Similarity in data distributions, overfitting and hyperparameter configurations

TL’s success depends critically on sufficient similarity between the source and target domains, particularly in the data distributions of predictor features, such as similar frequencies and magnitudes of anomalies (Lee et al., Reference Lee, Irish, Bensi and Marcy2021; Hamitouche and Molina, Reference Hamitouche and Molina2022). When this requirement does not hold, dataset shift occurs, whereby differences in data distributions undermine model generalization and can lead to negative transfer (Moreno-Torres et al., Reference Moreno-Torres, Raeder, Alaiz-Rodríguez, Chawla and Herrera2012; Chen et al., Reference Chen, Xu, Jiang, Yu, Lin, Bychkov, Hmelnov, Ruzhnikov, Zhu and Liu2021; Xu et al., Reference Xu, Lin, Hu, Wang, Wu, Zhang and Ran2023). Such dataset shifts may also emerge over time within the same coastal-estuarine system, as sea level rise, changing baseline water levels, subsidence or anthropogenic modifications alter the distribution of WLs and flood drivers (Ohenhen et al., Reference Ohenhen, Shirzaei, Davis, Tiwari, Nicholls, Dasho, Sadhasivam, Seeger, Werth, Chadwick, Onyike, Lucy, Atkins, Daramola, Ankamah, Minderhoud, Oelsmann and Yemele2026). Overfitting also limits effective TL, where DL models learn overly specific details from the training data and fail to capture generalizable patterns between source and target domains (Pan and Yang, Reference Pan and Yang2010; Peng et al., Reference Peng, Wu, Gao, Yi, Xiong, Yang and Cheng2022). Overfitting introduces noise into the transfer process and undermines predictive performance in the target domain, especially when training datasets are limited to extreme conditions or are unrepresentative of broader flooding scenarios. Moreover, models are typically developed by tuning hyperparameters to the specific conditions of the training domain, to maximize accuracy on the training set. The strong dependence of optimal hyperparameters on particular datasets complicates the effectiveness of TL, as these configurations may not transfer well to the target domain (Ma et al., Reference Ma, Cheng, Jiang, Chen, Wang and Zhai2020; Tran et al., Reference Tran, Schneider, Weber and Qin2020; Dong et al., Reference Dong, Wang, Amankwah, Wei, Hu and Feng2021; Marco et al., Reference Marco, Ahmad and Ahmad2022; Wang et al., Reference Wang, Jin, Schmitt and Olhofer2023).

Lagged and hysteresis effects

Conventional DL models often lack an explicit representation of how extreme water levels (EWLs) and associated flooding propagate from a point source across space and do not inherently encode storm-track direction (Lee et al., Reference Lee, Irish, Bensi and Marcy2021; Zhang et al., Reference Zhang, Zhang, Li and Feng2025). As a result, they struggle to capture spatially varying lags at the timing of peak water levels (WLs). For example, peak WLs recorded at coastal locations can occur hours to days before those of upstream or inland areas, and importantly, such lags vary nonlinearly in space and time (Xiao et al., Reference Xiao, Yang, Wang, Sun, Wigmosta and Judi2021; Dykstra et al., Reference Dykstra, Dzwonkowski and Torres2022). Spatially, WL variations at one location influence adjacent areas through physical forcing mechanisms such as bottom friction that controls flood wave propagation and dissipation of energy in coastal-estuarine systems. Likewise, coastal hydrodynamic nonlinear interactions (Xiao et al., Reference Xiao, Yang, Wang, Sun, Wigmosta and Judi2021; Moftakhari et al., Reference Moftakhari, Muñoz, Akbari Asanjan, AghaKouchak, Moradkhani and Jay2024; Sakib et al., Reference Sakib, Muñoz and Wahl2025), together with morphology, can either amplify or attenuate WLs (Prandle, Reference Prandle1985; Hoitink and Jay, Reference Hoitink and Jay2016; Talke and Jay, Reference Talke and Jay2020). Temporally, the timing of peak WLs varies across inland, transition and coastal regions due to factors like distance from the flood source, bathymetry, backwater effects and flood connectivity, introducing lagged and hysteresis effects (Brunner et al., Reference Brunner, Gilleland, Wood, Swain and Clark2020; Talke and Jay, Reference Talke and Jay2020). If models implicitly assume near-simultaneous peak occurrences across a spatial domain, they can yield erroneous lead or lag time predictions, resulting in overestimation or underestimation of flood impacts (Yu et al., Reference Yu, Huang and Li2024). When flood propagation from point sources is not adequately represented in the DL architecture, transferred models tend to misalign the magnitude and timing of flood peaks across space.

