The Fusion Mechanism and Prospective Application of Physics-Informed Machine Learning in Bridge Lifecycle Health Monitoring

Abstract

Bridge health monitoring is crucial for ensuring the safety and durability of infrastructure. In traditional methods, physics-based models have high interpretability but are difficult to handle complex nonlinear problems, while purely data-driven machine learning methods are limited by data scarcity and physical inconsistency. Physics-informed machine learning, as an emerging “gray box” paradigm, effectively integrates the advantages of both by embedding physical laws (such as control equations) into machine learning models in the form of constraints, priors, or residuals. This article systematically elaborates on the core fusion mechanism of physics-informed machine learning (PIML) in bridge engineering, innovative applications throughout the entire lifecycle of design, construction, operation, and maintenance, as well as its unique data augmentation strategy. Research has shown that PIML can significantly improve the accuracy and robustness of damage identification, load inversion, and performance prediction, and is the core engine for constructing dynamic and predictive digital twin systems. Despite facing challenges in complex physical modeling, loss function balancing, and engineering interpretability, PIML represents a fundamental shift in bridge health monitoring towards intelligent and predictive maintenance by combining advanced strategies such as active learning and meta learning with IoT technology.

1. Introduction

As the hub of modern transportation infrastructure, the structural safety and durability of bridges are directly related to economic development and public safety [1]. However, under the long-term coupling effects of environmental erosion, material aging, increasing traffic loads, and extreme natural disasters, bridge structures inevitably experience performance degradation and accumulated damage, which may even lead to catastrophic consequences [2,3]. Therefore, developing efficient and accurate structural health monitoring methods to achieve real-time perception of bridge structural status, early diagnosis of damage, and safety prognosis has become a crucial and challenging task in the field of civil engineering.

Traditional bridge health monitoring methods mainly follow two paradigms: physically model-based methods and data-driven methods. Although physical models (such as finite element model updates [4,5,6]) have clear physical mechanisms and high interpretability, their construction heavily relies on expert knowledge, and they are often computationally expensive and have insufficient adaptability when facing structural nonlinearity and model uncertainty problems. On the other hand, data-driven methods represented by machine learning can mine potential patterns from massive monitoring data and demonstrate powerful capabilities in damage classification [7], response prediction [8], and anomaly detection [9]. However, these “black box” models often lack physical consistency in their prediction results, and their generalization ability significantly decreases when training data is scarce or noisy, making it difficult to apply them to the complex and ever-changing environment of real bridges in bridge health monitoring (BHM) [10].

To overcome the above bottlenecks, PIML has emerged, which is known as a “gray box” modeling paradigm that integrates physical laws and data intelligence [11]. PIML distinguishes itself from earlier, more loosely coupled hybrid approaches (e.g., simply using physical model outputs as features in a separate machine learning model, or using data-driven models to fit parameters within a fixed physics-based framework). Instead, PIML’s core innovation is the deep and systematic embedding of physical laws (such as governing equations, conservation laws, boundary conditions) directly into the training process and/or the architecture of the machine learning model itself [12,13]. This fusion mechanism enables PIML to inherit the ability of machine learning to process high-dimensional and nonlinear data, as well as the interpretability and extrapolation of physical models, providing a new technological path for solving practical monitoring problems, such as small samples and high noise.

