1 Introduction↩︎

Surrogate modelling has become an indispensable tool for approximating complex computational systems across diverse fields, including engineering, natural sciences, machine learning, and artificial intelligence. By serving as cost-effective substitutes for expensive simulations or experiments, surrogate models (SMs) enable researchers to explore design spaces, optimise processes, and make predictions with significantly reduced computational overhead [1]. The landscape of surrogate modelling has evolved dramatically in recent years, driven in large part by advances in artificial intelligence. Traditional methodologies, such as nonparametric statistical methods (e.g., Gaussian processes [2]–[4], splines [5], hierarchical or mixed-variable models [6], and polynomial chaos expansion [7]) have been complemented, and in some cases outpaced, by modern AI-driven approaches. These include neural network-based surrogates [8], physics-informed neural networks [9], Bayesian neural networks [10], and conditional deep generative models [11]. Emerging paradigms such as world models, initially proposed in reinforcement learning to predict state transitions [12], and digital twins, originally defined as real-time digital mirrors of physical processes [13] but now broadly applied to system replicas, are further reshaping the field, pushing the boundaries of what surrogate models can achieve.

However, this rapid proliferation of AI-driven methods has led to a fragmented landscape. Application domains often rely on bespoke approaches, complicating performance evaluation and making it challenging to establish best practices. Key decisions, such as whether a model should be deterministic or probabilistic, whether it should incorporate domain knowledge, and how its quality should be assessed, are frequently handled inconsistently or overlooked entirely. These inconsistencies hinder reproducibility and cross-disciplinary knowledge transfer, limiting the broader impact of surrogate modelling advancements.

The primary objective of this paper is to make a case for such a unified reporting standard, particularly in light of the transformative impact of AI on surrogate modelling. A unified reporting standard would specify key components that each surrogate model should document, including input data formats, sampling design for data collection, model selection, training loss functions, evaluation metrics, uncertainty quantification, and performance on downstream tasks. By doing so, it would enhance the reliability of surrogate models and facilitate cross-domain collaborations, ensuring that advancements in one field can be effectively translated to others [14].

The need for standardisation is particularly pressing given the expanding use of SMs in critical applications such as climate modelling [15]–[18], electric motor engineering [19], reservoir development [20], epidemiology [21]–[26], drug development, protein design [27], neuroscience applications [28], physical sciences [29], groundwater modelling [30], [31], wildfire nowcasting [32], and sea-ice modelling [33]. Without a common reporting standard, it is difficult to assess the reliability, limitations, and appropriate use of SMs, particularly as they are increasingly adopted in high-stakes domains. By proposing a structured and comprehensive schema for surrogate model reporting, this paper seeks to catalyse a shift toward more consistent and transparent practices in surrogate modelling. We emphasise that the Surrogate Model Reporting Standard (SMRS) we propose is intended to be lightweight and modular.

The remainder of the paper is organised as follows: Section 2 introduces the proposed unified reporting standard and its key components (with a link to the Case Studies demonstrating the evaluation of the proposed schema on several published surrogates); Section 3 presents alternative perspectives and addresses concerns about standardisation; and Section 4 summarises the contributions and offers a call to action for the community.

2 Proposed reporting schema for surrogate models↩︎

We propose a unified reporting schema (1) that identifies the essential components each application of surrogate modelling should document. These include data sources and formats, sampling design, model structure and assumptions, training methodology, evaluation criteria, and uncertainty quantification. Inspired by reporting practices such as “model cards”  [34], this schema is adapted to the specific modelling practices, constraints, and scientific goals encountered in surrogate modelling across disciplines. Each stage of the modelling pipeline corresponds to a dimension along which developers are encouraged to explicitly report decisions made during the modelling process.

This structured approach is intended to promote transparency, improve reproducibility, and facilitate meaningful comparisons across surrogate models. In our review of 17 recent studies (see Case Studies), we observed substantial variation in which aspects of model development are reported. While most papers describe model architectures and predictive performance, few consistently report how data were collected, how sampling decisions were made, whether uncertainty was quantified, or how limitations were handled. This heterogeneity makes it difficult to assess model reliability or applicability, particularly in high-stakes or cross-domain contexts.

The schema we present is modular and model-agnostic: it accommodates a broad range of modelling approaches, from classical statistical surrogates to modern AI-based generative methods. Figure 1 outlines the pipeline that motivates the reporting structure. The subsequent subsections detail each component, and the schema may be used as a checklist throughout the model development cycle—prior to, during, and after model training—to support methodological completeness and robust scientific communication.