Training DL models only on extreme conditions to improve the model’s performance

Training DL models only on extreme conditions could be disadvantageous for two main reasons. First, there might be insufficient training data for extreme events (or WLs) at any area (or gauge station). As an illustrative example, and recognizing that extreme event frequency and duration vary substantially by region and threshold definition (e.g., annual maxima, peaks-over-threshold or return periods), events lasting about 2–4 days and occurring twice every 5 years in a given area would amount to only about 16 events, or 32–64 extreme days out of ~14,600 days in over 40 years. Such a limited number of extreme events is typically inadequate for training a DL model unless supplemented with many synthetic events. Second, a model trained exclusively on extreme conditions does not recognize sudden changes or anomalies between normal and extreme conditions, even though distinguishing these regimes is a primary objective of flood prediction models. In that case, it is unclear whether the model has truly learned to identify extreme events. It is only by training on the full historical record while explicitly emphasizing extreme periods (e.g., through loss reweighting or architectural choices) that we can be more confident that the model will accurately detect the timing and occurrence of extremes.

Assessing accuracy solely on goodness-of-fit metrics

Model accuracy in DL flood prediction is often evaluated based on favorable goodness-of-fit metrics. However, this approach can be deceptive, particularly for imbalanced datasets emerging in flood modeling. For example, in a dataset of 10,000 instances where only 500 represent flood events, a model that predicts “no flood” for every case would still achieve 95% accuracy, even though it fails to identify any flood events. Also, accurate prediction of peak WL magnitude is often prioritized, with timing considered secondary once validation accuracy exceeds a high threshold (Dong et al., Reference Dong, Wang, Amankwah, Wei, Hu and Feng2021). Yet, small timing errors between predicted and actual peaks of storm tide can lead to large discrepancies in flood impact assessments, underscoring the need for precise timing in spatiotemporal analyses. Correct temporal variations are critical for effective real-time flood response, particularly in large domains with heterogeneous flood dynamics.

Explainable deep learning

The ability of DL models to identify complex nonlinear interactions between input features and target variables is sometimes misinterpreted as evidence that they understand the underlying physics. This raises concerns about their interpretability, as tools such as SHAP, LIME and permutation importance primarily quantify the contribution of predictor variables to training accuracy rather than their physical relevance to flood processes. For DL models, these nonlinear interactions are learned from the data distributions (Reichstein et al., Reference Reichstein, Camps-Valls, Stevens, Jung, Denzler, Carvalhais and Prabhat2019), and TL is typically more accurate when this distribution is similar in both training and test sets (Gong et al., Reference Gong, Zhang, Liu, Tao, Glymour and Schölkopf2016; Zhuang et al., Reference Zhuang, Qi, Duan, Xi, Zhu, Zhu, Xiong and He2020), even in the absence of explicit physical understanding. Data distributions are shaped by physical conditions (Figure 2), including topography, hydrological and climatic characteristics, which influence critical variables such as WLs (Marcos et al., Reference Marcos, Rohmer, Vousdoukas, Mentaschi, Le Cozannet and Amores2019; Serafin et al., Reference Serafin, Ruggiero, Barnard and Stockdon2019; Almar et al., Reference Almar, Ranasinghe, Bergsma, Diaz, Melet, Papa, Vousdoukas, Athanasiou, Dada, Almeida and Kestenare2021; Costa et al., Reference Costa, Bryan and Coco2023). Physical differences across geographical domains can lead to divergent data distributions, posing a significant challenge for TL techniques (Daramola et al., Reference Daramola, Muñoz, Muñoz, Saksena and Irish2025b, Reference Daramola, Muñoz, Sakib, Thurman and Allen2026).

