Impact of endogenous learning curves on maritime transition pathways

The maritime industry is a crucial hard-to-abate sector that is expected to depend on high-energy density renewable liquid fuels in the future. Traditionally, decarbonization pathways have been assessed assuming exogenous cost trajectories for renewable liquid fuels based on an exogenous learning curve. While past studies have looked at the impact of endogenizing learning curves for a specific technology utilizing linear approximation, a fully endogenous direct non-linear implementation of learning curves in a detailed sectoral model (maritime industry) that explores dynamics concerning sensitive parameters does not yet exist. Here, we apply an open-source optimization model for decarbonizing the maritime industry and further develop the model by encompassing a nonconvex mixed-integer quadratically constrained programming approach to analyze the impact of endogenized learning curves for renewable fuel costs following an experience curve approach. We find that global greenhouse gas emissions are significantly lower (up to 25% over a 30 year horizon) when utilizing endogenously modeled prices for renewable fuels compared to commonly used exogenous learning frameworks. Furthermore, we find that conventional modeling approaches overestimate the cost of climate mitigation, which can have significant policy implication related to carbon pricing and fuel efficiency requirements. In a broader context, this emphasizes the potential opportunities that can be achieved if policymakers and companies accelerate investments that drive down the costs of renewable technologies efficiently and thus trigger endogenous experience-based learning in real life.


Introduction
Abating climate change and adapting to its negative impacts on the environment is one of the economy and society's most pressing challenges.Modeling of climate mitigation pathways requires in-depth knowledge of technological, societal, and economic dynamics across sectors.Global mitigation pathways are traditionally computed using integrated assessment models (IAMs) and are increasingly influential in the global climate mitigation debate, where they are used in policy assessment [1] or environmental legislative analysis reports [2,3].While IAMs provide valuable global insights and explore sectoral and economy-wide mitigation pathways to limiting global temperature increase [4], they rely on an aggregate representation of energy technologies, where cost developments are typically based on exogenous learning curves.
Technology cost development is a critical parameter in IAM S as well as in large-scale energy system models, and it can impact the transition pathways towards a net zero GHG emission society.These exogenously defined cost developments are often based on the concept of experience curves, meaning that cost improves as production increases, which was described in 1936 [5] and have been used in many different applications outside of optimization models.It has mainly been applied in empirical studies to show the learning potential for different sectors [6,7] such as ship production [8,9], consumer products [10], energy demand technologies [11], or environmental control technologies [12,13].
In the past, technology cost projections have been underestimating the development of different technologies, such as solar photovoltaic (PV) or batteries, yielding an overestimation of the cost of future climate mitigation.For example, a meta-study examining 15 different IAMs showed that the cost of PV in 2020 has already fallen below the exogenously given cost parameters for 2050 [4].Another study showed that cost projections for PV, batteries, and polymer electrolyte membrane (PEM) electrolysis, made by IAMs and even the International Energy Agency, are significantly higher than historical developments [14].Multiple other studies highlight the impacts of the systematic underestimation of cost declines, especially for renewables, and therefore call for endogenous modeling of cost trajectories in larger IAM S and energy system models [15][16][17][18][19][20].In this context, the difference between endogenous variables and exogenous parameters are defined as: 'endogenous' variables are determined within the model, while 'exogenous' parameters are external inputs to the model.
However, in modern IAMs and energy system models, the concept of implementing fully endogenous experience curves concerning the costs of technologies is excluded due to computational feasibility [21,22].Incorporating future cost estimates that endogenously depend on investments in a certain technology turns future cost estimates from a parameter into a variable in the optimization model.This turns the problem into a nonconvex and non-linear problem [22], which ultimately leads to significantly higher complexity and, therefore, computational effort.The impact of exogenously given cost assumptions rather than endogenously given becomes even more critical when utilizing the perfect foresight assumption, as the model can delay investments until they become cheaper according to the exogenously given cost function.