While recent reviews have discussed PIML in general computational mechanics or broad civil engineering contexts, there remains a notable absence of systematic synthesis specifically tailored to the unique complexities of bridge engineering, such as aerodynamic instability, scour-induced failure, and high-dimensional vehicle–bridge coupling systems. Most existing surveys focus predominantly on damage detection in the operation phase, often overlooking the potential of PIML in the design, construction, and predictive maintenance phases. To bridge this gap, this article aims to systematically elucidate the fusion mechanisms and prospective applications of PIML throughout the entire bridge lifecycle. The main contributions of this review are threefold. (1) Unlike generic classifications, this paper deconstructs PIML methodologies into four distinct paths relevant to bridge structures: physical constraints (regularization), physical priors (architecture), hybrid modeling (residual learning), and physical discovery (sparse identification). This framework clarifies how different embedding strategies address specific bridge engineering challenges, such as model uncertainty and data scarcity. (2) This paper extends the scope of PIML application beyond traditional damage detection. This review comprehensively surveys innovative applications across the full lifecycle, ranging from high-fidelity virtual wind tunnel simulations in the design phase and strain field reconstruction in the construction phase, to digital twin-based prognostic maintenance in the operation phase. (3) Recognizing the gap between academic research and engineering practice, we critically analyze current bottlenecks, including multi-objective loss balancing and cross-structure generalization. We further propose forward-looking strategies, such as physics-guided active learning and meta-learning, to facilitate the deployment of PIML in real-world bridge management systems.

2. Survey Methodology

To ensure a comprehensive and rigorous review of the state-of-the-art in PIML for bridge engineering, this study adopted a systematic literature review (SLR) approach. This methodology ensures the reproducibility of the research and minimizes selection bias.

2.1. Search Strategy and Data Sources

A comprehensive search was conducted across four major academic databases: Web of Science (WoS), Scopus, IEEE Xplore, and the ASCE Library. These databases were selected to cover high-impact journals in civil engineering, computer science, and mechanical systems.

The search query was designed to capture the intersection of three domains: Methodology (PIML), Application Object (Bridges), and Task (Health Monitoring/Lifecycle Management). The specific Boolean search strings used were as follows: (“Physics-Informed Machine Learning” OR “Physics-Guided Machine Learning” OR “PINN” OR “Physics-Informed Neural Networks”) AND (“Bridge” OR “Civil Infrastructure”) AND (“Structural Health Monitoring” OR “Damage Detection” OR “Digital Twin” OR “Load Identification”).

Note on terminology: Particular attention was paid to variations in terminology. While “Physics-Informed Machine Learning (PIML)” is the standard term adopted in this review, searches also included “Physics-Guided” and “Theory-Guided” to ensure no relevant early-stage research was omitted.

2.2. Inclusion and Exclusion Criteria

To ensure the quality and relevance of the review, the retrieved records were screened based on the following criteria:

Inclusion Criteria: Articles must explicitly propose or apply a machine learning model that integrates physical laws (ODEs, PDEs, physical constraints) for bridge engineering applications. Peer-reviewed journal articles and high-impact conference proceedings published between 2018 and 2025 (given the recent emergence of PINNs). Full text available in English.

Exclusion Criteria: Studies using standard ML (e.g., CNN, LSTM) without explicit physical integration. Studies focusing solely on Finite Element Model (FEM) updating without a learning component. Articles applying PIML to non-civil structures (e.g., biological systems, fluid dynamics without structural interaction), unless offering a critical transferable methodology.

2.3. Data Extraction and Classification Framework

After screening, the selected papers were analyzed and classified according to a two-dimensional framework: (1) how physics is embedded (e.g., loss function constraints, architecture design, or hybrid residual modeling) and (2) the specific engineering phase addressed (design/simulation, construction, or operation/maintenance). This systematic framework allows for a structured evaluation of PIML’s capabilities and limitations across different engineering contexts, moving beyond a simple enumeration of studies.

2.4. Implementation Tools

The literature management and deduplication were performed using EndNote (version 20). The screening, data extraction, and classification processes were conducted manually by the author team, with results organized and analyzed in a structured spreadsheet to ensure consistency and facilitate the identification of research trends.

3. The Bottleneck and Evolution of Traditional Bridge Health Monitoring Methods

The development process of bridge health monitoring is essentially a collision, verification, and evolution of two paradigms driven by physical mechanisms and data-driven approaches. Although both have their own focuses, they both face inherent bottlenecks in practical applications, which together give rise to an inherent need to evolve towards a fusion paradigm [14].

