How transparent is water? Addressing ethical concerns in AI surrogate development for nearshore wave modelling and the natural sciences Open Access

The field of ethics refers to the discernment of right and wrong doing by a set of principles. AI is a set of models that learn rules or principles based on a collection of training data. As AI is expected to also discern between right and wrong within training and its predictions, the concept of ethics is relevant to AI development.

In the context of surrogate numerical modelling, AI models are used to replace established governing equations and methods to make predictions in a cost-effective and timely manner. The results of these models will be adopted and trusted by their users and to inform decision-making. Ethics must therefore be considered to ensure that AI-driven methods produce fair, accurate and safe results.

• Bias and discrimination

• Denial of individual autonomy and rights

• Non-transparent, unexplainable or unjustifiable outcomes

• Invasions of privacy

• Isolation and disintegration of social connection

• Unreliable, unsafe or poor-quality outcomes

For AI surrogates of numerical models, points 3 and 6 are the most poignant concerns. As numerical models follow established governing equations, the absence of governing equations raises risks in applications where extreme values can occur. A non-transparent or unexplainable model yields uncertainty, particularly if the AI is used to predict physical phenomena. In this case, it is difficult for the user to demonstrate a coherent workflow and reasoning, casting their work open to scrutiny.

Unreliable, unsafe or poor-quality outcomes is a major concern for AI surrogates of numerical models. AI surrogates are developed for complex problems, where computational requirements are too great. When a trained AI is adopted after development, it is not always obvious if the model has performed to a poor standard.

It is the responsibility of the AI developers to ensure that models are designed, developed and tested to encourage best practices. Figure 1 displays the support, underwrite and motivate (SUM) values presented by the Alan Turing Institute. These values should be considered throughout each stage of development in the innovation lifecycle. Innovation projects undergo a cyclic nature from assessing project scope to planning and problem formulation, thereafter design, development and testing followed by implementation and then reassessment.

Since AI surrogates for numerical models do not use personal data or interpret human qualities, their interpretation in relation to the SUM values is not explicit. Much like the popular large language models (LLMs) or AI models used for classification tasks, AI models applied to problems in the physical sciences inform innovation and affect human quality of life. It is therefore important that ethical principles of adopting and developing AI are applied to the field of physical sciences to continue responsible use of AI, which is respectful of the potential harms that can be caused by AI systems.

A respect-embedded AI is one that allows users to make well-considered informed decisions and unique contributions. Using an AI surrogate gives faster results, which better facilitates collaboration. AI technologies developed with care are thoughtfully presented for proper adoption to avoid misuse, which can lead to human harm. AI can be developed to protect social values by ensuring its adoption empowers and advances the pre-existing interests, reaching as many individuals as possible. As an overarching theme, AI technologies must be developed with a big-picture mindset. Considering the wider impacts of using the AI technology developed and potential ramifications acts as a pivoting point for improving innovation practices, the following paper is centred on the application of AI to develop nearshore wave model surrogates as a practical application and example to frame the concepts of ethical AI within the physical sciences. This area of AI development is of interest due to its relevance to the offshore energy industry. The strides made in AI surrogate development in nearshore wave models affect the viability of offshore energy generation, which greatly affects human quality of life and wellbeing.

Readers are encouraged to draw parallels between the application of AI to nearshore wave modelling and other physical phenomena, as the presented circular distribution scheme framework, which is designed to address the topics of transparency and bias within AI can be applied to all applications of AI within the physical sciences

In our rapidly changing climate, energy generation per capita must match increased demand from population rise and globalisation. With limited resources on land, nearshore and offshore energy production draws more investment for innovation and construction projects (Pick, 2023, p. 14). In the offshore renewables sector, the installation and maintenance of offshore renewable energy generation such as wind, solar and wave farms are costly and require careful planning. High costs must be offset by renewable energy farms that are both operational and efficient in the long term.

As part of the net-zero energy transition, offshore renewable energy generation is expected to increase (Pick, 2023, p. 19). New installations are situated further from the coastline where more high-energy waves and storm events are expected alongside greater energy returns (Estates, 2023, p. 34).

To evaluate risks involved with planned operations and make informed strategic planning decisions, wave models are used to identify feasible sites (Gudmestad, 2020; Neill, 2024) and weather windows to carry out operations and management (O&M) activity. However, the use of nearshore wave models entails technical obstacles, which render the planning stage of offshore renewable energy development slow and costly.

Widely used solutions for wave models require high-level expertise and expensive and sought-after computer architecture to run. Furthermore, these models do not scale efficiently for long-term periods or fine resolution simulation of sites of interest (Rautenbach et al., 2021). In such circumstances, low-resolution surrogate models can be used, which poses concern in uncertainty risk in construction and maintenance.

Cutting-edge AI and machine learning frameworks offer the promise of alleviating the technical issues involved in nearshore wave modelling. Once trained, AI and machine learning models run with diminished computational demand and time. These benefits allow easier access to large-scale models that are required for offshore development. The reduced computational time can allow for more rigorous testing and research at multiple sites, which can reduce uncertainty risk in strategic planning.

The use of AI is unique to traditional numerical schemes as its predictive power heavily relies on the data set used to train it. Numerical schemes instead rely on the simplification and formulation of non-linear physics equations. In this way, the pathway to acceptance and large-scale actualisation of AI models notably differ from their traditional counterpart. Traditional wave models use numerical solving schemes to resolve physical governing equations giving them clear prospective transparency (Felzmann et al., 2019). With transparency, it is easier to determine causes for bias within measurements and in resolving simulations. Identifying model transparency and bias are key for the use of AI in an established modelling community, particularly in a high-risk sector such as offshore renewables development. At present, installing offshore renewables presents a combination of unpredictable environmental conditions, highly complex operations and the constant adoption of state-of-the-art technology. The quality of renewable energy infrastructure is dependent on the experience of personnel and the availability of funds should unexpected delays occur. Both considerations are highly variable in the early stages of offshore renewables transition.