2.1 Do you really need a surrogate?↩︎

Before addressing how to construct a surrogate model, it is important to first assess whether one is needed in the first place. Surrogate modelling refers to the approximation of an existing, typically expensive, generative model – often a mechanistic simulator or physical system. Unlike general predictive models trained on observational data, surrogates aim to emulate known processes that are slow, non-differentiable, or otherwise costly to evaluate. While all surrogate models are predictive, not all predictive models are surrogates. The defining feature is that a surrogate stands in for a known but costly or inaccessible process, rather than modelling observational data in the absence of a mechanistic ground truth.

A surrogate is typically appropriate when the goal is to replace a computationally intensive simulator or emulate a well-defined input–output relationship. If, instead, the aim is to predict from empirical data without reference to an underlying model, the task may better fit within standard supervised learning. In many cases, a surrogate may be unnecessary or even counterproductive. Performance issues may stem from inefficient code rather than model complexity, and can often be resolved via profiling and refactoring code, or using optimisation techniques such as vectorisation, parallelisation, or just-in-time compilation (e.g., using tools such as JAX [35] or Julia [36]). If existing surrogates suffice, or if the problem is low-dimensional and computationally cheap, additional modelling may be redundant. Likewise, highly non-linear or discontinuous systems may defy accurate approximation, favouring direct numerical or hybrid methods.

Surrogates are most useful when simulations are prohibitively expensive, the input–output map is sufficiently smooth, and repeated evaluations are needed—for example, in optimisation, design exploration, or uncertainty quantification. Clarifying these conditions early helps ensure surrogate modelling is applied where it offers real scientific or computational value.

2.2 Data collection and generation↩︎

The quality and representativeness of training data are critical to the success of surrogate models. In the following subsection, we outline different sampling designs to support experimental design. In the reporting mechanism, the researchers would document and motivate the sampling design choice to assist in reproducibility. If the training data do not adequately represent the system or process being emulated, the surrogate may exhibit biased behaviour, poor generalisation, or systematic prediction errors [37]. We recommend that surrogate model developers explicitly document how training data were obtained, the underlying assumptions, and the conditions under which the data are valid. This includes two core aspects: the mode of data generation and the sampling design. We also emphasise the importance of standardised data formats to support reproducibility and integration with domain-specific tooling.

2.2.0.1 Two modes of input data.

We distinguish two main modes of training data generation in surrogate modelling: (i) data collected from real-world systems and (ii) data generated from computational systems, including both offline (“pre-generated”) and online (“on-the-fly”) simulation.

(i) Real-world data are data acquired from physical experiments, observational campaigns, or operational systems such as sensor measurements in environmental monitoring, laboratory results in drug discovery, or clinical trial records in epidemiology. Real-world data are typically collected independently of the surrogate development process and are stored for later use. This mode introduces challenges around data quality, consistency, and completeness, especially when experimental conditions or metadata are poorly documented. Bias in measurement instrumentation or sample collection protocols may propagate into surrogate model errors if not accounted for explicitly.

(ii) Computational data are generated from numerical simulators, mechanistic models, or synthetic environments. They may be collected in two ways: an offline approach, in which simulations are run in batches and stored prior to surrogate training; or an online approach, in which new simulations are generated adaptively in response to the surrogate model’s current uncertainty or performance. The online mode is particularly suited to active learning or Bayesian optimisation workflows. Recently, the use of AI-based simulators, including neural partial differential equation (PDE) solvers and physics-informed neural networks (PINNs), has enabled large-scale data generation at reduced computational cost, serving as a valuable foundation for training data-hungry surrogates.

2.2.0.2 Sampling design.

Sampling strategy has a major influence on the representativeness, coverage, and generalisability of the surrogate model [38]. Simple strategies such as random sampling, which selects points uniformly at random from the input space, and grid sampling, which arranges points on a fixed mesh, are common starting points. While these approaches are straightforward to implement and interpret, they often fail to scale to high-dimensional spaces: random sampling can leave large gaps or clusters, while grid-based methods become infeasible due to the exponential growth in sample size with dimensionality.

An extension of random sampling involves drawing from a non-uniform prior distribution, which can be advantageous when prior knowledge is available about regions of interest in the input domain. For example, inputs known to be near decision boundaries or phase transitions may warrant denser sampling. However, in highly nonlinear systems, uniformity in the input space does not translate to uniformity in the output space, which can lead to biased surrogates unless this distortion is carefully accounted for.

