classifies synergy levels into “Low” (0–30), “Medium” (31–60), and “High” (61–100).

The calculation proceeds in four steps: (1) Standardization of basic indicators (Z-scores); (2) Initialization of weights based on historical baselines; (3) Adaptive Adjustment via feedback loop errors; and (4) Normalization of the final score. Specifically, the Normalized Impact Score ($S_{norm}$) for identifying system bottlenecks is calculated using a Min–Max normalization followed by weighted synthesis. The formula is defined as:

$$S_{norm}={\displaystyle \frac{X_{raw}-X_{min}}{X_{max}-X_{min}}}\times W_d$$

where $X_{raw}$ is the raw indicator value (e.g., patent count), $X_{min/max}$ are the boundary values derived from the 2020–2024 dataset, and $W_d$ is the dynamic weight of the corresponding dimension. For instance, the ‘IP Barriers’ score (0.276) cited in the results is derived from a raw WIPO score of 0.92 weighted by the real-time Technology factor (${\alpha }_t$).

3.5.2. Initial Weight Calibration (Data-Driven Basis)

A critical innovation of this study is that the initial parameters are not arbitrary but calibrated against historical empirical data. As visualized in Figure 2, the initial weights (${\alpha }_0=0.4,{\beta }_0=0.3,{\gamma }_0=0.3$) are derived from the distribution of 73 China–Korea hydrogen cooperation projects recorded between 2018 and 2020 [57,58,59]: a. Technology-Oriented (41%): 30 projects focused on R&D pilots and joint labs. b. Policy/Institutional (28%): 20 projects focused on standards alignment and MoUs. c. Supply Chain (31%): 23 projects focused on infrastructure and logistics.

To ensure model stability, these ratios were rounded to ${\alpha }_0=0.4$ (Tech) and ${\beta }_0={\gamma }_0=0.3$ (Policy/Chain). This “Technology-Led” initialization aligns with domain knowledge consistency checks [57,58,59] and was further validated by expert interviews at the 2023 China-Korea Hydrogen Industry Forum [59].

3.5.3. Dynamic Adjustment Logic

While initialized with historical data, the weights are dynamically updated using a gain scheduling mechanism based on two control signals:

• Perturbation Signal (Normalized GPR > 0.5): When the signal exceeds the threshold (0.5, representing a high-risk state based on [54]), the system automatically prioritizes stability. The algorithm increases the Supply Chain gain ($\gamma$) by 0.05 to reflect the structural shift towards resilience.
• Performance Feedback Signal: If the Technology subsystem shows positive gradients ($\Delta TS>0$) for two consecutive periods (matching the 2-year R&D cycle), the algorithm increases the Technology gain ($\alpha$) by 0.02 to model the momentum effect.

This logic is implemented in the Python function dynamic_weight_adjustment (Appendix A.5). Unlike static approaches, this framework minimizes system estimation error by actively responding to state changes. The specific parameter settings and their theoretical underpinnings are detailed in

Table 3. Key Model Parameters and Calibration Evidence.

Parameter	Value	Calibration Basis and Rationale
Initial weights ($\alpha ,\beta ,\gamma$)	0.4, 0.3, 0.3	Mirrors 2018–2020 project mix (Tech 41%, Policy 28%, Chain 31%) and expert interviews [57,58,59].
Technology decay rate ($\lambda$)	0.05	Leave-one-out cross-validation (2015–2022 patents). Minimizes MSE (0.008) and retains 61% of 3-year contribution (See Section 3.2 Assumption 1).
GPR Trigger Increment ($k$)	0.10	Simulated GPR ranges (0.42–0.58). Reduces DCCI variance by 11% without breaching weight constraints [52].
Rolling Adjustment Step ($\delta$)	0.05	5-period simulations balance timeliness (leads by 1 period) and stability (amplitude < 0.12).
Tech Decline Penalty ($p$)	0.05	Monte Carlo simulations: 0.03–0.05 DCCI drop for “2q Tech decline + mild GPR rise” ensures timely alerts.

.

To further validate the robustness of these calibrated parameters, Figure 2 illustrates the convergence of parameter optimization. The GPRd search results demonstrate that the chosen values minimize the mean squared error (MSE) between the model output and the validation dataset, ensuring the stability of the dynamic weighting mechanism under varying external conditions.

4. Results

4.1. System State Analysis

The application of the DCCI algorithm to the China–Korea hydrogen ecosystem (2020–2024) reveals a non-linear recovery trajectory in system synergy. The composite index ($DCC{I}_t$) rose from 0.38 in 2020 to 0.50 in 2024, exhibiting a Compound Annual Growth Rate (CAGR) of 7.1%. While this indicates a transition from a “weak coupling” to a “moderate coupling” state, the score remains below the critical stability threshold of 0.60.