The development of AI surrogates for nearshore wave models is growing traction (Shadmani et al., 2023, p. 5). The inherent risks involved in offshore planning call for discussion on the ethical practices that are considered in AI integration to combat climate change (Jain et al., 2023).

In the context of nearshore wave modelling for developing offshore renewable energy generation, the scope of this paper briefly addresses the understanding of mathematical transparency and bias in deep learning driven nearshore wave models. The next section focuses on AI transparency – a paradigm consideration in the ethics of AI. The purpose of this section is to outline the accepted baseline transparency set by pre-existing numerical models. The transparency expectations of AI surrogate models are then detailed and compared to accepted practice. The following section concerns bias in AI models. The debate on AI bias is generally reserved for decision-making AI; therefore, the sources of AI numerical model surrogates are explained in terms of statistical uncertainty concepts. Attention is then brought to the importance of defining the limits of the AI’s training data to inform safe adoption of the model.

The final section discusses the requisites for the use of simulated data-driven AI models akin to their physics driven counterpart, and introduces the circular development scheme (CDS) framework, The CDS framework is a proposed framework that can be adopted by AI developers in the physical sciences to assist the development of transparent and unbiased AI. As the CDS framework can be applied to all areas of AI development in the physical sciences, its generality can also yield issues due to the bespoke nature of AI in the physical sciences, where each AI model is applied to an exact physical phenomenon. The limitations of the CDS are also discussed alongside proposed issue mitigation strategies for future AI developers

Transparency is a computational concern that has increased along with the interest in AI. The word transparency itself is multifaceted in its uses across disciplines (Larsson and Heintz, 2020, p. 5). In the context of AI development, AI transparency gives an understanding of how AI systems make decisions or predictions, why they produce their results and of what data is being used. In essence, if an AI is transparent, it is possible to explain its system and inner workings at both a high- and low-level sense. The very definition of AI transparency is a subject of debate (Larsson and Heintz, 2020, p. 5) due to the qualitative sense of explainability. As the understanding of transparency is not clear cut, neither is the detail of explainability.

Transparency and explainability are themselves related but unique concepts. Transparency refers to how an AI may be audited, whereas explainability refers to how intelligible the mechanisms are behind the AI. An AI can be transparent but not explainable, and vice versa.

Within the physical sciences, source code for AI models is often published as open source. Any well-published open-source code will include one or several “read me” files, which dictate the architecture of the code and the purpose of each function and script, with the author’s comments throughout the scripts. These measures are in place so that when the open-source code is used by another contributor, the code has technical openness, meaning it can be deployed in another scenario or edited with reasonable effort given that the contributor has the appropriate skill level to modify and adopt the source code for the AI model in the first place.

The source code for AI can be split into three parts: the core AI function, which is the model itself and the pre-processing and post-processing scripts surrounding the core AI model, which are essential to make the AI model work as intended, processing its inputs and producing its prescribed outputs. This is known as the back-end of the code.

A transparent back-end is one that is well commented and well structured, but an explainable back-end uses an AI structure and pre-/post-processing techniques, which can be understandable to another developer of a similar skillset. For an AI model to be seen to have trustworthy performance in extreme cases, it must be both technically open and understandable so that the assumptions made in the entire architecture can be examined and improved when the AI model outputs are not satisfactory.

To avoid the debate of mutual necessity of transparency and explainability within this article, transparent AI is referred to as source code for the full stack which is both auditable and intelligible by a contributor with a similar skillset to the original author(s).

Whilst some models can be physics-informed or include logistical constraints, each AI framework uses rules and structure that is purposefully not prescribed by the model developer (Zerilli et al., 2019, p. 663). Instead, the model is expected to recognise non-linear patterns and learn implicit rules based on the collation of training data. The model’s learnt behaviour is desirable in problems that have inherent randomness (Battjes and Janssen, 1978) or have governing rules of the system, which tend more towards descriptive than prescriptive in real world applications. The accuracy of AI is typically measured via error metrics; however, model assessment requires both quantitative and qualitative analysis to explore the variability of its predictive power.

Without rigorous testing on unseen data alongside statistical validation, it is not clear exactly what rules the AI is learning to make predictions within the system. If the AI has learnt rules that are arbitrary and irrelevant to the physical system, then the model becomes unreliable and unsafe. In the context of surface wave modelling, an inaccurate hindcast model misinforms O&M strategic planning timelines. If planners are misinformed on operation weather windows, there will be unplanned delays and significant waste of resources (O’Connor et al., 2012, p. 2). If an inaccurate forecast consists of an under-prediction of energy within the sea state, there is a risk of damage to vessels, equipment and offshore structures. If in reality the sea waves are higher than the construction thresholds, the misinformation from the model jeopardises the safety of deployed crew members. If an inaccurate forecast consists of an under-prediction of energy within the sea state, there is a risk of damage to vessels, equipment and offshore structures. If in reality the sea waves are higher than the construction thresholds, the misinformation from the model jeopardises the safety of deployed crew members.

Due to the inherent risks involved from an inaccurate model, the concept of transparency is important. The inner workings of the model must be understood to foster trust between AI systems and their users. As AI is used to make predictions on unseen data, it is important that the user can understand how the AI makes its predictions to understand where and how errors may occur.