3.1. Physical Model: The “Idealization” Dilemma Under High Interpretability

The method based on physical models (also known as the model updating method) takes the finite element model as the core [15,16], calibrates the model parameters to match the response with the measured data, and thus achieves damage identification. The core advantage of this type of method lies in its solid physical foundation and high interpretability of the results. They do not rely on a large amount of historical damage data and can be diagnosed solely by comparing mathematical models with on-site testing, which is particularly important for existing bridges lacking damage records.

(1)

Model uncertainty: Finite element models are essentially simplifications of real structures. Simplification assumptions, inaccurate boundary conditions, and idealization of material constitutive relationships during the modeling process can introduce significant modeling errors, leading to “model distortion” [17].

(2)

High computational cost: For large and complex bridge structures, the establishment and iterative updating of high-fidelity finite element models require significant computational resources and time, making it difficult to meet the requirements of real-time or quasi-real-time monitoring [18].

(3)

Insufficient nonlinear processing capability: Traditional model updating methods are mostly based on linear or weak nonlinear assumptions, which make it difficult to effectively capture strong nonlinear damage processes such as concrete cracking and steel yield, limiting their application in structural limit state assessment [19].

Case studies, such as model updates for the Z24 bridge [17] and Bayesian model updates for the steel truss bridge [20], have successfully demonstrated the capability of this method, but also fully exposed its high dependence on model accuracy and computational resources. To mitigate the computational burden of full-model updating, alternative strategies like the stiffness separation method for partial-model-based identification have been developed for long-span steel truss bridges, offering a balance between physical interpretability and analysis efficiency.

3.2. Data Driven Approach: The “Black Box” Behind Flexibility and Data Dependencies

With the development of sensing technology and artificial intelligence [21], pure data-driven methods (especially machine learning) have injected new vitality into BHM [22]. This type of method does not require an explicit physical model and directly learns the complex mapping relationship between damage-sensitive features and structural states from monitoring data such as acceleration and strain.

Its significant advantages are reflected in the following:

(1)

Powerful pattern recognition capability: It is capable of capturing subtle damage features that are difficult for the human eye or traditional methods to detect from massive, high-dimensional data.

(2)

Flexibility in handling complexity and nonlinearity: It has a natural adaptability to the nonlinear and non-stationary characteristics of structural behavior.

(3)

Fast inference speed: Once the model training is completed, its online application inference speed is extremely fast, suitable for real-time state evaluation.

However, as a “black box” model, its inherent flaws severely limit its credibility in safety-critical bridge engineering:

(1)

Physical inconsistency: Model predictions may violate fundamental physical laws (such as energy conservation), leading to absurd results in data-scarce regions [23].

(2)

Weak generalization ability: Model performance heavily relies on the quality and completeness of training data. When environmental conditions, load patterns, or damage types exceed the range of the training set, its performance will sharply decline [24]. For example, collecting labeled data of real bridges in various damage states is extremely costly and unethical, resulting in a scarcity of damage samples.

(3)

Overfitting risk: The model may only remember the noise or specific patterns in the training data, rather than the true damage mechanism, resulting in poor performance on unknown data.

Numerous cases highlight its duality: backpropagation neural networks and long short-term memory networks perform well in predicting the crack width of continuous beam bridges [8]. Support vector machine and K-nearest neighbor classifier achieve high accuracy in bridge damage localization [7,25]. However, these successes are all based on the ideal premise of high data quality and similar operating conditions to the training set.

3.3. From Opposition to Complementarity: The Inevitability of Integration

In summary, there is a complementary bottleneck relationship between physical models and data-driven methods (Figure 1): physical models have rich knowledge but inflexible data, while data-driven methods are flexible but physically ignorant. Physical models are limited by “model uncertainty”, while data-driven methods are limited by “data uncertainty”.

The evolutionary logic clearly points to the inevitable path of combining the advantages of the two: using physical laws to constrain and guide data-driven models to improve their extrapolation ability and reliability, and simultaneously utilizing data-driven methods to modify and enhance physical models to reduce their uncertainty and computational costs. This evolution from “opposition” to “complementarity” directly laid a solid logical foundation for the rise in PIML.