Figure 2.

Conceptualization of the influence of data distribution and physical conditions in transfer learning performance for extreme water level (EWL) prediction. The deep learning (DL) model is first trained at an ocean-exposed station (domain 1), where it achieves accurate pattern recognition of EWLs (panel a). When the DL model is transferred to a barrier-protected station (domain 2) of a different morphologic setting, shifts in predictor distributions lead to degraded performance in terms of the average KGE and NSE values (panels b and c).

Figure 2. Long description

The diagram consists of three main panels and two central icons connected by dashed blue arrows.

Panel a, at the top left, is a line graph titled Accurate pattern recognition. The y-axis is Water level in meters from negative 0.5 to 1.5. The x-axis shows dates from 15-Sep-2003 to 21-Sep-2003. A solid red line for observations and a dashed black line for predictions overlap closely, with K G E 0.80 and N S E 0.97.

At the top center is a bar chart icon labeled Data distribution features.

Panel c, at the top right, contains four satellite photos of different coastal morphologies labeled with north arrows and scale bars, representing Physical conditions such as bathymetry and morphology.

Panel b, in the center, is titled Transfer learning. It contains a map showing three stations: T 1 on an exposed coast, and T 2 and T 3 behind a barrier. Arrows point from T 1 to T 2 and T 3. Below the map is a line graph titled Transfer from T 1 to T 2. The y-axis is Water level in meters from 0 to 3. The x-axis shows dates from 06-Oct-2016 to 12-Oct-2016. A dashed red line for observations sits below a solid black line for predictions, showing degraded performance with Average K G E 0.36 and Average N S E negative 0.37.

At the bottom left is a Neural Network model icon, which receives arrows from panel a and points toward the transfer learning process in panel b.

Prioritize storm-relevant extreme patterns in the learning of the water level signal

First, the selection of input features and DL architectures should be informed by physical processes that capture the events’ EWLs and associated flood dynamics. DL modelers should then aim to ground both the model structure and improvements in training accuracy in the physical drivers of flooding (Kumar et al., Reference Kumar, Sharma, Mangukiya, Tiwari, Ramkar, Rathnayake, Kumar, Sharma, Mangukiya, Tiwari, Ramkar and Rathnayake2025). That is, architectural modifications so that modules, data pathways and fusion operations reflect the real physical decomposition and coupling of processes (e.g., tides, surge, river flow, rainfall-runoff and waves). In coastal-estuarine systems subject to compound flooding, TL-based flood models should also evaluate whether these interacting drivers are comparable between source and target domains. Moreover, methodological advances should emphasize training strategies that improve a model’s sensitivity to physically meaningful flood-related signals (e.g., periods of high-WLs, surge, etc.), rather than optimizing primarily for frequent, repetitive patterns in the training data.