Consequently, more sophisticated approaches follow space-filling or adaptive strategies. Common space-filling designs include Latin hypercube sampling (LHS), Sobol and Halton sequences, and orthogonal array-based designs. These techniques offer better coverage with fewer points, especially in moderate-dimensional problems. For problems where certain regions of the input space are more informative or uncertain, adaptive sampling methods allow the model to iteratively propose new points for evaluation, guided by uncertainty estimates, error bounds, or domain knowledge. This helps balance the trade-off between exploration and exploitation.

A promising direction is to use AI-based strategies for adaptive exploration of the input space. Classical techniques such as active learning (AL) and Bayesian optimisation (BO) target regions of high uncertainty or expected gain, using query strategies that efficiently guide data collection [39], [40]. BO remains particularly efficient in low-dimensional spaces. Recent advances in meta-learning have further improved the rapid adaptation of sampling strategies across related tasks [41]. Extending these ideas, reinforcement learning (RL) offers a flexible framework, where a policy agent learns to propose input points that reduce surrogate model uncertainty or improve expected downstream performance [42], [43]. While RL offers dynamic adaptation, it often requires careful reward design and a substantial number of initial samples. Together, these approaches help mitigate the curse of dimensionality by focusing computational effort on informative regions of the input space.

2.2.0.3 Standardised data formats.

To support transparency, reusability, and integration with domain workflows, we recommend using established data standards wherever possible. Domain-specific and general-purpose formats can improve interoperability across research groups and allow surrogate models to be evaluated or reused more systematically. Examples include NetCDF for climate science [44], SMILES strings in molecular chemistry [45], HDF5 for engineering [46], Parquet for large tabular datasets [47], and GeoTIFF for raster-based geographic inputs [48].

Metadata standards such as the CF Conventions [49] or Dublin Core [50] further support reproducibility by encoding information about units, spatial and temporal resolution, variable definitions, and provenance. Consistent formatting is especially important when applying foundation-model-based data preprocessing or augmentation methods, which rely on predictable structure across inputs. When such formats are not used, authors should still clearly describe the structure, units, and assumptions encoded in their input data.

Fidelity level. Many scientific and engineering workflows provide outputs at several levels of fidelity: from coarse, inexpensive approximations to accurate but costly simulators. Multi-fidelity surrogates exploit this hierarchy by using low-fidelity data for broad exploration and high-fidelity data for refinement, thereby cutting the overall simulation budget [51], [52]. We therefore recommend documenting (i) which fidelity levels were used to train/evaluate the surrogate and (ii) how, if at all, cross-fidelity information was integrated (e.g., co-kriging, transfer learning, hierarchical loss terms).

Heterogeneous or fidelity-ambiguous datasets. In some scientific applications, surrogate models draw upon data from multiple simulators or measurement campaigns that differ in scale, noise level, or modelling assumptions, yet do not form a clear fidelity hierarchy. To accommodate such cases, the SMRS introduces a multi-source fidelity table in which each source is listed with its defining attributes, such as resolution, uncertainty level, governing equations or instruments, and mapped onto shared “fidelity axes” such as spatial, temporal, or physical realism. The comparability of each source can then be marked as comparable, partial, or not comparable. When no meaningful hierarchy exists, authors should indicate N/A and provide a short justification (e.g., “distinct experimental protocols, no common reference”). This structured record encourages transparent reconciliation of heterogeneous datasets and supports reproducible evaluation through stratified testing, such as leave-one-source-out cross-validation.

2.3 Model class selection↩︎

The choice of model class fundamentally shapes a surrogate’s capabilities, including its expressiveness, scalability, and ability to represent uncertainty. We recommend that surrogate modelling studies explicitly report key properties of the selected model class: treatment of uncertainty, parameterisation structure, conditionality, and any domain-specific constraints. This section describes each of these components in turn. Critically, they should also report the underlying model assumptions, as these can strongly affect performance; for example, an inappropriate kernel choice in Gaussian process models can lead to catastrophic failure of the emulator.