In order to account more sophisticatedly for experience curve effects, Way et al [14] conducted a comprehensive study to provide empirically grounded technology cost forecasts and assess the impact on the energy transition using three exogenously incorporated cost developments.Zeyen et al [22] applied a piecewise linear approximation approach to assessing the impact of renewable hydrogen production in a European energy system, where every modeled area is represented as a price-maker.There has been one example, Grubler and Gritsevskii [23], of a fully non-linear implementation of endogenous learning using a traditional log-linear experience curve in a highly simplified optimization model.Grubler and Gritsevskii [23] showed that with the perfect foresight assumptions, an optimization model chooses to invest significantly earlier in the 'winning' technology [23].
In this study, we build upon Grubler and Gritsevskii [23] by applying fully endogenous experience-based learning curves to a detailed sectoral maritime optimization model featuring dynamics related to the availability of renewable fuels, upscaling of renewable fuels, retrofitting options of the existing fleet, newbuild options, a variety of engines and associated infrastructure (fuel tanks, auxiliary engines), carbon pricing policy and fuel efficiency gains.This allows us to gain a holistic perspective on one specific sector, i.e. the maritime sector, utilizing a fully endogenous technology learning approach and thereby identifying the system dynamics and drivers of uncertainty in the context of endogenous learning, which has not been done before.
In this study, we apply the open-source optimization model for decarbonizing the maritime industry, SEAMAPS [24], and further develop the model by encompassing a nonconvex mixed-integer quadratically constrained programming (nonconvex MIQCP) approach to analyze the impact of endogenized learning curves for renewable fuel costs.In doing so, we go beyond existing literature as it narrows down the exact impact of endogenous learning curves on sectoral emissions for a hard-to-abate sector and further examines dynamics between emissions, costs, and policy instruments, such as carbon prices.This significantly improves the knowledge base towards the impacts of fully endogenous learning in optimization models and its dynamics towards important assumptions such as the shape of the experience curve or the starting threshold of the experience-based learning.Utilizing these findings, we challenge the commonly used exogenous learning curves used in policy making, such as IAMs and large-scale energy system models, and provide insights into the potential under/ overestimation of climate challenges ahead of us.

Methods
In this study, we apply the open-source optimization model SEAMAPS [25] to derive maritime decarbonization pathways.We further extend SEAMAPS to fully model endogenous learning curves via a direct non-linear implementation-rather than a piecewise linear approximation-by formulating the optimization problem as a nonconvex MIQCP problem.This mathematical problem formulation is required as SEAMAPS is already a mixed integer-constrained problem due to binary constraints concerning the upscaling of certain technologies (see model description in figure 1).
The methodology used in this study aims to compare the commonly used exogenous learning curves for low-carbon fuel approach with the endogenized learning curve for low-carbon fuel approach.This comparison allows for the identification of changes in results related to emissions, costs, and policy measures to decarbonize the maritime industry.First, we run the model with exogenous cost development based on linear cost decay, regardless of the technology-specific experience.Then, we run the endogenized cost development linked to the experience gathered in the respective low-carbon fuel technology and compare the results.The endogenized learning curves have only been applied to the modeled green fuels in this study (NH3 and MeOH).The prices of fossil fuels like coal, oil, and gas fluctuate unpredictably, yet when accounting for inflation, current prices closely resemble those of 140 years ago, with no observable long-term trend [14].For this reason we have not allowed experience based learning for fossil fuels in this study.For a detailed list of modeled fuels see supplementary information section 2.