The issue of explainable AI is often applied to AI model scenarios where sensitive data is used in training and where the AI itself makes decisions that can have dangerous or harmful consequences if made incorrectly (Miller, 2017). Examples of these use cases are in facial recognition and driverless cars.

However, the use of AI surrogates of physics-based models still poses the question for transparency for the model’s results to be trusted in atypical scenarios. To better understand the concept of transparency for AI in nearshore wave models, the transparency of numerical nearshore wave models is of comparative interest.

The nearshore wave field experiences random waves (Figlus, 2022, p. 37) as well as higher-order wave interactions. Both of these aspects are approximated in numerical nearshore wave model frameworks to increase the likelihood of successful completion of the simulation and to decrease the computational demand of the model. Many numerical wave models use linear wave theory, with the inclusion of non-linear, second-order dissipation effects through wave-wave and wave-bathymetry interaction. Linear wave theory was first developed from first principles (Sorensen, 1993) and validated in a controlled environment such as a wave tank. However, to extrapolate this theory to model in situ, offshore waves yield logistical inconsistencies, which affect the model’s accuracy. On the offshore free surface, waves propagate as packets of overlapping waves with varying frequencies, described as a sum of harmonic waves. A representation is shown in Figure 2. When wave interaction occurs, the distribution of wave harmonics alters as wave components super-impose. Modelling wave interactions hence requires the consideration of wave harmonics higher than the first order.

The nearshore wave climate can contain a combination of deep and shallow water. In deep water, quadruplet wave-wave interactions dominate the spectrum (SWAN, 1993, p. 17).

In shallow water, triad wave-wave interactions dictate the wave field; low-energy wave frequencies shift to higher energy frequencies, resulting in higher harmonics. Higher harmonic waves can result in free waves (Kuznetsov and Saprykina, 2021; Hult et al., 2010), which then make significant contributions by resulting in further interactions at first and second order. Due to computational constraints, quadruplet interactions are coarsely approximated, and low-frequency energy generation (SWAN, 1993, p. 17) is not considered.

Furthermore, nearshore wave domains are simulated over a discretised grid, so there will be significant wave interactions that occur in between computational grid points. The result of the nearshore wave model simulation is therefore a statistical approximation of the wave climate, which is often under or over-predicted (Rogers et al., 2007; van der Westhuysen, 2010) when the sea floor is rough or contains sporadic steep gradients.

Numerical wave models must be calibrated as a combinatory choice of numerous approximation schemes for high-order physical phenomena to produce simulation results similar to deployed wave buoy measurements. It is possible to use alternative equations for considerations such as the wind input, the wave set-up, breaking interactions, and so on. Certain configurations of equations prove to be more accurate in particular bathymetric conditions, such as open versus closed basins. Due to the multiple sources of approximation, the exact reasoning for the differing accuracy between configurations is not fully understood to model users and developers (SWAN, 1993, p. 17). Furthermore, approximation schemes contain tuneable parameters, which are neither explained nor empirically verifiable. However, various considerations are still trialled during the model calibration period. The end results are generally accepted by the modelling community, given that the modellers provide statistical measures of error against measured data such as the linear correlation coefficient, R², RMSE or MAE and the p-statistic.

Regardless of the inaccuracies discussed that are inherent to approximation schemes in numerical models, users still posit that such discrepancies are likely to occur whilst ascribing confidence to the given results. The standard for numerical model transparency is set in modelling practice.

In publications regarding simulations, it is not expected nor possible to give comprehensive explanations for each discrepancy that arises in a simulation, simulation results are expected to be approximations to a reasonable degree as it is computationally impractical to calculate the exact higher order terms of an equation. Within nearshore wave modelling, the background mathematics concerns the kinematics of wave theory, and there are errors that will occur due to approximations made for practicality. Other fields within the physical sciences are governed by some kinematic equations; carrying out simulation tasks in other physical sciences will harbour the same constraints. For example, in the study of thermodynamics and heat transfer, Fourier’s law and the heat equation are used, much like in wave theory, thermodynamic equations also include higher-order terms, which face computational constraints within numerical modelling, and simulation is also accepted as an approximation. Numerical approximations can be drawn from derivation from first principles but can also be drawn from and validated using curve fitting techniques. Curve fitting involves applying empirically collected data to a derived physical equation or approximation scheme to verify whether the assumptions made are appropriate for describing the physical process at hand. Depending on the problem, curve fitting involves a combination of calculus (Transtrum et al., 2011), differential equations (Li et al., 2017) and numerical analysis (Gavin, 2019).

Training an AI model is closely related to curve fitting, since both involve adjusting parameters to minimise the error between predictions and observed data. However, AI models are more powerful because they extend curve fitting to high-dimensional, non-linear mappings between input and output spaces. Whereas curve fitting focuses on approximating data with a chosen function, modern AI can be seen as learning flexible functions that capture complex structures in data, which can be studied using tools from geometry and topology.

At its core, supervised learning can be understood as a form of curve fitting. The objective of training a model is to search through possible parameters θ to find a function fθ (x) that best maps inputs to outputs. Given a fixed data set of input–output pairs, training seeks the parameter set that minimises the error that the AI model predicts, which is determined by the chosen loss function L(θ). The process begins with an initial parameter estimate; an optimisation algorithm then updates the tuneable parameters based on the calculated error. These steps are repeated until the model is suitably trained.