When only 32–64 extreme days are available out of ~14,600 days, as in the illustrative example in section “Training DL models only on extreme conditions to improve the model’s performance,” extremes become underrepresented in the training data, making it difficult for DL models to learn and detect EWLs. In such cases, it is important to modify the architecture to focus on what matters most (Daramola et al., Reference Daramola, Muñoz, Muñoz, Saksena and Irish2025b), which is to prioritize storm-relevant patterns in the learning of WL signals (Figure 2a). For example, an attention mechanism (Vaswani et al., Reference Vaswani, Shazeer, Parmar, Uszkoreit, Jones, Gomez, Kaiser and Polosukhin2017) can be introduced and customized to emphasize the influence of EWL periods (Yang et al., Reference Yang, Zhang, Zhang, Lin, Wang and Feng2024), thereby improving the model’s ability to learn and represent these events (Orozco López et al., Reference Orozco López, Kaplan and Linhoss2024). In practice, high attention weights often concentrate on time windows where the dynamics are more complex or harder to approximate, which frequently coincide with periods of EWLs (Daramola et al., Reference Daramola, Muñoz, Muñoz, Saksena and Irish2025b). If such techniques are incorporated into DL architectures, models are better positioned to capture flood events in unseen test datasets after the training stage and predict their magnitudes and timing with higher accuracy (Zhang et al., Reference Zhang, Zhang, Li and Feng2025). While such techniques do not fully replace the role of explicit conservation equations, they enhance the capture of sudden and/or extreme changes in the WL signal and ensure internal consistency in the learned data patterns.

Embed spatial propagation consistent with coastal-estuarine hydrodynamics around physically aware DL frameworks

For DL models that aim to propagate EWLs from tide-gauge point sources across a domain, sparse observation networks make it difficult to learn how EWLs evolve spatially (Figure 3b). A relatively simple strategy is to split a model domain into clusters with their centroid coinciding with the location of representative gauges. In that sense, time series from each gauge can represent the coastal-estuarine system’s response of the corresponding cluster to extreme conditions (Daramola et al., Reference Daramola, Muñoz, Moftakhari and Moradkhani2025a). Nevertheless, this approach does not account for variability within the cluster and thus cannot resolve spatial differences in the timing and magnitude of extremes (Farahmand et al., Reference Farahmand, Xu and Mostafavi2023; Yu et al., Reference Yu, Huang and Li2024; Fathi et al., Reference Fathi, Liu, Fernandes, Hren, Terry, Nataraj and Smith2025).

Figure 3.

(a) A 40-day time series window of observed water levels, predicted astronomical tides and nontidal residuals (NTR) with the shaded interval highlighting storm-driven extreme period. (b) Study domain showing spatial partitioning (clusters) around tide gauges (red crosses) and the corresponding graph representation. The inset illustrates an eight-node neighborhood connectivity used in the graph convolutional network framework, where each grid cell/node exchanges information with its surrounding neighbors to propagate WL signals from gauge locations across the model domain.

Figure 3. Long description

Panel a is a line graph titled 40 days window, 3 day time step h. The Y-axis represents Water level in meters, ranging from negative 0.5 to 2.0. The X-axis spans from September 1, 2003, to October 8, 2003. Three lines are plotted: a blue line for Actual water level, a green line for N T R, and an orange line for Tide prediction. A vertical orange shaded region around September 18 highlights a significant spike where the actual water level reaches nearly 2.0 meters, driven by a sharp increase in the N T R green line while the tide prediction remains low.

Panel b is a geographical map with Latitude on the Y-axis and Longitude on the X-axis. The map shows a coastal region partitioned into polygonal clusters. Red crosses labeled i sub 1 through i sub 21 mark tide gauge locations. The clusters are concentrated along a central waterway. In the bottom-right of panel b, an inset titled 8-node connectivity shows a central node i with eight arrows pointing outward to numbered nodes 1 through 8 in a compass-like arrangement, representing the spatial information exchange used in the graph convolutional network.

Sophisticated approaches like using encoder-decoder architectures (e.g., U-Net) can transform sparse gauge information into a latent space representation that is then decoded to produce dense WL maps. While this enables propagation from scarce observations to a dense grid, the resulting fields are often closer to a learned interpolation than a true estimation of the underlying dynamics, particularly in regions far from gauges or under unprecedented extreme events. In contrast, graph convolutional networks (GCNs) can be configured with each grid cell treated as a node and edges connecting its neighbors within the model domain (Daramola et al., Reference Daramola, Muñoz, Sakib, Thurman and Allen2026). Gauge locations act as observed source nodes, and information is propagated iteratively from node to node through the graph until the entire domain is covered. By explicitly using local connectivity to propagate WL signals, GCN-based approaches could provide spatial propagation that is more representative of the expected coastal-estuarine hydrodynamics than cluster-based or purely latent space interpolation approaches; thus, supporting more robust TL across heterogeneous domains. Hence, with the accurate capture of extreme patterns, TL is organized meaningfully rather than on purely statistical probability.