The temporal evolution of the system, illustrated in Figure 3, highlights a structural asymmetry among subsystems:

• Supply Chain Resilience (SCR): This subsystem acts as the primary stabilizer, with its state score surging to 0.71 in 2024. This performance is highly correlated (r = 0.89, p < 0.01) with external benchmarks such as the IEA’s East Asia Logistics Resilience Index [5]. The contribution analysis (Figure 4) confirms that SCR accounted for 43% of the total system synergy in 2024, driven by the expansion of cross-border material flux and redundant storage capacities.
• Technology Synergy (TS): Conversely, the Technology subsystem functions as a limiting factor, lagging significantly with a score of 0.35. The trajectory shows a dampening effect, where initial gains in 2021 were offset by the stagnation in standard alignment protocols [60].
• Regulatory Alignment (RA): This subsystem demonstrates a converging trend (Score 0.50), reflecting a gradual synchronization of policy vectors exceeding the IEA global policy maturity benchmark of 0.45 [55], though residual divergence in subsidy mechanisms persists.

To further elucidate the internal mechanics driving the composite score’s trajectory shown in Figure 3, we decomposed the index to analyze the relative weight and contribution of each subsystem. This structural breakdown, visualized in Figure 4, reveals the shifting dominance of specific drivers over time. Specifically, Supply Chain Resilience has emerged as the dominant vector, contributing 43% to the total system synergy score in 2024 (up from 39% in 2020). This increasing contribution is a direct result of the adaptive algorithm amplifying the weight of the supply chain dimension ($\gamma$) in response to elevated geopolitical risk signals. Conversely, the contribution of Technology Synergy remains suppressed (28%), reflecting the persistent bottlenecks in technical interoperability.

4.2. Subsystem Performance Heatmap

To diagnose the root causes of system impedance, we decomposed the subsystem scores into 12 secondary indicators. Figure 5 presents the heatmap of normalized indicator values, revealing specific “cold spots” (constraints) and “hot spots” (drivers).

• High-Gain Indicators (Drivers): The Transport Reliability metric recorded a near-optimal score of 0.95 in 2024. However, interpretation requires distinguishing between input and outcome variables: this score is heavily weighted by a 58% year-on-year increase in safety drill frequency (Input) rather than solely by zero-incident rates (Outcome). Similarly, Node Diversity improved consistently (0.74), validating the system’s robustness against single-point failures in the supply network.
• High-Impedance Indicators (Constraints): The Standard Synchronization metric remains critically low (0.05), identifying the lack of mutual recognition for 17 key hydrogen fueling protocols as a primary blockage [60]. Furthermore, Patent Sharing Rate (0.32) exhibits a slow time-constant, indicating high friction in intellectual property transfer. Operational inefficiencies are also evident in human capital flows, where visa processing latencies have resulted in a talent arrival rate of less than 60% for joint projects [61,62]. The Regulatory Vector Similarity (0.55) has improved but remains constrained by the misalignment of R&D subsidy calculations (Indicator 7).

4.3. Algorithm Validation and Comparative Benchmarking

To rigorously validate the robustness of the DCCI framework, we utilized a dual-validation strategy: (1) Internal Mechanism Validation, comparing the dynamic algorithm against a static baseline to verify the efficacy of the weighting logic; and (2) External Quantitative Benchmarking, comparing DCCI against established alternative indices to prove its superior accuracy and responsiveness.

Internal Validation: Dynamic vs. Static Weighting

We first validated the “Triple Dynamic Response” mechanism by simulating two scenarios: a. Scenario A (Dynamic Model): The proposed DCCI with adaptive weights triggered by external risk and performance feedback. b. Scenario B (Static Baseline): A traditional linear model with fixed weights ($\alpha =\beta =\gamma =0.33$).

Weight Calibration Logic: The dynamic triggers in Scenario A were systematically calibrated to match industrial realities [13]: the Tech Trigger ($\delta =0.02$) reflects the 1.5–2 year R&D iteration cycle of hydrogen technologies, while the Risk Trigger ($k=0.10$) was determined via Monte Carlo simulation to maximize variance reduction.

Table 4. DCCI Scores Comparison: Dynamic vs. Static Weighting (2020–2024).