4. The Core Fusion Mechanism and Modeling Path of PIML

PIML is not a single algorithm, but a methodological system whose core lies in how to deeply integrate prior physical knowledge with data-driven models in different ways and at different stages. This fusion mainly follows the following four core paths [26], forming a complete spectrum from “soft constraints” to “hard embeddings”.

4.1. Physics-Informed Machine Learning as Constraint: Regularizer in Loss Function

This is the most mainstream and direct fusion mechanism, whose core idea is to introduce physical laws (usually in the form of partial differential equations (PDEs) [27], boundary conditions, or initial conditions) as penalty terms into the loss function of machine learning models.

(1)

Mechanism: The total loss function $\mathcal{L}$ of the model is usually constructed as follows:

$$\mathcal{L}={\mathcal{L}}_{data}+{\lambda \mathcal{L}}_{physics}$$

(1)

Among them, ${\mathcal{L}}_{data}$ measures the degree of fit between model predictions and observed data, ${\mathcal{L}}_{physics}$ quantifies the degree to which model predictions violate known physical laws (such as PDE residuals), and $\lambda$ is a trade-off hyperparameter.

(2)

Typical representative: A PINN [28]. As shown in Figure 2, a PINN calculates the derivative of the network output with respect to the input through automatic differentiation, and directly evaluates the PDE residual, thereby satisfying both data fitting and physical consistency during training.

(3)

Bridge application case: (1) Displacement reconstruction: [29] Using physics-informed convolutional neural networks, the differential relationship between displacement and acceleration was embedded into the loss function, and the full process displacement of the bridge under traffic loads was successfully reconstructed based solely on strain and acceleration data. (2) Nonlinear damage identification: [30] Integrating the dynamic control equation of the bridge pier into the loss function enables the PINN to accurately identify the location and degree of nonlinear damage in reinforced concrete bridge piers based solely on seismic response data.

(4)

Concrete illustration for bridge monitoring: A practical example can elucidate this fusion process. Consider the task of reconstructing the full dynamic displacement field of a bridge deck using sparse acceleration measurements—a common challenge in monitoring. The physics law here is Newton’s second law: acceleration is the second derivative of displacement with respect to time. A PINN set up for this task would use a neural network that takes spatial location and time as inputs and directly outputs a predicted displacement field. The data loss term compares the network’s predicted accelerations (obtained by automatically differentiating the network’s displacement output twice with respect to time) against the measured sparse acceleration data. Crucially, the physics loss term is computed at a large number of randomly sampled points across the bridge domain and time period; it penalizes the discrepancy between the network’s predicted acceleration and the second time derivative of its own predicted displacement. By minimizing the total loss, the network is forced to learn a displacement field that not only fits the few available sensor readings but also inherently obeys the fundamental kinematic relationship between displacement and acceleration at all points. This demonstrates how the known differential equation is embedded as a soft constraint, enabling accurate full-field prediction from limited measurements.

This method uses physical knowledge as a “soft constraint” to guide the model to make physically reasonable inferences in areas with sparse or missing data, significantly enhancing the model’s generalization ability.

4.2. Physics-Informed Machine Learning as a Prior: Model Architecture and Initialization Guidance

This type of method embeds physics knowledge at a deeper level into the “skeleton” of machine learning models or is used to guide the starting point of the model.

Mechanism

(1)

Architecture design: Design a dedicated network structure that directly corresponds to the components or mathematical operations of the physical system in terms of its layers, nodes, or connection methods. For example, the multi-scale homogenized deep neural network proposed in has a network hierarchy that strictly corresponds to the multi-scale physical model of water flow [31], using physical properties as activation functions to achieve high-precision prediction of flood surface displacement.