Due to a quadratic term representing experiencebased costs development in the objective function (see equation ( 1)), we derive an MIQCP optimization problem.Within SEAMAPS, costs for renewable fuels become a variable when implementing the endogenous learning curves.This is required as costs are influenced by the installed capacity of the respective fuel technology and thus decay over time inspired by an experience curve [5].This curve from Wright's experience curve theory [5], was established in 1936 after observing a decline in cost for aircraft production with increasing production performance.Further, this MIQCP optimization problem is nonconvex as the feasibility set is nonconvex.Therefore, we relax the MIP-Gap parameter included in the solver, which in this study is Gurobi.The MIP-Gap parameter controls the minimal quality of the final set of solutions and illustrates how far the current solution can be from the best possible solution in terms of the objective function.In this study, we show solutions computed with a MIP-Gap of 0.005.The difference in computational time between the exogenous model and endogenous model is around 10-fold.Exogenous model running time is around 10 s per scenario while the endogenous model running time is around 100 s.This of course depends on the MIP-Gap (0.005 in this case) and the local machine (16 RAM in this case).
In this study, SEAMAPS provides the leastcost decarbonization pathways for the global maritime sector (see figure 1 for a modeling overview).SEAMAPS combines (1) constraints of upscaling renewable fuel production capacities, (2) transparency of emissions along the entire supply chain of renewable fuels, (3) representation of biomass availability, (4) emission reduction goals motivated by Paris narratives, and ( 5) decision modeling based on least-cost optimization.
The aforementioned Paris Agreement narratives used in this study represent a stylised decarbonization pathway for the maritime industry of a 'well below 2 degrees' scenario [26,27] motivated by the Intergovernmental Panel on Climate Change reports.This scenario is characterized by a short-term decarbonization target of 25% by 2030, and reaching net zero by 2070.When comparing cumulative emissions in this study with this scenario, we sum the area under the curve and linearly interpolate between the shortterm and long-term targets.This target is less ambitious than the current legislation of the International Maritime Organization (IMO) (which aims for the industry to reach net zero by 2050).However, given the popularity of the 'well below 2 degrees' [26,27] pathway, we have used this decarbonization target when comparing the cumulative emissions of different modelling techniques (endogenized fuel cost vs.exogenized fuel cost) in the context of this study.
Furthermore, and most importantly, in this study, we further develop the model formulation of SEAMAPS to entail constraints related to the respective fuel costs, making them endogenous and subject to the utilized capacity in the respective fuel technology.The cost estimates for the base year (2020) were calculated using a fuel cost optimization model [28]that tested different locations based on their respective solar and wind profiles to produce green fuels.For this analysis, we have chosen the cheapest options, which is Morocco, and added the transport costs and profit margin to bring the fuel to Rotterdam (for more details see the supplementary information (SI)).
SEAMAPS perform a least-cost optimization of fueling options to supply the maritime industry.The elements in the objective function can be divided into two main parts; one part which concerns all costs related to the fleet, including the investment costs for additional vessels, operations, and maintenance costs; and the second part which concerns the fuel costs.The fuel consumption of each vessel in the fleet is multiplied by the fuel costs (including fuel taxes, if any).
The objective function in SEAMAPS: where INV s is the investment expenditure for a new build average vessel of type, s, NB s,y is new built ships of ship-type, s, in year, y, OEM s is the operation and maintenance cost for a vessel of type, s, SS s,y is shipstock of ship-type, s, in year, y, F f,s,y is the amount of fuel used per fuel-type, f, ship-type, s, and year, y, FC f,y is the fuel cost per fuel type, f,(endogenous or exogenous) and year, y, and FT f,y is the fuel tax added on top of fuel cost per fuel type, f, and year, y.In this study, the carbon tax is exogenously given for each scenario run and added accordingly to the respective fuel cost per year.The contribution of the carbon tax to the total fuel cost depends on the underlying fuel emissions, including carbon, methane, and nitrous oxide emissions, and utilizes a global warming potential of 100 years.Furthermore, SEAMAPS features a life-cycle perspective on green fuels, taking into account the infrastructure emissions of building fuel plants, wind turbines, or solar panels.Therefore, emissions are based on a Well-To-Wake basis and depend on the production location of the respective fuel and the current year.For more details about the bottom-up modeling of fuel emissions, please see the following publications [28][29][30] and the SI sections 3, 6 and 7.