In neural networks, a sub-category of AI, tuneable parameters (weights and biases) determine how data flows between layers. Each layer applies a nonlinear transformation, or mapping, to its inputs. This mapping process can be analysed using mathematical tools from topology: for example, feed-forward neural networks used in classification tasks have been studied in terms of mappings between metric spaces (Pritchett, 1998):

With each new layer of an AI model, some data from the previous layer will be omitted in the next. This is known as an information bottleneck and is a common phenomenon in deep learning (Kawaguchi et al., 2023). When too much information has been lost between layers, the AI model cannot complete training. In a topological sense, there is a group of possible functions that govern the system at hand that can be approximated by the AI model. When data is lost through bottlenecking, the number of possible functions diminishes, and the ideal underlying function may be erroneously omitted. Skip connections are often included in deep learning models to reduce the effects of bottlenecking. Skip connections reintroduce all of the output from a previous layer into the current layer, meaning that none of the information from the previous layer is lost, and the scope for possible approximated functions has been restored.

Topology extends to cover the use of skip connections to create trainable deep learning models (Naitzat et al., 2020). The mathematical branch of topology was developed largely the late 19th century to the present. In contrast to the field of kinematics where basic concepts are taught at the high-school level, the pre-requisite knowledge for both topology and Bayesian statistics is generally sequestered until degree-level mathematics study. It follows that a small population of the mathematically educated will be able to understand the mathematical concepts behind a neural network; however, it is still possible to understand that AI surrogates can possess a similar level of transparency to the numerical wave models given the relevant education. The issue of transparency of the model in this sense can be reconsidered as a question of knowledge inclusiveness.

Because the layers of an AI model reshape the space that confines the data, curve fitting in AI is far more complex than in traditional physical models. To frame an analogy, non-linear curve fitting is like bending a piece of wire into smooth curves between data points, whereas neural network training is like arranging a series of distorted mirrors in a maze so that you can see the exit when looking in at the entrance. Fitting a non-linear curve alters a single shape to match two sets of data, whilst an AI model stacks many simple transformations and remaps the entire space in a controlled way so that the underlying pattern becomes clear.

In this context of AI training, the performance of the model is highly dependent on the initial values set before training and the choice of optimisation algorithm. As AI structures have thousands of tuneable parameters, it is difficult to ensure the optimal combination has been made during training. This issue is a source of non-transparency within an AI setup. Common practice for early-stage developers involves trial and error, which is much like the standard of calibration for numerical models within the wave modelling field.

Recent research has applied Bayesian approaches to model re-calibration. Following a Bayesian approach, the weights, a class of tuneable parameters within an AI model are assigned a probabilistic distribution instead of a fixed value. Bayesian AI is gaining traction in the physical sciences and is more transparent compared to AI models trained with fixed-value weights. Because a distribution is assigned to each weight, it is possible to quantify the level of uncertainty with each estimate of the model, which fosters a much higher level of trust to fixed-weight AI models (Zhao et al., 2021; Kuleshov et al., 2018; Kuleshov and Deshpande, 2022).

For a collection of desired inputs from the AI model’s training data set, a collection of desired outputs, known as the ground truth, is supplied to the model. Current optimisation methods yield the best single-value weight estimates that minimise the error between the AI model’s prediction and the ground truth data. The “best” is dependent on a number of factors, which are chosen by the AI developer.

Bayesian approaches are unique because they integrate prior knowledge during training and provide a posterior predictive distribution, that is, a distribution that shows the prediction and the uncertainty around it. AI models that use a Bayesian approach allow the user to make informed decisions on the predictions of the trained AI, given the probability of its accuracy. Bayesian-trained AI encourages user agency as the user can decide for themselves whether to trust the AI model given the projected accuracy in its prediction. As the user is able to assess the accuracy, this fosters trust in the design and trained tuneable parameters of the AI model.

Unlike the classic cases of facial recognition and driverless cars, there is an underlying set of partial differential equations (PDEs) that govern the nearshore wave system, which can therefore be learnt and used to explain the AI training process. Physics-informed neural networks have purposeful embedding of governing kinematic equations, where there is generally a two-part system, comprised of a neural network approximator and a PDE to compute the training loss (Alkhadhr and Almekkawy, 2023). Data-driven models are trained using data generated from a numerical wave model. As a more compact option, the AI surrogate will instead implicitly learn the same formulae that are used to govern the physics-based counterpart. In this way, the AI nearshore wave model surrogate is predictable as when trained properly; the model results should act as a curve-fitted approximation to the underlying physics equations in the training data. With increased popularity, it may be possible to extend this research to downscaling surrogate models for natural sciences, in this case, for nearshore wave modelling.

For AI applied to classification tasks, the development of tandem “explainer models” is being explored to increase transparency of the model (Ribeiro et al., 2016, p. 1136). In this way, it is possible for a user to verify that the logical deductions of the AI are of sound reasoning.

In any case, an AI model must be rigorously tested to define the limits of its accurate predictions. This methodology is similar to the calibration of numerical models, where different schema are applied and compared against the measured data to find the best fit for the particular domain. At present, AI surrogate models are trained using numerically simulated data as ground truth. It is therefore reasonable to posit that the AI model has predicted equable solutions by approximating the underlying governing equations of the numerical simulation in the respective training domain.

The ethical issue of bias for AI wave models differs from AI applied to personal data, such as gender and racial bias Ntoutsi et al. (2020). Decision-making AI is a principal focal point in the topic of bias in AI, where bias is typically referred to in the context of perpetuating demographic stereotypes.