Deterministic vs probabilistic surrogates and uncertainty quantification. Deterministic (point-estimate) surrogates—splines [5] or standard feed-forward neural networks—return a single prediction per input and are typically trained by minimising a scalar loss. They are computationally efficient and often adequate for systems governed by deterministic laws. In contrast, probabilistic surrogates output a full predictive distribution, which is indispensable when modelling inherently stochastic simulators (e.g.agent-based models [21]), when accounting for parameter uncertainty, or when downstream tasks demand uncertainty propagation. Gaussian processes, Bayesian neural networks, and deep generative surrogates such as diffusion models [33] exemplify this class. Where these techniques are too expensive, approximate probabilistic techniques such as variational inference [53] can be considered. Authors should state explicitly whether a surrogate is deterministic or probabilistic, and under what modelling assumptions. Deterministic surrogates can often be augmented to provide uncertainty quantification via add-on schemes, such as deep ensembles [54] or Monte-Carlo (MC) dropout [55], [56]. When surrogate predictions are used downstream, propagating epistemic and aleatoric uncertainty—or, failing that, performing a rigorous sensitivity analysis—is essential to avoid biased decisions [57]. We therefore recommend reporting (i) whether predictive uncertainty is estimated, (ii) the method used (ensemble, MC-dropout, VI, etc.), (iii) how the resulting uncertainty is applied in the modelling pipeline, and, if applicable, (iv) whether sensitivity analysis is performed.

Parametric vs.nonparametric models. Parametric models use a fixed set of parameters and a predefined functional form, making them suitable for large datasets and high-dimensional settings. Examples include classical neural networks, splines, and transformer-based surrogates [58], [59]. Nonparametric models, such as Gaussian processes, adapt their complexity to the data and are effective in low-data regimes or when the system is poorly characterised. We recommend specifying whether the surrogate is parametric or nonparametric, and what trade-offs this entails for scalability and inductive bias.

Conditionality. Many surrogates condition outputs not only on inputs but also on auxiliary variables, such as boundary conditions or environmental settings. These conditional surrogates are especially useful for scenario analysis or modelling system families [11]. We recommend reporting whether the surrogate is conditional and specifying the conditioning variables, as this impacts generalisability.

Domain-specific constraints. Surrogates often need to respect known constraints, such as physical laws, conservation, or monotonicity. These can be embedded in the architecture or enforced via the loss function. Examples include PINNs [9] for differential equations, geometry-aware surrogates [60], and monotonic models [61]. Incorporating such constraints enhances interpretability and robustness. We recommend stating whether and how domain constraints are applied.

2.4 Learning methods↩︎

Surrogate models can be trained using a range of learning paradigms, depending on the surrogate’s structure, the nature of available data, and the requirements of the downstream task. While optimisation remains the most common approach, alternative strategies such as Bayesian inference, simulation-based inference, and reinforcement learning are increasingly used—especially when uncertainty quantification or data scarcity are critical concerns. We recommend that surrogate modelling studies clearly report the learning paradigm used in enough detail to ensure reproducibility.

Most surrogates, whether deterministic or probabilistic, are trained by explicit optimisation — either using standard algorithms such as gradient descent or quasi-Newton methods [62] or stochastic‐gradient methods such as Adam [63] or RMSProp [64], with meta-heuristics used when objectives are non-differentiable [65]. Classical Bayesian surrogates add a prior and compute the posterior explicitly in conjugate settings (e.g.with Gaussian processes) or via Markov chain Monte Carlo including its Hamiltonian variants [66]–[68]; when those are too slow, variational inference turns posterior estimation back into optimisation [53]. Generalised Bayesian inference [69], [70] widens this framework by replacing the likelihood with a task-specific loss,often a Bregman divergence [71] or proper scoring rule [72], to gain robustness to misspecification [73], [74]. High-dimensional or multi-modal outputs motivate deep generative surrogates, including variational auto-encoders [75], normalising flows [76], [77], diffusion models [78] and neural likelihood estimators [79], [80]. When explicit likelihoods are unavailable but simulators exist, simulation-based inference trains the same architectures on synthetic data [81]–[83]. Adaptive scenarios can instead be framed as reinforcement learning [84], in which a policy selects inputs or refines the surrogate to maximise an information-theoretic or task reward. Finally, AutoML systems automate architecture and hyper-parameter search through Bayesian optimisation or evolutionary strategies [85]. For any of these paradigms, authors should state: the objective or loss being optimised; the optimiser, sampler or RL algorithm; the learning-rate schedule and early-stopping rules; the prior or scoring rule if Bayesian or generalised Bayesian; the design and volume of simulator runs if using simulation-based inference; and the search space and evaluation metric when employing AutoML.