(2)

Initialization guidance: Pre-train the network using “low-fidelity” data generated by physical simulation [32], and then fine-tune it using real “high-fidelity” data (Figure 3). This physics-guided transfer learning can provide the model with an initial state that is closer to the global optimal solution, effectively accelerating convergence and improving performance [33]. Through this method, high accuracy in damage identification of concrete slab bridges has been successfully achieved using small-sample, high-fidelity data.

4.3. Physics-Informed Machine Learning as Residuals: Hybrid Modeling Paradigm

Hybrid modeling acknowledges the imperfections of pure physical models and utilizes machine learning to learn their “residuals” or “errors”, which is a practical and efficient fusion path.

Mechanism: As shown in Figure 4, this paradigm can be subdivided into the following:

(1)

Residual learning: ML models learn the differences between physical model predictions and measured data. For example, Wan et al. [34] use Gaussian process models to learn the residuals of finite element model modal prediction, thereby achieving efficient model updates and damage identification.

(2)

Sequence coupling: The output of the physical model serves as the input feature of the ML model. For example, Svendsen et al. [35] inputs the dynamic response of finite element simulation into a support vector machine for steel bridge damage identification under changing environmental conditions.

(3)

ML embedding in physical models: ML is used to replace a component in the physical model that is difficult to describe accurately (such as constitutive relationships). In multi-stage damage identification [36], neural networks are used to process modal parameters generated by physical models to identify specific damaged components.

The hybrid model has a high acceptance in engineering practice because it maximizes the use of existing, validated physical models while using data-driven methods to compensate for their shortcomings. Due to this balance of trust, practicality, and demonstrated effectiveness in handling real-world data variability and model error, the hybrid modeling paradigm is currently among the most promising and widely applied PIML paths for bridge health monitoring.

4.4. Physics-Informed Machine Learning as a Discovery Target: Sparse Identification of Control Equations

This type of method pushes the initiative of PIML to a higher level, with the aim of discovering potential, insufficiently understood physical laws from data rather than utilizing known physics.

(1)

Mechanism: Using techniques such as sparse regression [37] or symbolic regression [38], the simplest combination of mathematical terms that best describes the dynamics of observed data is automatically selected from a large candidate function library (such as polynomials, trigonometric functions, etc.), resulting in an explicit control equation (Figure 5).

(2)

Bridge application potential: Although direct applications to bridges remain limited in the current literature, this method has great potential for revealing the complex and nonlinear dynamic behavior of bridges under extreme loads or material degradation processes and can provide data-driven insights for establishing more accurate theoretical models.

In summary, the fusion mechanism of PIML exhibits multi-level and multi-path characteristics. From acting as a “supervisor” in the loss function, to embodying the “design blueprint” of network architecture, to acting as a “corrector” in hybrid models and even becoming a “discovery tool” for exploring unknown patterns, these paths together constitute the powerful methodological foundation of PIML, enabling it to flexibly respond to various complex application scenarios in bridge health monitoring.

5. Application Scenarios of PIML in the Entire Lifecycle of Bridges

The value of PIML is not limited to improving the accuracy of damage identification for existing structures, but its deeper potential lies in empowering the full lifecycle management of bridges. By deeply integrating physical mechanisms with monitoring/simulation data, PIML provides smarter and more accurate decision support for every stage from design, construction, to operation and maintenance (as shown in Figure 6).

5.1. Design and Planning Phase: High Fidelity Virtual Simulation and Performance Prediction

Prior to the completion of the bridge, PIML is capable of constructing high-precision “pre-life digital twins” for optimizing design schemes and predicting long-term performance.

(1)

Wind and flow field simulation: Traditional computational fluid dynamics simulation is computationally expensive. PIML can quickly predict the wind field distribution around the bridge body by embedding the Navier–Stokes equations. For example, Yan et al. use PINN to accurately predict the flow field around the tower of a cable-stayed bridge [39], providing an efficient tool for wind load calculation and wind vibration analysis.

(2)

Load response prediction: In the scheme stage, PIML can learn the data of parameterized finite element models and establish a fast surrogate model from design parameters to structural response, which is used to quickly evaluate the safety of different design schemes under extreme loads (such as earthquakes and strong winds).