The two steps discussed above are physics-guided machine learning techniques, in which the physical characteristics of extreme events determine feature selection, network architecture and training design, as well as the estimation of model predictions. Hence, physics-guided DL models can explore the connection among physical components, processes and data distributions, which is essential for enhancing the performance and applicability of TL across geographically and morphologically distinctive regions. By elucidating these connections, modelers can develop more informed strategies for selecting appropriate source domains and adapting DL models to account for physical variations. Physical awareness in DL frameworks is, therefore, crucial because it validates whether the chosen input features can improve the model’s performance when compared to physics-based model simulations. On the other hand, it provides information on the similarities and differences in dynamic processes, understanding the conditions that matter for model transferability.

Establishing physics-informed machine learning

There are three main classes of physics-informed machine learning (PIML), namely, physics-informed neural networks (PINNs), differentiable modeling (DM) and physics-guided machine learning, each with distinct strengths. PINNs enforce the system’s governing equations and associated boundary or initial conditions by embedding them into neural network training, most commonly through residual terms in the loss function (Sun et al., Reference Sun, Yoon, Shih and Zhong2022; Qin et al., Reference Qin, Su, Chu, Zhang and Song2023). By contrast, DM couples process-based equations and learnable components within a fully end-to-end differentiable framework. In DM, the physical equations provide structural priors, whereas neural networks are used to learn parameterizations, unresolved processes or model residuals (Shen et al., Reference Shen, Appling, Gentine, Bandai, Gupta, Tartakovsky, Baity-Jesi, Fenicia, Kifer, Li, Liu, Ren, Zheng, Harman, Clark, Farthing, Feng, Kumar, Aboelyazeed, Rahmani, Song, Beck, Bindas, Dwivedi, Fang, Höge, Rackauckas, Mohanty, Roy, Xu and Lawson2023). At a broader level, physics-guided ML (section “Extreme water level patterns and propagation from observation stations”) refers to the general strategy of injecting physical knowledge into machine learning models through architectural constraints, regularization, priors, pretraining or other mechanisms to improve physical realism and robustness (Daramola et al., Reference Daramola, Muñoz, Sakib, Thurman and Allen2026). All three approaches are important for advancing coastal flood prediction, but each has limitations when applied to coastal systems characterized by complex nonlinearity, multiscale spatiotemporal variability and, in some cases, turbulence-affected hydrodynamics.

Unified coastal-estuarine flood prediction framework

Physics-informed ML approaches can be integrated into a unified flood prediction framework. Here, neural operators serve as rapid surrogate solvers for near-shore shallow water equations, and differentiable hydrological models provide more accurate upstream river discharge boundary conditions. Hence, they enable generalization across diverse coastal systems through TL. For instance, Fourier Neural Operators (FNOs) learn solution operators for parametric partial differential equations (PDEs), mapping initial and boundary conditions directly to solutions without explicit time-stepping and achieving speedups of $ {10}^2-{10}^5 $ over conventional numerical solvers (Li et al., Reference Li, Kovachki, Azizzadenesheli, Liu, Bhattacharya, Stuart and Anandkumar2021). Extensions such as Spherical FNOs enable stable long-term rollouts for shallow water dynamics on the sphere (Bonev et al., Reference Bonev, Kurth, Hundt, Pathak, Baust, Kashinath and Anandkumar2023), while graph-based operator architectures naturally accommodate the unstructured meshes characteristic of coastal domains (Shi et al., Reference Shi, Xu, Wurster, Guo, Woodring, Van Roekel and Shen2022).