However, in the physical sciences, model bias is often a systematic over- or underprediction of the desired value(s). In the context of wave action models, bias in the model results in an over- or under-prediction of the energy present in the wave climate. Using biased forcing data and tuneable parameters (Zhang et al., 2023; Amarouche et al., 2023; Zoljoodi, 2017) is an identified source of epistemic errors for numerical wave action models, yielding biased results.

Similarly, AI model surrogates can either extrapolate bias in the pre-existing underlying models or create new sources of bias from the training and development process.

Due to the unavailability of measured and gridded surface wave data, an AI nearshore wave model surrogate must be trained using data from models using numerical integration or from estimations via satellite image data. The random nature of waves (Battjes and Janssen, 1978) ensures there will always be a level of aleatoric uncertainty in the model that cannot be captured by numerical models that are governed by approximated equations at the first and second order. Therefore, it is in the AI developers’ best interest to minimise the epistemic uncertainty in the AI model’s training data.

AI surrogates treat the modelled training data as ground truth. They are therefore unable to discern bias and noise in the training data and will inherently adopt the same bias that exists in the modelled data. The AI will also be unaware of the inherited noise from training with biased data.

Bias can be removed from the training data only through prior bias-correction (Li and Zhang, 2019) instead of during AI training. Bias in a model is the result of systematic errors within the model’s results. A biased model will give results that are from a different distribution to the supplied ground truth. The extremity of the bias is determined by the consistency and severity of the errors from the model results compared to the ground truth.

The Simulating Waves Nearshore (SWAN), TELEMAC and Wave Watch 3 (WW3) numerical models are widely used in nearshore wave modelling applications. They have been developed in The Netherlands, France and the USA, respectively. Geographically, these sites are situated with close proximity to the North Atlantic Ocean and have comparable wave climates. Their test cases are situated in the surrounding waters, yet the models are released for worldwide use. Therefore, bias will inevitably occur due to the use of these numerical models in previously unseen domains.

There are calibration recommendations available for domains similar to the respective test case; however, there is little guidance on model calibration to prepare for global variability. The distribution shift of the wave climate across domains is a source of error when the tuning parameters are not adapted accordingly.

Models such as the SWAN model are reported to produce systematic under-prediction of wave height. Without careful screening of training data to avoid bias, it will be inherited by the AI surrogate.

Bias generated by the AI framework often occurs from issues in the data used to train the model (Roselli et al., 2019). Powerful AI models require a large training data set to encompass the variety of test-case scenarios that may surface. However, when presented with a case that substantially differs from the training data set, the AI surrogate can return wildly inaccurate predictions. In the development stages of the AI model, testing should reveal well defined in situ limits (Nalisnick et al., 2019).

Purely numerical nearshore wave models must be calibrated before use and validated using measured wave buoy data to quantify known biases. Nearshore domains can be categorised according to their geographical area, seabed roughness, the dominance of currents versus wind waves and the steepness gradient of waves approaching the coastline, to name a few. Each of these factors are principal considerations in the calibration stage of developing a nearshore wave model as they induce differing wave interactions with land and other waves. These governing factors contribute to underlying statistical distribution of the wave climate data that will be used to train the AI.

It is important to test the performance of AI surrogates according to varying distinguishing features of the domain to identify domains with similar oceanographic properties and ensure that the AI model will be used on data that falls within the distribution of the training data set (Moreno-Torres et al., 2012, p. 523). Research must then be conducted on the AI’s ability to make predictions for previously unseen domains to define the limitations of the training data.

To track the shift of dominant features, it is key to firstly establish the important factors at the pre-existing training data sites. Consideration of whether various extra domains share these common factors is then possible, to determine whether it is appropriate to use the same AI model on the new domain.

As a practical example, river inlets are an important consideration close to the coastline. However, inlets are irrelevant for domains that are a considerable distance from a river. It follows that an AI trained on a site that includes a river inlet differs in dominant features to an area of coast that is close to a continental shelf. These two areas will have different leading factors that determine the sea state; therefore, an AI trained on one of these areas will likely not perform well on the other.

Changes in classification labels are known as a class shift, a label shift or a prior probability shift (Moreno-Torres et al., 2012, p. 523). When modelling the wave climate, the dominance of wind waves, swell and currents are natural classifying labels as the interchanging dominance results in a shift of the spectral distribution of surface waves. Figure 3 visualises the variation of offshore wave types. Within the categories of wave type dominance, other factors such as seabed roughness, white-capping and depth-induced wave breaking will also induce a co-variate shift between a training data site and other domains within the same class.

To understand how the severity of the shift will affect the accuracy of the model, it is important to establish bounds for classification based on the differences of AI accuracy in various sites. Perhaps, a clustering scheme can be reiterated in response to the change in accuracy across domains to formulate feasible parameters for robust AI prediction. Bayesian methods of deep learning have also been proposed to obtain well-calibrated predictions on distribution shifted data (Seligmann et al., 2023).

Methodologies for eliminating AI bias through training data selection are actively explored in facial recognition (Naqa and Drukker, 2023) and medical diagnostics (Gichoya et al., 2023).

Without clearly defined limits within the training data, the model user may be unknowing of the test cases that lie outside the scope of the training data set. If the trained model is continuously given cases that differ from the training data set, the model will continuously display bias. A biased wave model can result in under-predicted wave heights and energy generation, which can be catastrophic for offshore deployments and activity during high-energy or storm scenarios. If the biased AI model is used to inform decision-making in the offshore renewable energy sector, daily under-prediction of energy can result in unprofitable renewable energy projects, which damage the energy transition movement.

