Toward a hybrid machine Learning–physics framework for cohesive soil erosion in climate-resilient civil infrastructure

Abstract

Cohesive soil erosion remains a critical yet insufficiently resolved challenge in geotechnical engineering, particularly in the context of climate change and sustainable civil infrastructure. Increasing frequency and intensity of extreme hydrological events, including flooding, storm surge, rapid drawdown, and prolonged rainfall associated with nonstationary climate conditions, are accelerating cohesive soil erosion processes that threaten levees, embankments, bridge foundations, dams, and nature-based shoreline systems. These climate-driven erosion processes introduce growing uncertainty into long-term infrastructure performance and resilience-oriented engineering design. Unlike non-cohesive sediment transport, cohesive soil erosion is governed by complex physicochemical interactions, including interparticle bonding, electrochemical forces, soil fabric, consolidation history, and biological activity (Zhu et al. 2008).Traditional approaches to cohesive erosion modeling rely heavily on empirical formulations, such as excess shear stress models, which express erosion rate as a function of applied shear stress relative to a critical threshold. While these models are widely used in engineering practice, their predictive capability is often limited due to site-specific calibration requirements and poor transferability under changing environmental conditions (Utley and Wynn 2012). At the other end of the spectrum, highfidelity numerical approaches, including CFD-DEM and pore-scale simulations, provide mechanistic insight but remain computationally expensive and difficult to parameterize for field-scale applications (Rahimi-Larki et al. 2025;Rahimi-Larki, Vollmann, and Jin 2024;Saparbayeva and Balakin 2023;Xu, Vaughan, and Wang 2025;Xu, Wang, and Abegaz 2025).Recent advances in machine learning (ML) offer new opportunities to address these limitations (Karniadakis et al. 2021;Raissi, Perdikaris, and Karniadakis 2019). Data-driven approaches have demonstrated success in modeling complex nonlinear systems, inferring hidden parameters, and accelerating simulations (Karniadakis et al. 2021). In particular, hybrid ML frameworks that combine physics-based models with data-driven learning have emerged as promising tools for multiscale systems (Willard et al. 2020;Yu and Wang 2024). For example, a recent hybrid approach integrates physics-guided parameter inference with physics-agnostic temporal prediction to model complex collective dynamics across scales (Xu et al. 2026;Levine and Tu 2024;Yu and Wang 2024). Although developed in a different domain, the underlying concept-assigning modeling strategies according to scale-provides a useful perspective for cohesive soil erosion. This opinion article argues that a hybrid ML-physics framework represents a necessary next step for cohesive erosion modeling in sustainable civil infrastructure. We discuss the strengths and limitations of existing methods, outline a conceptual framework, and highlight research directions that align with climate-adaptive and sustainability goals.Unlike many existing physics-informed machine learning frameworks that focus on a single modeling scale or isolated computational task, the proposed framework emphasizes a scale-aware hybrid integration strategy specifically tailored for cohesive soil erosion (Vu et al. 2020;Nearing et al. 2005). The novelty of the framework does not lie in the development of a new machine learning algorithm, but rather in the coordinated assignment of modeling paradigms according to physical scale, governing processes, and data availability (Phoon and Zhang 2023). At the microscale, physics-guided machine learning is used for parameter inference and characterization of interparticle bonding behavior. At the process scale, physics-based numerical models such as CFD-DEM and continuum erosion formulations are augmented using machine learning for surrogate modeling, adaptive calibration, and computational acceleration. At the infrastructure scale, physics-informed or physics-agnostic machine learning models are employed for large-scale prediction, monitoring, and climate-adaptive risk assessment. By explicitly linking these scales within a unified workflow, the framework seeks to address a longstanding gap between high-fidelity mechanistic understanding and practical infrastructure-scale implementation. Furthermore, the framework is motivated not only by predictive performance, but also by emerging needs in climate-resilient infrastructure, uncertaintyaware decision-making, and future digital twin integration (Tao et al. 2019;Boje et al. 2020;Fuller et al. 2020).The primary contribution of this Opinion article is the proposal of a multiscale, scale-aware hybrid ML-physics framework for cohesive soil erosion that explicitly integrates different modeling paradigms according to physical scale and data availability, while connecting microscale soil behavior to infrastructure-scale prediction and monitoring.Physics-guided and physics-informed machine learning approaches have emerged as promising tools for addressing the limitations of purely empirical or purely data-driven erosion models. In physicsguided ML, mechanistic understanding is used to inform model structure, parameter inference, or feature selection, while physics-informed ML incorporates governing equations, conservation laws, or physical constraints directly into the learning process. These approaches may improve predictive robustness, reduce physically unrealistic behavior, and enhance extrapolation capability