2.5 Evaluation metrics and benchmarks↩︎

A surrogate model must be evaluated not only for its predictive accuracy, but also for how well it supports the scientific or engineering task for which it was developed. We distinguish between diagnostic evaluation, which assesses statistical properties of the surrogate model itself, and task-based evaluation, which measures how well the surrogate performs in downstream applications. We recommend that all surrogate modelling studies report their evaluation methodology, including the metrics used, any ground truth comparisons, and details of benchmarking datasets or protocols.

While evaluation metrics often mirror the training objective, they can and should diverge to assess broader aspects such as uncertainty quantification, calibration, robustness, and domain-specific requirements. For example, a model trained via likelihood maximisation may be evaluated using calibration or task-level regret instead of predictive accuracy alone.

2.5.0.1 Diagnostic evaluation: distributional similarity.

For probabilistic surrogate models, it is vital to measure how well the predicted output distribution aligns with that of the true simulator. Divergence metrics such as the maximum mean discrepancy (MMD) [86], the Fréchet distance—implemented as the Fréchet Inception Distance (FID) in generative tasks [87]—and the sliced Wasserstein distance are effective in high‐dimensional settings. These diagnostics are indispensable when the surrogate seeks to capture epistemic or latent variability. A recent survey [88] maps metric choice to data modality. Authors should state the metric used, its feature representation, and whether distances are computed per output dimension, jointly, or via summary statistics.

2.5.0.2 Diagnostic evaluation: calibration.

Calibration gauges how well a model’s stated uncertainty reflects the variability seen in data. For Bayesian and other probabilistic surrogates, simulation-based calibration (SBC) [89]–[91] validates posterior consistency by: (i) sampling synthetic datasets from the prior predictive, (ii) refitting the model to each dataset, and (iii) checking that ground-truth parameters rank uniformly within the recovered posteriors. A well-calibrated surrogate yields a flat rank histogram. We advise performing and reporting SBC or an equivalent diagnostic whenever surrogate predictions are probabilistic or used in downstream inference.

2.5.0.3 Diagnostic evaluation: estimated generalisation performance of the model.

Measures such as Akaike information criteria (AIC) [92] and Deviance information criteria (DIC) [93] can be used to compare several statistical models and asses their predictive performances. In a fully Bayesian setting, leave-one-out cross-validation (LOO-CV) and the Watanabe-Akaike information criterion (WAIC) both provide a nearly unbiased estimate of the expected predictive ability of a given model [94] and can be used to compare and average several candidate models [95].

2.5.0.4 Task-based evaluation.

In many applications, surrogate models are embedded within broader decision-making pipelines. Examples include Bayesian optimisation [40], active learning [96], design of experiments [97], and uncertainty propagation [98]. In these contexts, surrogate quality should be assessed based on how it affects performance in the downstream task. For example, in optimisation, regret quantifies the efficiency with which the surrogate identifies the optimum. In uncertainty quantification, metrics such as coverage probability or predictive intervals may be more informative than mean squared error. We recommend that evaluation reports include not only predictive metrics, but also task-aligned performance indicators.

Task-based evaluation protocols and stress testing. In addition to conventional accuracy measures, the SMRS encourages authors to report metrics that directly reflect performance on the scientific or operational task for which the surrogate is built. Each study should specify a task family (e.g., optimisation, uncertainty propagation, control, forecasting) and report at least two task-relevant metrics. Examples include: quantile or extreme-event errors for climate and risk modelling; calibration and coverage probabilities for probabilistic inference; regret or sample efficiency for optimisation; and computational cost or energy use for engineering applications. Authors should also provide (i) a simple baseline model for context, (ii) a statement of compute budget or wall-time used for evaluation, and (iii) at least one stress test that probes model robustness—such as out-of-distribution scenarios, long-horizon predictions, or noisy boundary conditions. All metrics, baselines, and test conditions should be reported alongside random seeds and code paths, enabling like-for-like comparison across papers. When certain metrics do not apply, the relevant entry in the SMRS card can be marked N/A with a short justification. This explicit structure ensures that task-specific evaluation becomes reproducible and comparable across domains.