Additional constraints are added to adapt the future fuel mix to the future challenge of this hardto-abate sector.The most relevant constraints of the SEAMAPS model are described in the following: Transport demand: This constraint limits the supply in the SEAMAPS model to the exogenous demand projections of the IMO [31] (D y,sc ) per year, y, and ship category, sc.We use an SSP1-type [32] demand.This ensures that supply and demand are matched and that no excess demand or supply in the model could distort the results.It is important to note that demand strongly influences the results of the future fuel mix and that this variable may need to be replaced by endogenous demand projections in the future to create a more inherent modelling process.SS s,y is the stock of ships, s, at year, y. ρ s,y the average transport work of ship, s, in year, y. β sc,s is a matrix relating the ship category, sc,(container, tanker, bulk, cargo, other) and the ship type, s, (ship category associated with a specific engine).The unit of the transport demand and transport work in SEAMAPS is giga-tons per nautical mile.
Fuel consumption: The fuel used (F f,s,y ) by ships of type, s, and fuel, f, in year, y, equals the transport demand.The transport demand of the fleet of ships of type, s, is equal to the ship stock (SS s,y ) of that type (the number of ships of type s in the fleet) and year, y, multiplied by the average transport work (ρ s,y ). per ship-segment, s, and year, y.The fuel consumption is calculated using the specific fuel consumption (α f,s ) per fuel type, f, and ship type, s.SEAMAPS uses a diverse fuel mix to satisfy demand, with any type of fuel being a viable option.The unit of fuel consumption in SEAMAPS is peta-joule (PJ).
Fuel availability: For all fuels and all years, the amount of fuel used for the whole shipping fleet cannot exceed the fuel available, which is represented by δ f,y per fuel, f, and year, y.The unit of fuel availability in SEAMAPS is PJ.
Upscaling renewable fuel production capacities: For all fuels, f, and all years, y, the available fuel δ f,y is equal to the previous year's fuel availability multiplied by τ , which represents the yearly growth of renewable fuel production capacities This constraint ensures that upscaling only begins once the model invests in the respective renewable fuel for the first time.The study assumes a conventional growth rate of 50% per year for the upscaling of renewable fuel capacity.This slope has been motivated by diffusion speeds of historical solar PV growth and wind turbines for the case of conventional growth and the diffusion speed of US nuclear weapons and US aircraft during World War II for the case of unconventional growth [33].
Endogenous learning of fuel-costs: For all fuels, f, and all years, y, the endogenous learning cost variable FC f,y is equal to the initial bottom-up-modeled fuel cost estimate from 2020 times the learning parameter L f,y per fuel, f, and year, y.This learning parameter is being estimated endogenously making the optimization problem both non-linear and nonconvex, which is challenging to solve.Generally, there are two options to find a solution for the non-linear and nonconvex problem.The first option is a piecewise linear approximation, and the second option is direct non-linear implementation [22].In this study, we use the directnon-linear implementation.Thus, this problem is defined as a nonconvex MIQCP model.To determine the values for the learning parameter f,y , we implemented a threshold approach.This threshold approach is dependent on the experience of a particular fuel technology, and thereby the investments in the specific technology (F f,s,y in the model).Once a certain threshold of fuel-specific investments is reached, the learning parameter L f,y declines from 1 to a maximum of 0.6.This slope is being motivated by Way et al [14].The thresholds used for this study can be changed respectively to be able to model different policy scenarios that would foster faster endogenous learning (lower thresholds to trigger a decline in cost) or lower endogenous learning (higher thresholds to trigger a decline in cost).Further information about the applied thresholds in this study can be found in the supplementary information (SI).

Results
We find that the cumulative emission as an output of the decarbonization model for endogenously modeled cost estimates are significantly lower than in the exogenously given cost estimates.By endogenizing learning rates and assuming a full foresight horizon, the model realizes the potential of initiating investments in renewable fuels earlier, as more investments will create opportunities for decay in costs and essentially make it more profitable in the future, given that the maritime industry has to be decarbonized in line with the Paris Agreement.Thus, the adoption of renewable technologies happens significantly earlier, and therefore, cumulative emissions of the endogenously modeled cost (endogenous learning) setups are considerably lower than in the exogenously given (exogenous learning) cases (see figure 2(a)).Furthermore, we can identify that supporting the scale-up (e.g. through high subsidies) to lower the threshold can also lower the cost for climate mitigation significantly (see figure 2(a)).