under changing environmental conditions.Within cohesive soil erosion applications, physics-informed and physics-guided ML methodologies may support several important functions across scales. At the microscale, they may assist in inferring difficult-to-measure parameters such as critical shear stress, cohesive bond strength, and timedependent degradation behavior from experimental observations or high-fidelity simulations. At the process scale, machine learning may accelerate CFD-DEM and continuum erosion simulations through surrogate modeling, adaptive calibration, and learned constitutive relationships. At the infrastructure scale, physics-informed ML may support large-scale prediction and adaptive risk assessment while preserving consistency with governing hydrological and geotechnical principles.Unlike many existing physics-informed ML studies that focus primarily on single-scale PDE solving or surrogate modeling, cohesive soil erosion presents a fundamentally multiscale challenge involving interactions among soil microstructure, hydraulic forcing, environmental variability, and infrastructure response. This motivates the need for scale-aware hybrid frameworks capable of integrating mechanistic understanding with data-driven adaptability under climate-driven and nonstationary conditions.Empirical models, particularly excess shear stress formulations, remain the foundation of most engineering applications. These models typically express erosion rate as:□□□□ = □□□□ □□□□ (□□□□ -□□□□ □□□□ ) (1)where τc is the critical shear stress and kd is an erodibility coefficient. While straightforward, both parameters are highly variable and sensitive to soil composition, structure, and environmental conditions (Osman and Thorne 1988;Knapen, Poesen, and De Baets 2007;Yuan et al. 2022).A key limitation is that these parameters cannot be reliably predicted from basic soil properties. Instead, they require laboratory or field testing, such as jet erosion tests, which are often costly and not scalable (Al-Madhhachi et al. 2013;Maltauro et al. 2024;Yamaguchi and Sekiguchi 2011). Moreover, empirical models do not explicitly account for time-dependent processes such as consolidation, cracking, or biological stabilization, which are increasingly important under climatedriven loading cycles.Another major limitation of empirical erosion formulations is their limited transferability under nonstationary climate conditions, where future hydrological loading regimes may differ substantially from historical calibration datasets. As climate-driven erosion processes become increasingly dynamic and episodic, purely empirical formulations may struggle to provide reliable long-term infrastructure risk assessment.Mechanistic approaches, including CFD-DEM and continuum-based erosion models, attempt to explicitly represent fluid-soil interactions and detachment processes. These models provide valuable insight into microscale mechanisms such as bond breakage, floc detachment, and turbulence-driven erosion (Vowinckel et al. 2019;Rahimi-Larki et al. 2026). Mechanistic approaches are particularly valuable for investigating erosion mechanisms under extreme hydrological loading conditions, including overtopping, storm-induced wave attack, and transient hydraulic forcing associated with climate extremes.Despite their strengths, their practical application remains limited. They are often computationally intensive, making large-scale or long-term simulations difficult. In addition, accurately parameterizing interparticle forces and cohesive behavior is challenging due to the complex and heterogeneous nature of cohesive soils. Furthermore, scaling these models from controlled laboratory conditions to field-scale applications introduces additional uncertainty and complexity. Uncertainty quantification remains essential for engineering implementation of hybrid erosion models. Future frameworks should incorporate probabilistic machine learning, Bayesian parameter inference, and ensemble prediction approaches to estimate confidence bounds associated with erosion predictions, material variability, and future climate forcing scenarios. Together, these limitations highlight a fundamental gap between mechanistic understanding and practical engineering implementation.Empirical, mechanistic, and hybrid ML-physics approaches each offer distinct advantages and limitations for cohesive soil erosion modeling. Traditional empirical formulations remain attractive for engineering practice because of their relative simplicity, computational efficiency, and ease of implementation. However, their predictive capability often depends heavily on site-specific calibration and may exhibit limited transferability under nonstationary climate conditions or evolving hydraulic loading regimes.Mechanistic approaches, including CFD-DEM and continuum erosion simulations, provide greater physical fidelity by explicitly representing fluid-soil interactions, particle detachment processes, and microscale cohesive behavior. These methods offer valuable mechanistic insight but are frequently associated with high computational cost, parameterization complexity, and scalability limitations for long-term infrastructure applications.Hybrid ML-physics frameworks may provide a balance between these paradigms by integrating mechanistic understanding with data-driven adaptability. Machine learning components may accelerate simulations through surrogate modeling, improve parameter inference, and support infrastructure-scale prediction while preserving physical consistency through mechanistic constraints. Such hybrid approaches may therefore offer improved scalability