2.5.0.5 Benchmarking.

Unlike task-based evaluation, which inspects a single surrogate on one user-defined task, benchmarking pits multiple surrogates against a shared testbed, enabling fair comparison and reproducibility. Benchmark suites should span diverse modalities (e.g., PDE solvers, agent-based models, environmental simulators), include ground-truth outputs, and record the assumptions of both data and task. Ideally, they expose multi-fidelity levels and scenarios that probe distribution shift or domain extrapolation. Generic repositories such as OpenML, UCI, and Kaggle help, but surrogate-specific, versioned datasets with unified protocols remain scarce. We therefore call for curated, trust-aware benchmarks [99], and encourage authors to declare whether they used public benchmarks, in-house simulators, or synthetic data, and to release code or protocols. Adaptive, AI-generated test distributions may further stress-test surrogates and highlight failure modes.

2.6 Case studies↩︎

To illustrate how existing research aligns with or diverges from our unified surrogate modelling framework, the Case Studies provides reviews of three recent studies using SMs. These papers were selected as examples after reviewing 17 papers from various fields and determining which had the most detail to demonstrate the implementation of the SMRS framework. Each study is mapped onto the key components of our pipeline. Overall, these case studies reveal both the versatility of surrogate modelling, evidenced by its diverse applications, and the fragmentation that occurs in practice. However, the potential to learn from and reproduce these SMs is difficult without a standardised reporting framework. Extracting the relevant information from dense articles in a different domain is difficult and places an immense burden on the researcher attempting to do so. We hope that the demonstration of the SMRS in practice will speak volumes and demonstrate the ease with which relevant information can be accessed.

3 Alternative views↩︎

While a unified reporting schema for surrogate models promises significant benefits, several alternative perspectives raise valid concerns about feasibility, scope, and potential unintended consequences. We address three key critiques below and explain how our framework is designed to accommodate these concerns.

3.0.0.1 Domain-specific practices are essential.

A common concern is that surrogate modelling workflows are inherently domain-specific. For example, climate science demands rigorous uncertainty quantification [100], while aerospace applications prioritise real-time prediction and strict physical constraints [1]. Tools such as the Surrogate Modelling Toolbox (SMT) [6] and physics-informed neural networks (PINNs) [9] succeed precisely because they are tailored to specific physical regimes and data structures. Critics may argue that standardisation risks enforcing generic practices that are misaligned with field-specific constraints, such as molecular string representations in drug discovery [45] or stochasticity in agent-based epidemiological models [24]. However, our proposed schema is intentionally modular and non-prescriptive. It aims to harmonise reporting practices—such as how uncertainty is characterised or how sampling design is justified—without constraining modelling choices. Domain-specific formats, simulators, and evaluation protocols can be retained, while benefiting from improved clarity, reproducibility, and comparability. We view the framework as an enabler of cross-pollination, not a constraint on disciplinary depth.

3.0.0.2 Integration with existing tools and incentives is challenging.

Many scientific and engineering fields rely on legacy software (e.g., MODFLOW for groundwater modelling [101], NetLogo for agent-based systems [102]) or proprietary environments (e.g., ANSYS², COMSOL³), which often use bespoke data formats and provide limited support for modern metadata or validation protocols. Retrofitting such systems for standardisation can be not only technically daunting but also misaligned with prevailing academic and industrial goals, which often prioritise rapid results and project-specific outputs over generalisation, benchmarking and tedious documentation. Given these challenges, we advocate for incremental and pragmatic adoption. For example, workflows based on pre-generated simulation data (Section 2) can integrate standardised reporting during post-processing, without altering upstream simulators. Experiences from efforts such as the FAIR principles [103] demonstrate that reporting practices can evolve when supported by suitable tools, community engagement, and institutional mandates.

3.0.0.3 Standardisation may inhibit innovation.

A final concern is that any formal schema risks ossifying the field or prematurely constraining methodological innovation. Fast-evolving areas like generative surrogates (e.g., diffusion models [33]) or transformer-based architectures [8] often outpace benchmarking infrastructure or evaluation protocols. We emphasise that the proposed schema does not prescribe particular models, training paradigms, or data modalities. Rather, it encourages transparent documentation and consistent reporting across diverse approaches. This improves interpretability, enables reproducibility, and accelerates innovation by making differences in assumptions and performance explicit. Open-ended benchmarks and modular checklists allow new methods to be compared without suppressing novelty.

These critiques highlight legitimate tensions between flexibility and standardisation. Our framework responds by focusing on reporting, not regulation: it is designed to surface assumptions, highlight best practices, and support methodological rigour, not to dictate modelling choices.