Publications involving numerical nearshore wave models include details of the calibrated parameters and features of the domain, which affect the calculated energy spectra of the waves as reference for readers. Akin to the numerical model, it is essential that AI surrogate entails geographic details and statistical measures of the training data are included. This information informs AI model’s end-users as guidance for a suitable domain choice and can ascribe confidence in end-users on the reliability of the model. The user will be able to discern the scale of epistemic uncertainty that is affected by the training data.

Alongside use within clearly defined training data limits, end users can also re-train a released pre-trained model Venkateswarlu et al. (2023) for domain-specific applications. The re-training data set then acts to update the original data set and improve the model’s accuracy for a specific modelling task for the end-user in a process known as transfer learning (Iman et al., 2023; Su and Vijay-Shanker, 2022).

During re-training, the weights of the model are automatically updated, so it is possible to re-train the model by supplying additional data and without changing the underlying model structure. Improvements to the model from the modelling community can therefore be instated without the need for high-level coding skills allowing for decentralisation of the AI surrogate development. Lowering the requisite coding skill level allows for a larger pool of contributors to the AI surrogate’s development, meaning that the scope for training data variety and quantity can increase quickly.

Compared to the development of models that resolve governing equations, it is easier to develop AI-based models as multiple versions can be released as a result of adapting training data sets. Numerical models operate on a centralised basis, meaning that the models are originally produced by a development team as part of a modelling software suite and are then adopted by the wider research community. When community-proposed variations of numerical models gain popularity, they are added to modelling software. In the nearshore wave model field, the numerical models use outdated coding languages that are difficult to use. SWAN, TELEMAC and WW3 use the language Fortran 95 that was developed in the late 1990s and has a considerably smaller community of users. AI development is coded in newer, high-level coding languages such as Python, where there is more coding support available.

Improvements introduced by other users need also be formally coded into the model framework by the same development team to ensure that the model runs smoothly.

Another advantage to developing an AI model surrogate is the enhanced speed of simulations (Fukami and Fukagata, 2019). Time saved on computation can instead be expended on improving models in either a case-by-case or a global sense. It may be possible with future development to further characterise bias according to relevant modelling factors, such as the domain location, the size of the domain and the temporal and spatial resolution.

As with all modelling applications, the presence of bias is inevitable. To treat the issue of bias responsibly, measures must be exerted throughout development to quantify bias well and inform users of the predictive limits of an AI surrogate for best practice.

The key ethical issues and solutions discussed in the previous sections have been written with a focus on developing AI for surrogate nearshore wave modelling.

To collate the included ideas for best practices, a framework for developing AI surrogates is presented in this section. The included framework is designed to act as a working guide for developing an adaptable AI surrogate for modelling of natural systems. The guide can be used as a reference from early-stage case study application and referred to throughout the development of an AI model.

At the early stage of developing an AI framework, the aim is to develop a neural network structure with inputs that reflect the system in a particular study.

To expand a working early-stage AI model, it is important to uphold training data to consistent error measures. Continual bias and uncertainty quantification allows traceable development from early stages where changes are made incrementally. The CDS acts as a cyclic diagram corresponding to the iterative process of AI expansion. Each new application or considerable change to the AI model corresponds to a new iteration of the cycle, with more data being added to the neural network. As more data is added, the neural network may need to increase in complexity to avoid over/under-fitting, and well-encompass the underlying physics within the model.

Increasing model complexity can take the form of additional contributing inputs, or changes to the neural network structure such as adjustments to the depth, width, component types, regularisation and residual connections. Each new version must be applied to previous use cases to establish changes in predictive accuracy.

A diagram of the circular framework is displayed in Figure 4. The importance of each stage in the workflow is thereafter discussed:

• Obtain, prepare and quality check training data: For data-driven AI solutions, the quality of the training data is fundamental to the use-case applicability of the AI surrogate. This step can be skipped if no new data is added into the AI model.

With AI expansion, the sources of training data will naturally diversify. Establishing the error, noise and bias across sources will be indicative of an acceptable base standard. Comparing sources of data highlights the need for bias and noise-correction where necessary.

Quantifying known biases further indicates the maximum expected accuracy of the model to both developers and users. The highest achievable accuracy is a useful measure for AIs that are trained to recreate “ground truth” data ^[1]. Bias in the model can also occur from using inputs with varying standard deviations and ranges. The data must be normalised accordingly to balance the input data ranges in order of importance.

After quantification and correction, the data must be prepared for model input. Natural systems are time-dependent and have physical boundaries to be encoded during AI training. Accuracy will decrease in the model if the training data is not formatted to highlight patterns within the data.

Prior understanding of the seasonal decomposition within the training data indicates the required time-span considered during AI training. The features of the input must be considered to highlight spatial dependencies. Further normalisation aids to scale the data and indicate its importance according to the relative order of each input feature’s range:

• Developing the new model in verifiable or pre-used cases: With pre-processed training data, the neural network structure can be adapted.

In this stage, further additions to the AI model input/NN structure should be implemented with spatio-temporal dependency in mind. The role of the developer in this step is to structure the model inputs and the neural network components so that the existent trends and cycles within the natural system are encoded in both a high- and low-level sense. To comply with seasonal decomposition trends and other known spatio-temporal trends and cycles, the developer can shape the input, choose the dominant features that affect the subject to model at hand and choose appropriate neural network structures to test. Adopting such an approach acts to allow the neural network to encompass the intended intrinsic dependencies and avoid developing a model with bias.

For example, regularisation (Njieutcheu Tassi et al., 2023), normalisation (Peng et al., 2019, p. 67) and residual methods (Zhang et al., 2017) can be used to ensure training convergence with added complexity and increasing input size within the neural network. They can also be used to regulate the distribution of the data throughout the network to avoid loss of data. Adaptations to the neural network must be tested on previously used or empirically verifiable case studies to quantify the improvement of the model. Large improvements in accuracy are indications of effective model development.