Year	GPR Value	Dynamic Weighting (Scenario A)	Static Weighting (Scenario B)	Score Difference (A–B)	Key Weight Adjustment (Scenario A)
2020	0.42	0.38	0.36	+0.02	Initial weights ($\alpha =0.4,\beta =0.3,\gamma =0.3$)
2021	0.45	0.41	0.40	+0.01	Performance trigger: Tech growth, $\alpha$ increased to 0.42
2022	0.51	0.45	0.43	+0.02	Risk trigger: GPR > 0.5, $\gamma$ increased to 0.35; $\alpha =0.37,\beta =0.28$
2023	0.55	0.47	0.47	0.00	Stable weights ($\alpha =0.37,\beta =0.28,\gamma =0.35$)
2024	0.58	0.50	0.50	0.00	Stable weights ($\alpha =0.37,\beta =0.28,\gamma =0.35$)

presents the simulation results. While the Static model (Scenario B) remained unresponsive during the 2022 geopolitical shock (GPR = 0.51), the Dynamic model (Scenario A) successfully triggered a risk response (increasing $\gamma$ for supply chain resilience), resulting in a score divergence of +0.02. This confirms that the dynamic mechanism effectively captures non-linear system fluctuations that static models miss.

The dynamic nature of the DCCI framework allows for real-time recalibration of system parameters, as detailed below:

• Response to Risk Signal (2022): When the Geopolitical Risk Index (GPR) breached the critical threshold of 0.5 (GPR = 0.51), the dynamic algorithm automatically triggered the Gain Scheduling mechanism, increasing the Supply Chain weight ($\gamma$) by 0.05. This adjustment resulted in a corrected state estimate of 0.45 (vs. 0.43 in the static model), accurately reflecting the system’s strategic shift towards resilience buffering.
• Response to Performance Feedback (2021): In response to consecutive positive gradients in technology output ($\Delta TS>0$), the algorithm amplified the Technology gain ($\alpha$) to 0.42, capturing the momentum of early-stage pilot projects.
• Robustness: Bootstrapping analysis (1000 resamples) and sensitivity tests on the threshold parameter (0.5 ± 0.02) showed that the output deviation remained within ±1.5%, confirming algorithmic stability.

Figure 6 contrasts the state estimation trajectories of both models. The dynamic algorithm demonstrates higher fidelity in capturing system responses to external perturbations. Specifically, the divergence between the two trajectories becomes most pronounced during the high-volatility period of 2022. While the Static Model suggests a linear, unperturbed growth path (0.43), the Dynamic Model output (0.45) exhibits a necessary state correction. This inflection reflects the system’s absorption of the geopolitical shock (GPR > 0.5), where the Gain Scheduling mechanism effectively reallocated weight from the high-impedance Technology dimension to the robust Supply Chain dimension. This dynamic correction prevents the estimation bias inherent in static models, which fail to account for the strategic shift towards resilience buffering during crises. Conversely, in 2021, the algorithm correctly amplified the Technology gain ($\alpha$) to 0.42 in response to consecutive positive gradients ($\Delta TS>0$), capturing the momentum of early-stage pilot projects.

Sensitivity testing further confirms algorithmic robustness. We performed a localized perturbation analysis on the critical GPR trigger threshold, varying it within the interval [0.48, 0.52]. The results indicate that the DCCI composite score exhibits high stability, with a maximum output deviation of only ±1.5%. This implies that the framework functions as a stable low-pass filter, ignoring minor noise in risk signals while responding robustly to structural shifts. Additionally, varying the performance feedback cycle (e.g., adjusting the look-back window from 2 years to 1 or 3 years) resulted in a marginal state deviation of less than 2%. This structural stability confirms that the ‘Triple Dynamic Response’ mechanism provides a reliable, noise-filtered estimation of ecosystem synergy, making it suitable for long-term engineering monitoring and strategic planning.

4.4. Quantitative Benchmarking Against Alternative Architectures

To address the limitations of purely qualitative comparisons and robustly validate the DCCI framework, we conducted a quantitative benchmark analysis against two prevailing alternative modeling schemes: a. China Hydrogen Development Index (CHDI): Represents the “Industrial Comprehensive” model, focusing on domestic industrial scale and innovation metrics without cross-border weighting. b. Traditional Cooperation Index (TCI): Represents the “Static Two-Dimensional” model, which linearly aggregates trade volume and technology patents without dynamic risk adjustment.

We evaluated these models against the DCCI using three performance metrics: Correlation Coefficient ($r$) with actual cooperation project counts (ground truth), Mean Absolute Error (MAE) in capturing trend turning points, and Dynamic Response Speed (lag time in quarters).

As evidenced in

Table 5. Quantitative Performance Comparison of Modeling Architectures.