We identify that the endogenously modeled cost estimates decay significantly quicker than exogenously modeled costs to their exogenously given minimum of a 40% decay compared to 2020 levels (assumption motivated by Way et al 2022 [14]) (see figure 2(b)).We use the 40% cost-decay in 2050 compared to 2020 cost estimates, as the model needs some exogenously defined learning potential.This learning potential is then applied to both the endogenous learning cases and the exogenous learning scenarios to have a reasonable comparison between the endogenous and exogenous modeling of low-carbon technology cost and, thus, identify the impacts of applying endogenous learning.The 40% used in this study can be seen as a rather pessimistic look at history learning curves for costs of solar PV (see figure 2(b)), where we can identify a cost decay of 80% within 10 years for fixed axis solar PV [34].However, the learning potential needs to be provided; otherwise, the cost will decay toward zero.Yet the model's behavior, namely investing much earlier into renewable technologies if we use endogenous learning rates for low-carbon technology costs compared to exogenous learning rates, remains the same no matter which exogenously defined learning potential is being used.This way of modeling always leads to earlier adoption of renewable technologies (see figure 2(c)) and, therefore, lower cumulative emissions over the modeling horizon.For this study, we have aggregated the green fuels modeled within SEAMAPS (see section two of the SI).This is because, for this type of analysis, it does not matter whether green ammonia or bio-emethanol will be the dominant fuel of the future, as the focus is purely on the impact of applying endogenous learning rates for these types of fuels (see more details on the derivation of initial fuel costs in the SI sections 3, 6 and 7).
Further, we show the robustness of our results based on sensitivity analysis in figure 3 where we test different levels of carbon pricing pathways, learning rates, and learning curve shapes on cumulative emissions and fuel cost projections.The carbon pricing trajectory, as shown in figure 4, has a significant impact on the results.Yet, we also find that the learning rates are highly significant regarding the impact towards cumulative emissions.The shape of the learning curve, i.e. whether a more linear curve or a s-shaped curve is being assumed, has a small but significant impact on the results, as can be seen in figure 3.In the scenarios where we tested a linear curve, the model (figures 3(c) and (b)) do not identify a winning renewable technology as the cost savings are distributed linearly across the modeled learning function.The model finds it easier to identify and invest heavily in the winning low-carbon technology when assuming an s-shaped curve in the learning function.This is due to the fact that experience in the respective technology is distributed non-linearly, and thus, cost savings happen faster compared to a linear distribution.Further, in the high carbon pricing case (500EUR/tCO2eq on average over the 30 years modeling horizon) an increase in the speed of learning does not change the outcome towards cumulative emissions (see figures 3(b) and (d)).This is because with high carbon pricing, green fuels will be forced into the fuel mix much earlier, and as there is no fossil fuel in the system anymore, the cumulative emission will be the same across different learning rates.
Further research could investigate the topic of assuming perfect foresight or a more rolling horizon in the modeling framework to understand the dynamics related to this assumption.In this research, the assumption of perfect foresight has remained unchallenged, and challenging this assumption could uncover fresh perspectives on modeling an endogenous learning curve for addressing the cost of climate mitigation in industries that are difficult to decarbonize, such as the maritime sector.[26].Y-axis explanation: 1 = low thresholds (high subsidies) 95 = high threshold (low subsidies).