and adaptive prediction capability for climate-resilient infrastructure systems operating under evolving environmental conditions.Table 1 summarizes the relative strengths, limitations, computational characteristics, and infrastructure applicability of empirical, mechanistic, machine learning, and hybrid ML-physics approaches for cohesive soil erosion modeling. As shown in Table 1, hybrid ML-physics approaches have the potential to balance physical interpretability and computational scalability while supporting multiscale erosion prediction under changing environmental conditions.Existing physics-informed machine learning frameworks are often designed for solving governing equations, surrogate modeling, or parameter estimation within a single physical scale. In contrast, cohesive soil erosion presents a fundamentally multiscale challenge involving microscale interparticle bonding, process-scale hydraulic detachment, and infrastructure-scale environmental forcing. The proposed framework therefore emphasizes scale-aware orchestration of modeling paradigms rather than reliance on a single ML architecture. This distinction is particularly important for climate-resilient infrastructure applications where data availability, computational constraints, and uncertainty vary significantly across scales.A hybrid framework identifies a pathway toward bridging the gap between empirical simplicity and mechanistic fidelity by combining physics-based models with machine learning across multiple scales. The framework can be conceptualized as three interconnected layers:At the microscale, physics-guided machine learning can be employed to infer erosion-related parameters that are difficult to measure directly, including critical shear stress, bond strength distributions, cohesive force characteristics, and time-dependent degradation behavior. This approach integrates experimental observations-such as jet erosion tests and flume studies-with physics-based numerical models to establish relationships between observable system responses and underlying physical parameters. Similar strategies have been successfully applied in other complex dynamical systems to estimate hidden variables. By enhancing parameter estimation, this method can significantly reduce uncertainty in erosion modeling. However, its effectiveness depends strongly on the availability, quality, and representativeness of training data.At the process scale, traditional approaches such as CFD-DEM and continuum erosion models can be enhanced through the integration of machine learning techniques. In this context, ML can be used to accelerate simulations by developing surrogate models, enable dynamic calibration of model parameters, and incorporate learned constitutive relationships that capture complex soil behavior. This hybridization preserves the physical foundation and interpretability of physics-based numerical models while improving computational efficiency and adaptability. Nevertheless, careful integration is required to ensure that the incorporation of data-driven components does not compromise physical consistency or violate governing principles.At the field scale, purely data-driven or physics-informed machine learning models can be employed to predict the spatiotemporal evolution of erosion using hydrologic and climatic inputs, soil properties, and monitoring data such as sensors and remote sensing. These models are particularly valuable for digital twin applications and real-time decision-making, as they enable continuous assessment of infrastructure performance under changing environmental conditions. While this approach supports large-scale and near real-time forecasting, its limitations include reduced interpretability and potential challenges in extrapolating beyond the range of training data.Within a future digital twin framework, field monitoring systems, remote sensing, and embedded sensors could continuously provide hydrological and geotechnical data for model updating. Hybrid ML-physics approaches may enable adaptive calibration of erosion predictions while preserving physical consistency through mechanistic constraints. Such integration could support real-time infrastructure condition assessment and predictive maintenance under evolving climate conditions.Figure 1 presents the conceptual workflow of the proposed hybrid ML-physics framework for cohesive soil erosion. The framework is organized into three interconnected modeling layers that operate across physical scales while exchanging information through parameter inference, model calibration, data assimilation, and adaptive updating. Climate and environmental forcing, including rainfall, flooding, wave action, and hydraulic shear stress, provide the external drivers that influence erosion processes across all scales.At the micro/bond scale, physics-guided machine learning is used to infer erosion-related parameters such as critical shear stress, erodibility coefficients, bond strength, and cohesion from laboratory testing, imaging data, and high-fidelity numerical simulations. These inferred parameters are subsequently transferred to the process scale, where physics-based numerical models, including CFD-DEM and continuum formulations, simulate soil detachment, sediment transport, and bed evolution under hydraulic loading conditions.Outputs from the process-scale simulations, together with environmental forcing data and field observations, are then incorporated into infrastructure-scale machine learning models that predict erosion progression, infrastructure performance, and associated risk. Infrastructure-scale predictions are supported by monitoring systems, embedded