Metric	DCCI (Proposed)	CHDI (Industrial)	TCI (Static)
Correlation with Project Trends ($r$)	0.89	0.63	0.72
Mean Absolute Error (MAE)	3.21	7.85	5.62
Response Latency	1 Quarter	4 Quarters	2 Quarters

, the DCCI significantly outperforms alternative models. The static TCI model exhibits a correlation of only 0.72 due to its failure to account for policy friction, while the domestic-focused CHDI (0.63) correlates poorly with cross-border synergy dynamics. Crucially, the DCCI achieves a response latency of just 1 quarter, compared to 4 quarters for the CHDI, validating that the “Triple Dynamic Response” mechanism effectively minimizes estimation lag.

5. Discussion

5.1. Technical Constraints Identification

The DCCI diagnostic reveals a critical structural imbalance: the ecosystem is characterized by robust material flows (Supply Chain Resilience) but high impedance in knowledge transfer (Technology Synergy). To rigorously quantify the determinants of this technological lag, we conducted a root-cause analysis based on the normalized scores of secondary indicators and expert-validated impact assessments. The analysis identifies five primary system constraints inhibiting synergy, as visualized in Figure 7:

• Intellectual Property (IP) Data Security (Impact Score 0.92): The lack of secure, standardized data exchange protocols constitutes the most severe constraint. Industrial stakeholders, particularly in the fuel cell sector, exhibit reluctance to share core proprietary data (e.g., MEA coating specifications) due to the absence of a trusted third-party custody mechanism. This has resulted in a high friction coefficient for technology transfer, limiting cross-border licensing efficiency.
• Protocol Latency (Impact Score 0.85): Technical interoperability is severely hampered by the lack of mutual recognition for 17 key technical standards, specifically regarding hydrogen refueling protocols and high-pressure storage vessel testing. This regulatory misalignment creates significant interface mismatches, necessitating redundant certification processes that delay project deployment by an average of 6–12 months.
• Funding Vector Mismatch (Impact Score 0.78): A divergence in R&D subsidy mechanisms reduces the viability of joint projects. The asymmetry between tax-credit-based incentives in one jurisdiction and direct-subsidy models in the other creates a “funding gap” for bilateral pilot programs, discouraging collaborative investment in high-risk, early-stage technologies.
• Operational Inefficiency in Joint Laboratories (Impact Score 0.70): despite the establishment of bilateral research platforms, their operational output remains suboptimal. Data indicates that only 40% of established joint labs achieve their annual collaboration targets, primarily due to administrative redundancies and the lack of unified project management protocols.
• Human Capital Mobility Constraints (Impact Score 0.65): The physical flow of technical expertise is constrained by procedural latencies. Visa processing delays (averaging 3–4 months) have resulted in a talent arrival rate of less than 60% for scheduled joint research initiatives [59,60], directly impacting the continuity of long-term R&D projects.

5.2. System Optimization Strategies and Technical Roadmap

Based on the diagnostic results, the ecosystem requires structural optimization to reduce impedance in technology transfer while maintaining supply chain resilience. We propose a technical roadmap focusing on data interoperability, standard synchronization, and algorithmic monitoring (

Table 6. Optimization Strategies for Ecosystem Synergy.

Diagnostic Signal (S < 0.4)	Technical/Operational Intervention	Expected System Response	Verifiable Metric
Technology Latency (Score 0.35)	a. Protocol Synchronization: Accelerate alignment of 17 pending ISO-compatible standards. b. Secure IP Architecture: Deploy a tiered-access IP custody platform with third-party verification. c. Fast-Track R&D Nodes: Establish dedicated joint labs with expedited equipment clearance.	Increase Tech gain ($\alpha$) efficiency; Raise score to 0.42.	Standards Alignment Score; Patent Velocity
Regulatory Divergence (Score 0.50)	a. Subsidy Vector Alignment: Harmonize R&D credit calculations. b. Carbon Credit Interoperability: Pilot mutual recognition of maritime carbon allowances. c. Sandbox Testing: Joint pilot zones for experimental regulations [63].	Stabilize Regulatory Alignment ($\beta$); Reduce vector divergence.	Policy Similarity Vector
Resilience Risk (GPR Sensitivity)	a. Dynamic Buffering: Implement dynamic inventory management for emergency stockpiles [64]. b. Civil Logistics Coordination: Standardize protocols for hydrogen-powered emergency equipment [65]. c. Data Corridor: Establish a desensitized data sharing protocol for transport safety.	Maintain Chain robustness ($\gamma \ge 0.70$); Dampen perturbation shock.	Stockpile Sufficiency; Drill Frequency
Monitoring Latency (45 days)	a. Real-time API: Deploy the Bilingual DCCI Dashboard API. b. Automated Reporting: Integrate project data feeds.	Reduce feedback loop latency to < 7 days.	Data Update Frequency
Supply Chain Synergy (GPR > 0.5)	a. Establish a standardized system for China–South Korea hydrogen storage and transportation; b. Build transnational logistics hubs (e.g., China-South Korea Changchun International Cooperation Demonstration Zone); c. Share supply chain risk early warning data	Shorten data update lag to 7 days.	Incorporate DCCI performance indicators into project evaluation

).