Aside from adjusting the neural network structure, large improvements can occur with an increase in training data size or included features. When the training accuracy plateaus or decreases, it can be an indication that the neural network needs a higher complexity to process the augmented input size.

A decrease in error can also indicate that additional training data has altered the distribution of the AI’s output data. In this instance, it is important to reconsider the physical system as a whole. Additional data or features may have induced a co-variate or a label shift, highlighting limitations with associated physical restraints.

As an example from the nearshore wave model problem, if the developer uses an AI model trained on swell-dominated sea, it is likely that the AI structure’s complexity is too low to be applied to a variety of sea states because, in a nearshore area, there are often multiple wave types present. Swell waves are often accompanied by wind-driven waves. By not including wind-wave data, the developer is making an assumption that the wind-driven waves are not relevant to the problem. If instead the developer increases the data set size by adding wind-wave-dominated wave data, the distribution of the AI outputs will change alongside the distribution of the inputs, giving a co-variate shift. If the developer then adds data from an area that has a strong tidal dominance, the data experiences a label shift as the swell-dominated area is far from the coastline as tidal effects are often neglected.

Adding variables or additional data sets sequentially allows the developer to explain and document the motivations behind adapting the neural network and aid the AI’s transparency. Changes can be tracked using prediction error metrics suited to the nature of the problem, or using architecture specific tools (Zou et al., 2024). Testing the domain in previously used test cases acts as a datum to measuring accuracy changes in the AI model, showcasing robust methodology:

• Defining AI limitations – applications to new scenarios: The purpose of this stage is to inform best adoption of the AI model in future work. AI models tend to be effective when the distribution of data in a new domain or time period is well represented within the distribution of the data used for training.

The context of defining AI limitations is reflective of the prior two steps. The size and distribution of the training data set and the complexity of the AI model due to the size and included NN structural components are indicative of use cases that are outside of the AI’s predictive range.

Demonstrations of use cases that are similar to the training data show users how the model can be adapted to their specific needs. Documentation on dissimilar use cases highlights the limitations of the models’ applications and the severity of the negative effects on model accuracy. The transparency of this information can be used to inform decision makers on the use of the AI model and serves to foster trust between users in the model.

Consequently, this stage highlights focus areas for further model improvements or the need to develop a new AI model for a separate class of use cases.

The presented framework functions under the assumption that the AI is not making critical decisions. AI surrogate modelling replaces the function of numerical models under governing equations as a means to expand access to data on physical systems. The model surrogate of the physical systems category of AI use cases focus on the AI’s ability to produce empirically verifiable data. Its mitigation of bias and transparency is valued by adopting a workflow akin to pre-existing schema in science and engineering research.

New versions of each model can then be applied to new case scenarios to establish the modelling successes and limitations. This process should be reflective, incremental and well-documented to increase AI explainability. Such practices align well with pre-existing modelling development within the scientific community and allow for a larger pool of developers to join the field of AI surrogate development.

Retaining decision-making to human agency remains ethical in modelling natural systems as long as decisions are informed by reliable and trusted data. As referenced in Section 2, clean data.

In this way, it is the responsibility of the developers to minimise bias and uncertainty, define clear limitations and to create models that are conceptually understandable to its end-users. Both the end-user and developers can then well-use and contribute to future versions of AI surrogates.

The CDS can be applied to all AI applications within the physical sciences, as it naturally follows the development of classical numerical models. Many applications of AI within physics start in the 1D schema (Kolukula and PLN, 2025). Within coastal engineering, AI was first seen to be applied to fixed measured locations to forecast upcoming wave heights over the single location. Whilst the performance of the AI was satisfactory, early AI models did not perform well in other regions or locations and did not perform as well in extreme conditions. This is because the AI model is approximating physics, which evolves in both space and time, rather than solely in the 1D sense. Later versions of AI models included convolutions, which account for spatial relationships between grids (Zou et al., 2024; Jing et al., 2022). The inclusion of convolutions meant that AI models could now account for 2D governing equations. AI models were now being trained in different areas to their testing sites, as the AI could be turned to recognise the kinematic effects over space as well as over time. Referring to the points raised in Section 2 on the complexity of underlying physical equations, early convolutional AI models performed well in deep water, but faced difficulties resolving the underlying action balance equation in shallow water, where the non-linear wave theory is present. In each of these phases, there has been incremental improvement and defined limitations of the model, meaning that the next AI developer can interpret the required areas for improvement.

This evolution of incremental and ethical AI development has been described within the field of AI in nearshore wave modelling but is prevalent across the physical sciences. The criticality of defining the limitations of a new surrogate model is heightened in AI development due to the nascence of the field. Compared to classical mechanics and linear approximation schemes of differential equations, which are grounded in well-established mathematical techniques, defining and testing new AI architectures and data processing techniques are often adopted through an experimental approach rather than following the strict rules of an applied mathematical framework. Choosing specific parameters such as the learning rate of the model, training data set size and the number of layers within the AI are known as the hyperparameters, as they must be chosen before the AI is trained. Whilst there are some methods that have been developed to optimise hyperparameter choice (Smith, 2018), these approaches are not yet widely used in AI development. Instead, many high-performance AI models use empirically determined parameters (Freitas Cunha et al., 2023; Chen et al., 2023; Jimbo et al., 2025; Huang, et al., 2022; Dasbach and Wiesen, 2023; Bocquet, 2023). Detailed reporting on methodology, empirical validation and clarity on areas for improvement from AI across the full back-end is imperative so that AI models can improve not only in accuracy and robustness but also in efficiency throughout the development process.