sensors, and remote sensing observations that continuously provide new information regarding environmental conditions and system response.The framework further incorporates feedback loops that enable adaptive model improvement.Infrastructure monitoring data are assimilated into machine learning models to improve predictive performance, while updated predictions can be used to recalibrate process-scale simulations and refine parameter estimation at smaller scales. Through these iterative interactions, the framework provides a repeatable pathway for integrating physics-based understanding with data-driven prediction, supporting sustainable and climate-resilient management of erosion-sensitive infrastructure systems. At the micro/bond scale, physics-guided machine learning infers erosion-related parameters such as critical shear stress, erodibility coefficients, bond strength, and cohesion from laboratory testing, imaging, and high-fidelity simulations. These parameters are transferred to process-scale physicsbased numerical models (e.g., CFD-DEM and continuum formulations) that simulate soil detachment, sediment transport, and bed evolution. At the infrastructure scale, machine learning models integrate environmental forcing, monitoring data, and remote sensing observations to predict erosion progression, infrastructure performance, and associated risk. Two-way exchanges between scales support parameter inference, model calibration, and data assimilation, while continuous monitoring feedback enables adaptive updating of machine learning models and calibration of process-scale simulations. The framework provides a pathway for integrating physics-based understanding and data-driven prediction to support sustainable and climate-resilient infrastructure management.The proposed framework may be implemented through a sequential workflow. First, laboratory experiments, imaging techniques, and high-fidelity simulations are used to infer erosion-related parameters through physics-guided machine learning. These parameters serve as inputs to processscale numerical models that simulate detachment, transport, and morphological evolution under hydraulic loading. Outputs from the process-scale simulations may then be combined with environmental forcing, monitoring data, and infrastructure information to train infrastructure-scale predictive models. Continuous monitoring data may further support adaptive calibration and model updating, creating a feedback mechanism that improves predictive performance over time. This workflow provides a repeatable pathway for integrating data-driven and physics-based approaches across scales.The proposed framework is not intended to directly model climate change processes; rather, it provides a modeling architecture capable of incorporating climate-related environmental forcing such as rainfall intensity, flooding frequency, storm surge loading, and hydrological variability. Through this capability, the framework may support assessment and management of erosion-sensitive infrastructure under evolving environmental conditions.. It supports climate-adaptive design by enabling prediction of erosion under future climate scenarios, and it facilitates the evaluation of nature-based solutions, including vegetation, bioengineering approaches, and living shoreline systems. In addition, the framework provides a means to assess the performance of sustainable and recycled materials subjected to erosive conditions. Its integration with monitoring data also makes it well-suited for digital twin applications, allowing continuous infrastructure assessment and informed decision-making. Furthermore, by improving predictive accuracy, the framework can help optimize maintenance strategies, thereby reducing unnecessary interventions and associated carbon emissions.Overall, these capabilities contribute to minimizing overdesign, extending infrastructure lifespan, and promoting more efficient and sustainable use of resources.The hybrid ML-physics framework represents a promising direction for cohesive soil erosion modeling, but several challenges must be addressed.Data availability and training-data limitations remain major challenges for the development of reliable hybrid ML-physics erosion frameworks. High-quality cohesive soil erosion datasets are relatively limited compared with those available for many machine learning applications. datasets often vary significantly in soil composition, hydraulic conditions, and environmental context, making integration difficult. In addition, many laboratory datasets are under controlled conditions that may not represent field-scale infrastructure behavior under extreme hydrological loading or nonstationary climate from models to infrastructure systems therefore remains a erosion processes may heterogeneous soil properties, evolving conditions, interactions, behavior, biological and climate-driven loading that are difficult to capture within limited training datasets. As a purely data-driven approaches may exhibit reduced predictive beyond the of available quantification is essential for engineering applications. Hybrid models must provide not only predictions but also confidence bounds to support decision-making. Future should integrate probabilistic ML frameworks to uncertainty and support infrastructure require development of erosion integration of laboratory and field monitoring systems, remote sensing observations, and learning frameworks capable of to evolving environmental conditions. data strategies may further improve model and support resilience-oriented infrastructure assessment under future climate consistency must remain a in