Sensitivity fidelity also matters. Behroozi et al. (Reference Behroozi, and and Kifer2025) showed that standard neural operators can learn highly accurate solution trajectories while producing substantially inaccurate parameter sensitivities (e.g., $ {R}^2>0.99 $ for solutions vs. $ {R}^2<0.21 $ for sensitivities), which could undermine their use in coupled optimization or data assimilation frameworks for coastal applications. Sensitivity-constrained neural operators (SC-FNOs) address this limitation by incorporating gradient supervision, maintaining sensitivity accuracy with only modest additional computational cost (~30–130% increase in training time). Despite these advances, neural operators still face challenges in capturing key near-shore processes, including shock phenomena (e.g., hydraulic jumps and bores), wetting and drying fronts and generalization to out-of-distribution bathymetric conditions.

Importantly, the quality of boundary conditions in coastal–estuarine models depends critically on the accuracy of upstream hydrologic predictions. Recent advances in differentiable hydrologic modeling provide substantially more accurate estimates of river discharge and freshwater inputs to coastal regions than traditional global water models. For example, Ji et al. (Reference Ji, Song, Bindas, Shen, Yang, Pan, Liu, Rahmani, Abbas, Beck, Lawson and Wada2025) introduced a high-resolution, physics-embedded differentiable model that identified previously unrecognized declining trends (>1.5% per year) in freshwater inputs to European estuaries, achieving significantly higher trend prediction accuracy ( $ {R}^2=0.68 $ ) than established global water models ( $ {R}^2<0.46 $ ). These models enforce strict mass balance and provide physically interpretable diagnostic variables (e.g., evapotranspiration, baseflow and soil moisture), thereby supporting both physical interpretation and stakeholder communication. Moreover, Song et al. (Reference Song, Sawadekar, Frame, Pan, Clark, Knoben, Wood, Lawson, Patel and Shen2026) demonstrated that differentiable hydrologic models outperform LSTM-based models under unseen extreme conditions (return periods >50 years), reducing peak flow errors in 80% of cases. This reflects mass conservation and storage-dependent flow constraints, which enable physically consistent responses to unprecedented inputs. Together, these advances suggest that improved predictions of extreme-event river discharge can provide more reliable boundary conditions for coastal flood models.

TL can leverage accumulated knowledge across systems to learn internal representations of recurring coastal–estuarine and riverine dynamics. For example, Ma et al. (Reference Ma, Feng, Lawson, Tsai, Liang, Huang, Sharma and Shen2021) demonstrated that LSTM models pretrained on 671 US basins can be successfully transferred to basins in Chile, Great Britain and China, achieving significantly improved performance even with only 1 year of local data. Moreover, the benefits of TL increase with the size and diversity of the source dataset, confirming that hydrologic systems worldwide share exploitable commonalities. This success, together with the demonstrated scaling benefits of large-data training in differentiable models (Ji et al., Reference Ji, Song, Bindas, Shen, Yang, Pan, Liu, Rahmani, Abbas, Beck, Lawson and Wada2025), motivates developing advanced unified models that encode general hydrologic and hydrodynamic knowledge (Shen et al., Reference Shen, Appling, Gentine, Bandai, Gupta, Tartakovsky, Baity-Jesi, Fenicia, Kifer, Li, Liu, Ren, Zheng, Harman, Clark, Farthing, Feng, Kumar, Aboelyazeed, Rahmani, Song, Beck, Bindas, Dwivedi, Fang, Höge, Rackauckas, Mohanty, Roy, Xu and Lawson2023). However, such models should be viewed as a research direction requiring careful global data curation, physics-aware pretraining, out-of-distribution evaluation and safeguards against transferring biases from data-rich to data-sparse regions. In operational frameworks, TL-based flood models must communicate uncertainty clearly, through probabilistic outputs with confidence intervals, to support emergency managers and decision-makers, particularly in data-limited regions.