Specific Implementation Note on Supply Chain: Given geopolitical sensitivities, we recommend focusing on a Civil Emergency Logistics Coordination mechanism. This would integrate hydrogen-powered emergency units (e.g., mobile power generators) into cross-border resilience assessments, enhancing humanitarian capabilities without triggering dual-use concerns [65].

5.3. Limitations and Future Work

While the DCCI framework offers a significant methodological advancement in quantifying cross-border energy synergy, several limitations intrinsic to the current modeling architecture warrant rigorous acknowledgment:

• Proxy Variable Latency and Noise: The reliance on proxy indicators for system resilience (e.g., safety drill frequency as a proxy for transport reliability) introduces a signal-to-noise ratio challenge. Although we applied normalization techniques, these input-based metrics may not fully capture outcome-based risks, potentially leading to an overestimation of system stability during low-frequency, high-impact events (black swan events). Future iterations will integrate real-time IoT sensor data from logistics nodes to replace static proxies with dynamic telemetry.
• NLP Vectorization Bias: The Sentence-BERT model utilized for regulatory alignment analysis, while robust, may contain residual linguistic bias (estimated at 2–3% variance) when processing context-specific legal terminology in Chinese and Korean. This semantic drift could affect the precision of the Regulatory Vector Similarity score. We propose fine-tuning a domain-specific Large Language Model (LLM) on a bilingual corpus of energy law to minimize this vectorization error.
• Heuristic Initialization Constraints: The initial weight parameters (${\alpha }_0,{\beta }_0,{\gamma }_0$) were derived from historical project distributions and expert heuristics. While the adaptive algorithm adjusts these weights dynamically, the starting state remains dependent on prior knowledge. Future research will employ Reinforcement Learning (RL) agents to autonomously optimize these initial parameters by simulating multi-year cooperation scenarios, thereby moving towards a fully unsupervised state estimation model.
• System Boundary Limitations: The current model focuses on bilateral interactions, treating global market variables (e.g., global hydrogen price fluctuations, third-party competition from Australia or the Middle East) as constant boundary conditions. Expanding the model to a multi-node network topology would allow for the assessment of how third-party perturbations propagate through the bilateral link.

6. Conclusions

This study establishes a quantitative, data-driven framework for monitoring the coupling efficiency of cross-border hydrogen ecosystems under stochastic external perturbations. By transitioning from static linear aggregation to a Triple Dynamic Response Algorithm, the proposed Dual Carbon Cooperation Index (DCCI) effectively captures the non-linear state transitions triggered by geopolitical risks and technological latencies.

Key empirical findings and methodological contributions include the following:

• System Trajectory and Asymmetry: The China–Korea hydrogen ecosystem exhibits a recovery trajectory, with the composite synergy score rising from 0.38 (2020) to 0.50 (2024) at a CAGR of 7.1%. However, a critical structural asymmetry persists: the system is stabilized by robust Supply Chain Resilience (Contribution: 43%) but severely damped by high impedance in Technology Synergy (Score: 0.35), specifically due to protocol mismatches in fuel cell standards and IP data security.
• Algorithmic Superiority: Comparative validation demonstrates that the dynamic weighting mechanism significantly reduces state estimation error. During the high-volatility period of 2022 (GPR > 0.5), the dynamic model correctly identified a state inflection point (Score 0.45), whereas the static model failed to account for the resilience buffering effect (Score 0.43). Sensitivity analysis confirms the algorithm’s stability, with output deviations remaining within ±1.5% under parameter perturbation.
• Engineering Implications: To optimize system synergy, we propose a technical roadmap focusing on protocol synchronization and digital trust architectures. Immediate priority should be given to establishing a secure, third-party-verified IP custody platform to lower the activation energy for technology transfer, alongside a dynamic inventory buffering mechanism to mitigate supply chain risks.

In conclusion, the DCCI framework provides energy policymakers and system engineers with a scalable, high-fidelity tool for diagnosing ecosystem health. Beyond the Sino–Korean context, this methodology offers a replicable template for assessing the resilience of transnational low-carbon energy networks globally.