Discussion
The modeling of endogenous learning curves for costs of renewable fuels, featuring an experience curve approach [5], revealed significantly lower cumulative emissions due to lower cost of climate mitigation compared to the commonly exogenously modeled learning curves.Yet the results in figure 2 are sensitive to the underlying scenario settings towards assumed carbon price trajectories, learning curve potential, and threshold to trigger the endogenous decay of costs.Similar uncertainties have been found in literature and therefore require a thorough sensitivity analysis to avoid biased results and implications [35].In this discussion, we focus on the carbon price projections and thresholds to trigger the endogenous learning in figure 3, while we also perform a sensitivity analysis on the shape of the learning curve and the learning rate in figure 3.
The carbon emission trajectories and thresholds are important parameters to further drive down cumulative emissions.The learning potential, which represents the level where the costs stabilize and cannot decrease further, is an influential exogenously defined parameter, yet we find in our larger-scale sensitivity analysis in figure 3 that this impact can be described as linear within the complex dynamics of the optimization problem.
The threshold to trigger the start of the endogenous decay of costs for renewable fuel technologies changes the underlying findings significantly.Previous research often uses a scenario design in which every doubling of capacity leads to a certain percentage decay of costs.Yet, this design is only useful if one only models a few modeling years, e.g. 5 year modeling steps in Zeyen et al [22], as it consequently would lead to an exponential function of decreasing costs, which would quickly approach zero.In our study, the optimization problem solves for every year over a 30 year horizon and therefore, we defined thresholds to be reached before the endogenous decay of costs for renewable fuels starts.In the broader sense we can see the opportunity that these thresholds can be interpreted as proxies for subsidies of the respective fuel technology, as a lower threshold fosters the decay of the costs significantly more than a high threshold.Thus, a low threshold to trigger the decay process can be interpreted as high subsidies in the R&D of the respective technology, and high thresholds can be construed as low subsidies in the R&D of the respective technology.Looking at today's real-world investment decision, we can identify a few projects and investments, such as investments in electrolyzer or renewable methanol compatible shipping vessel [36], that could be interpreted as triggering thresholds and thus support the idea of endogenous learning for future costs of a low-carbon technologies.
We show the dynamics between carbon pricing trajectories and different levels of thresholds as a proxy for subsidies in R&D for renewable fuel technologies in figure 4. The results are obtained by optimizing the SEAMAPS model with endogenous modeling of learning curves for renewable fuel costs multiple 100 times with different settings for each of the two parameters.Then, we compare cumulative emissions and find the solution space for the model to reach lower cumulative emissions than well below 2 • C emissions.In figure 4 the solution space, meaning the combination of threshold to trigger the endogenous learning in the model (y-axis) and the utilized average carbon price over the 30 year modeling horizon (xaxis) is shown.The solution space refers to the cumulative allowed carbon budget motivated by a Paris Agreement-compatible emission budget of well below two degrees.This means every combination right of the line is respecting the carbon budget (colored green tone) while every combination left of the line does not respect it (colored red tone).We assume a starting carbon price in 2020 at 50 EUR/tCO2eq, which then increases towards 2050.Thus, as an example, an average carbon price of 300 EUR/tCO2eq on the x-axis illustrates a case where we utilize a carbon-pricing trajectory starting from 50 EUR/tCO2eq in 2020 and increasing linearly to 550 EUR/tCO2eq by 2050.The y-axis in figure 3 shows the level of threshold required to trigger the s-curve learning rates for renewable fuel technology costs in percent of the total maritime fuel demand in 2020.Thus, 25% on the y-axis illustrates a scenario set in which the endogenously modeled fuel costs start to decay when the model uses 25% of renewable-fuel technology to serve its yearly total maritime demand (based on 2020 values: 11000PJ).