The proposed CDS avoids the use of technical language to accommodate for the flexibility of AI architectures and applications, due to the purposeful generality of the framework. The limitations include, but are not limited to, the following: there is uncertainty about what constitutes appropriate training data for the model. In this case, the AI model may not perform well at all, meaning some iteration between pre-processing data and model development in a verifiable case study may be required. Back and forth iteration makes it difficult to determine which stage of the framework the developer is in and when to progress to the next stage of the schema:

• Developing the model in verifiable or pre-used test cases can prove difficult to recreate. Often, data is not shared between researchers, be it for financial and institutional limitations, which come alongside the grant and proposal-based nature of research funding. Unlike in other AI research areas such as in the computer sciences where there are proposed data sets used as a datum to test the performance of the AI architecture, AI development in the physical sciences is tied to physical phenomena. There is the extra requirement of pre-processing data of good quality to train the model.

• There may not be a verifiable use case available. As AI in the physical sciences is indeed physically bound, it may be the case that the AI author is developing an AI model to a new field of study or research question. It therefore may not be possible to apply a new NN architecture to a verifiable use case. In such circumstances, the developer can refer back to the core principles of transparency and bias presented in the article and clearly articulate their applied methodology, reasoning and limitations in any published work.

The purpose of defining the limitations of the CDS is to encourage adopters to define reasonable success criteria for each stage of the process when developing their AI model. In any case, the limitations presented in the CDS framework may not be considered grave if the AI author clearly defines the known limitations and methodology in their documentation, which can allow transparency for the adopters and the opportunity to mitigate any bias present in the model in future development.

The CDS framework can be used in multiple ways. Each stage of the framework can be used as prompts to structure the related published documentation to the AI model. The CDS framework can also be defined for a specific discipline, either explicitly or implicitly. Examples of implicit use of the framework for domain-specific development can be seen in the wave models governed by the action balance equation. Jing et al.’s paper (Jing et al., 2022) where the AI model that computes a 1-h forecast was first tested in a well-researched area, the Gulf of Mexico, to define hyperparameters such as the number of layers, number of filters and size of the kernel used in the convolutional neural network (CNN). When the model was successfully developed, the AI was then applied to the coast near Zhanjiang City in China, as it has comparable bathymetry to the original case study in the Gulf of Mexico.

Another domain-specific and implicit application of the CDS framework can be observed in AI developed for welding problems (Papacharalampopoulos et al., 2020, p. 111); the AI can first be tested on a well-defined paradigm case, such as a simple geometry. With successful application of a welding model to simple geometry, further complexities can be added such as combining different materials (Dogra, 2018, p. 635). By explicitly stating the methodology used in the development of the AI, readers can better understand the assumptions and scenario-specific hyperparameters that may need to be tuned in further development of the work.

Readers are invited to explicitly define the CDS in their active field of study. It is with further contribution from the community that a robust framework for ethical AI development can be defined and improved upon.

When AI is used as a surrogate for physics-based models, its transparency and bias quantification should be held to comparable standards, ensuring that simulation results can be interpreted on an equal footing. As AI surrogates increase in popularity in the nearshore wave modelling field and the study of other physical phenomena, these aspects must be addressed with prescribed relevant guidelines to encourage responsible development and usage. The transparency of numerical models was initially discussed as a comparison for the AI surrogate. Although mathematical explanation of neural networks is currently limited to basic applications; it is argued that an AI surrogate model works as a curve-fitting tool to the underlying governing physical equations in the simulated training data. The transparency of the AI surrogate is therefore unique to physics-based models, as opposed to tasks such as facial recognition where there is no pre-defined governing equation.

Addressing bias in the model is also dependent on the simulated training data set. The bias of the AI will be inherited from the data set; therefore, it is the responsibility of developers to ensure that the data sets used in training have an enforced standard of accuracy and bias. Clearly documenting statistical measures alongside geographical features of the training data set allows the users to make informed decisions on using the model and re-training the model, if necessary.

The data set needs also to be of a variety appropriate to the model’s applications, including the resolution, domain type and simulation period. Care taken to fine-tune the AI structure and parameters leads to an AI surrogate that is well understood by users and developers in terms of its predictive power and limitations.

The CDS was introduced to serve as a practical method for adopting transparent AI and addressing AI bias effectively. The CDS follows a methodology that is applied to other types of modelling, making incremental improvements and clearly defining model methodology, successes and limitations to contribute to the scientific community and support the continuation of published research. The CDS was discussed in the context of nearshore wave modelling to provide tangible context for the schema. The limitations of the model in application were also discussed to encourage readers to adapt the model for their specific field of study.

The real benefit of AI development is its potential for inclusiveness and for collaboration. AI models are written in modern coding languages that are easily adaptable to a variety of computer architectures. AI model development is well equipped to eliminate bias as model variants can be iterated and adapted more quickly to specific user needs. For nearshore activity, such as aquaculture and renewable energy generation, an AI nearshore wave model can provide valuable long-term information on the wave climate, which would otherwise be unattainable due to the computational power and accessibility costs required for standard physics-based models. With low-biased AI simulations, offshore structures can be planned with longevity and robustness at the forefront.

By keeping the end-user as priority, AI can provide reliable and accessible solutions for the nearshore wave problem. AI surrogates for physics-based models can adopt the transparency of governing physics equations and provide an adoptable modelling platform, encouraging active bias mitigation.