hybrid ML-physics erosion modeling. While machine learning and computational efficiency, models should incorporate governing physical such as behavior, and mechanistic relationships to ensure and interpretability under addition, integration be essential for future of cohesive erosion modeling. Cohesive erosion interactions among sediment transport, and climate Future hybrid frameworks should therefore this multiscale while practical for engineering implementation and infrastructure management research should focus on hybrid frameworks capable of integrating mechanistic understanding with evolving environmental observations to support adaptive risk assessment and resilience-oriented infrastructure under future climate represents a major challenge for machine erosion prediction frameworks. ML models rely heavily on historical training datasets and may exhibit reduced predictive applied to nonstationary climate conditions involving rainfall hydrological storm surge variability, or increasingly extreme future environmental conditions may substantially from historical observations, purely data-driven models may struggle to beyond their training limitation is particularly important for climate-resilient infrastructure applications, where erosion-sensitive systems may be subjected to extreme hydrological loading conditions that are in existing datasets. Hybrid ML-physics approaches may help of these limitations by incorporating mechanistic constraints, conservation and physically informed relationships that improve model under conditions. Nevertheless, uncertainty adaptive model updating, and continuous monitoring remain essential for reliable infrastructure-scale prediction under evolving climate implementation of hybrid ML-physics erosion frameworks at the infrastructure scale presents several practical simulations involving levees, embankments, bridge foundations, dams, and shoreline systems may require computational particularly physics-based simulations with adaptive machine learning components over computational scalability while preserving physical fidelity therefore remains an important research may also require integration of heterogeneous data including embedded sensors, remote sensing observations, hydrological monitoring systems, and geotechnical in data quality, temporal and may introduce additional uncertainty into model Furthermore, continuous model updating under nonstationary climate conditions may require adaptive calibration and data strategies capable of incorporating evolving environmental implementation challenges include uncertainty across transferability between laboratory and field conditions, integration with infrastructure management systems, and interpretability of machine learning predictions for engineering decision-making. these challenges be essential for future of hybrid ML-physics frameworks in infrastructure assessment and adaptive risk management infrastructure-scale hybrid ML-physics erosion frameworks may also provide a foundation for future digital twin applications in climate-resilient civil infrastructure systems. such a framework, embedded sensors, remote sensing observations, hydrological monitoring systems, and geotechnical could continuously provide environmental and data for model updating and adaptive simulations may mechanistic while machine learning components could enable rapid prediction, and computational among monitoring systems, machine learning updating, and physics-based simulations may support adaptive infrastructure assessment under evolving environmental conditions and extreme hydrological loading. Such capabilities could improve long-term infrastructure monitoring, predictive and resilience-oriented risk management for erosion-sensitive systems including levees, embankments, dams, and shoreline challenges remain digital twin can be These challenges include data integration across uncertainty computational and under nonstationary climate conditions. digital twin integration should be as an emerging future direction for hybrid erosion modeling rather than a implementation cohesive soil erosion under climate-driven hydrological loading represents a fundamentally multiscale challenge that cannot be using purely empirical or purely mechanistic approaches Hybrid ML-physics frameworks offer a promising pathway toward integrating mechanistic computational and infrastructure-scale prediction within a unified modeling Although challenges including uncertainty computational and extrapolation under nonstationary climate conditions, such approaches may provide important opportunities for resilience-oriented infrastructure assessment and adaptive risk research should focus on development of cohesive erosion uncertaintyaware hybrid modeling multiscale data strategies, and integration of monitoring systems, remote sensing observations, and adaptive predictive models. also be to support future digital twin applications capable of continuous infrastructure monitoring and model updating under evolving environmental conditions. these advances may help establish erosion prediction frameworks capable of supporting and management of erosion-sensitive civil infrastructure the is conceptual in future implementation of hybrid ML-physics erosion frameworks require across multiple scales. include laboratory erosion such as jet erosion tests and flume with high-fidelity physics-based simulations including CFD-DEM models, and integration with field monitoring data from erosion-sensitive infrastructure under extreme hydrological loading and nonstationary climate conditions be particularly important for model and the the and the and the have and to the of the