It can be observed that with lower thresholds to trigger endogenous learning carbon pricing could be reduced by up to 100 EUR/tCO2eq for the maritime industry to achieve well-below 2 • C Paris Agreement compatible mitigation pathways.This reduction in cost could be achieved through endogenous learning to derive down renewable fuel cost technologies, with lower thresholds being triggered.These lower thresholds can be seen as subsidies for R&D of renewable fuel technology such as electrolyzer capacity.These findings can be seen as controversial with respect to today's funding of R&D for renewable fuel technology.For example, in Germany, R&D investments into renewable fuel technology from a government perspective are mainly funded by revenues from both the European Emission-Trade-Scheme and the national carbon pricing scheme [37].Thus, given our findings, a risk is that a 'chicken and egg' problem might occur, as high investments and subsidies for R&D of renewable fuel technology can only be achieved with high carbon prices.Yet we believe that given our novel modeling framework, which allows us to endogenize costs of renewable fuel technologies and associated with this effort towards lowering these costs, and the findings we present in figure 3, alternative ways of financing R&D in green fuel technologies must be explored as high carbon prices without functional redistribution schemes increase societal pressure significantly.Further, we argue that pushing for low carbon prices and making sure endogenous cost decay of renewable fuel technologies illustrates the societal optimum, and efforts towards this situation are worth pushing for.

Conclusion
We have modeled endogenous learning curves for renewable fuel technologies via direct non-linear implementation within a maritime optimization model and observed the dynamics between exogenously defined and endogenously defined costs.We identify opportunities that cumulative emissions are significantly lower (up to 25% over a 30 year horizon) when utilizing endogenously modeled prices for lowcarbon technologies (e.g.renewable fuels) compared to the exogenous learning approach due to lower cost of climate mitigation in the endogenized approach.Furthermore, we find that the assumption regarding the threshold required to trigger an experience curvemotivated decay of costs is essential in our modeling approach.When performing multiple hundreds sensitivity analyses featuring different threshold levels and different levels of societal costs (in the form of carbon pricing), we identify opportunities that societal costs can be up to 100 EUR/tCO2eq lower if early triggering of the experience curve can be reached.These findings show that optimal pathways for mitigating global climate change for the maritime industry can simultaneously be ambitious enough to be line with a Paris Agreement motivated emission reduction goal and come at a relatively (to other mitigation pathways without modeling of exogenous learning curves) low societal costs in terms of carbon pricing needed.Furthermore, our results show that investing in R&D for critical low-carbon technologies is an essential policy implication going forward to achieve an experience-based learning in the market.Thus, modelers and policy makers should consider the opportunities obtained by including endogenous learning curves in their decision making, as it allows to create more realistic estimates about future cost of climate mitigation.

Figure 1 .
Figure 1.Novel modeling environment to endogenize low-carbon fuel technology costs.

Figure 2 .
Figure 2. Comparison of exogenous vs. endogenous learning and its impact on emissions, costs, and fuel usage for a scenario with an average carbon price of 250 EUR/tCO2eq.(a) Cumulative emissions in MGtCO2eq for high and low thresholds to start endogenous learning scenario and exogenously learning reference case.(b) Fuel cost in M€2019/PJ of the modeled renewable fuels for high and low thresholds to start endogenous learning scenario and exogenously learning reference case.(c) Utilized fuel mix in PJ fuels for high and low threshold to start endogenous learning scenarios as well as exogenously learning reference case.

Figure 3 .
Figure 3. Conducting a sensitivity analysis on model dynamics involving fully endogenous learning curves for two distinct shapes and three varying learning rates.(a) Endogenous fuel cost in M€2019/PJ with different carbon pricing levels for the S-shaped learning curve as an output from endogenous learning curves approach.(b) Cumulative WTW emissions in GtCO2eq with different carbon pricing levels for the S-shaped learning curve as an output from endogenous learning curves approach.(c) Endogenous fuel cost in M€2019/PJ with different carbon pricing levels for the linear-shaped learning curve as an output from endogenous learning curves approach.(d) Cumulative WTW emissions in GtCO2eq with different carbon pricing levels for the linear-shaped learning curve as an output from endogenous learning curves approach.

Figure 4 .
Figure 4. Solutions space for reaching a sectoral maritime emission reduction target (green colored area) motivated by the Paris Agreement well below 2 C pathway[26].Y-axis explanation: 1 = low thresholds (high subsidies) 95 = high threshold (low subsidies).