4 Discussion↩︎

In this work, we have advocated for a unified reporting schema to address the growing methodological fragmentation in surrogate modelling. Our review (see Case Studies) highlights both the versatility of surrogate models and the lack of consistent documentation across domains and model classes. To address this gap, we propose the Surrogate Model Reporting Standard (SMRS), a lightweight, modular framework inspired by efforts such as model cards [34] and the FAIR principles [103].

Rather than prescribing specific tools or architectures, SMRS encourages transparent reporting of key modelling decisions, including data provenance, sampling design, model assumptions, learning method, and evaluation strategy. While many of these elements are already reported in practice, this is often done in an informal or inconsistent manner. SMRS provides a structured format aimed at improving reproducibility, supporting benchmarking, and enabling cross-disciplinary reuse. It is designed to be model-agnostic, domain-adaptable, and incrementally adoptable.

While many research papers now share code and data, open repositories alone do not ensure transparency or reproducibility. Codebases rarely state the scope, assumptions, or validity ranges of a surrogate model, and often omit design decisions that affect reuse. The Surrogate Model Reporting Standard complements open-sourcing by introducing a declarative layer that summarises what was done and, very importantly, what was not done. It explicitly records data source and generation process (e.g. offline / online generation, active-learning criteria), clarifies model assumptions (deterministic vs probabilistic, uncertainty calibration), and documents evaluation protocols and computational context (hardware, seeds, commit hashes). This concise, standardised record enables like-for-like comparisons across studies, improves auditability, and supports independent reproduction even when repositories evolve or become unavailable.

As surrogate models are increasingly deployed in high-stakes settings, from climate science to healthcare, standardised reporting will be essential for ensuring scientific credibility and real-world impact. We position SMRS as a pragmatic foundation for building more interpretable, reliable, and transferable surrogate modelling.

Practical adoption pathways. The SMRS is designed for incremental, low-friction integration into existing publication and review workflows. For authors, the recommended practice is to include a concise one-page SMRS card in the appendix and repository, listing all schema fields with evidence links, or marking Not reported / N/A where appropriate. This clarifies completeness and helps future researchers identify missing information. For reviewers, a condensed SMRS checklist offers a rapid way to verify methodological transparency and request clarifications before acceptance. The checklist focuses on coverage of the key components (data, model, learning, evaluation, and task performance), rather than on implementation details. For benchmark and survey creators, SMRS cards can serve as a foundation for curated, auditable repositories. Benchmark organisers may release third-party-audited SMRS cards for each dataset and model, enabling like-for-like comparison of surrogates under common metrics and protocols. By making reporting structured but not prescriptive, SMRS encourages community-driven convergence towards reproducible and interpretable surrogate modelling without introducing unnecessary administrative burden.

Acknowledgements↩︎

E.S. acknowledges support in part by the AI2050 program at Schmidt Sciences (Grant [G-22-64476]). T.H. is a Google DeepMind scholar and acknowledges the African Institute for Mathematical Sciences (AIMS), South Africa, for the opportunity to conduct this research as a part of his MSc. J.C. is partially supported by EPSRC grant EP/Y001028/1.

In the following section, we detail the implementation of SMRS in four exemplar papers [28], [104]–[106]. Before selecting these exemplar papers, we initially audited 17 publicly available papers from fields of climate science [104], [107], [108], complex systems [109], agent-based systems [110], [111], geophysical and Earth based modelling [105], [112]–[115], mechanics [116], material science [117] automated experiments modelling [118], as well as general physics [106], engineering [119] and deep learning applications [120]. While these selected papers are comprehensive, some details are missing, which we determine to the best of our knowledge, bearing in mind that completing these relies on cross-discipline assessments. The burden of interpretation is another motivating factor for the authors to do this in conjunction with the surrogate development. We assess the extent of the reported details with a basic code system, where a ✓indicates sufficient detail provided by the authors, a indicates some details were missing, and a ✗indicates the detail is not provided at all. In the perfect implementation of SMRS, all details would be included and marked with a ✓.

5 Using surrogate modelling to predict storm surge on evolving landscapes under climate change↩︎

6 Equation-free surrogate modelling of geophysical flows at the intersection of machine learning and data assimilation↩︎

7 Highly efficient modeling and optimization of neural fiber responses to electrical stimulation↩︎

8 Deep adaptive sampling for surrogate modelling without labeled data↩︎

References↩︎