5.2. Construction and Bridge Completion Stages: Closed-Loop Real-Time State Perception and Quality Control

During the construction period and the initial stage of bridge completion, PIML is capable of processing massive and heterogeneous monitoring data to achieve accurate evaluation of construction quality and initial structural state.

(1)

Real-time prediction of strain field: A PIML model has been developed, which can predict the full field two-dimensional strain distribution on the surface of concrete structures in real time with only a limited number of sensor data points, providing a visualization tool for stress control and defect identification during construction.

(2)

Initial cable force calibration and bridge completion status confirmation: For cable-stayed bridges and suspension bridges, the completed cable force is a key parameter. The physics-informed autoencoder framework can accurately identify cable forces from frequency response function data, ensuring that the completed bridge state meets design expectations [40].

5.3. Operation and Monitoring Stage: Early Diagnosis and Load Identification of Damage Under Multiple Disasters

This is currently the most widely used stage of PIML, whose core is to solve how to achieve early, accurate, and robust damage diagnosis in the context of environmental interference and operational loads.

(1)

Earthquake damage identification: Traditional methods are difficult to accurately quantify nonlinear damage after an earthquake [41]. Using PINN, the nonlinear damage distribution of reinforced concrete (RC) bridge piers was directly identified through seismic response data inversion, providing a key basis for post-earthquake emergency assessment and repair.

(2)

Vehicle and mobile load identification: The difficulty of BHM lies in identifying vehicle loads on bridges without interrupting traffic [42]. The dynamic equation of the vehicle bridge coupling system was embedded into the loss function of PINN, successfully achieving synchronous high-precision identification of the bridge influence line and multiple vehicle loads.

(3)

Prediction of scour depth: Bridge pier scour is the main cause of bridge water damage [43]. By integrating the hydrodynamic empirical formula (HEC-18) into a deep learning model [43], a physically guided erosion prediction framework was constructed, which can effectively predict the trend of the maximum erosion depth around the bridge pier.

Virtual sensing and response prediction of wind load: It is extremely difficult to directly measure wind load. By embedding the differential equation of wind-induced vibration into the Gaussian process latent force model, the estimation of wind loads on long-span suspension bridges and virtual sensing of unmeasured point responses have been achieved.

5.4. Maintenance and Prognostic Stage: Performance Degradation Prediction and Proactive Maintenance Driven by Digital Twins

PIML is the core technology for building dynamic digital twins with predictive capabilities, driving the transition of maintenance strategies from “according to plan” to “according to status”.

(1)

Structural degradation prediction: Simple data-driven models often lack a physical basis when predicting long-term degradation. Embedding ontological knowledge, such as material degradation models and structural mechanics, into neural networks significantly improves the long-term prediction accuracy of concrete bridge deck condition ratings, making them more in line with physical laws [44].

(2)

The research on digital twins and pre-diagnostic maintenance: some studies demonstrate how to use PINN to combine sensor data with control equations that reflect structural behavior to construct digital twins that can predict real-time structural response [45,46]. This twin can continuously update and predict future performance under specific loads or damage scenarios, enabling pre-diagnostic maintenance by developing maintenance plans before faults occur.

In summary, the application of PIML has been integrated throughout the lifecycle of bridges. PIML is transforming bridge health management from a passive process that relies on isolated, posterior data analysis to an active, collaborative, and intelligent system engineering based on deep fusion and forward-looking simulation, from a virtual laboratory in the design phase, to a quality microscope in the construction phase, to a 24/7 diagnostic doctor in the operation phase, and finally to a prognostic consultant in the maintenance phase.

6. Data Strategy and Enhancement Methods of PIML

Data is the cornerstone of machine learning, but in bridge health monitoring, obtaining a large amount of high-quality, especially real data with damage labels, is extremely difficult [47]. One of the core advantages of PIML is that it introduces physics knowledge to form a unique and efficient data strategy and enhancement method, fundamentally breaking through the bottleneck of pure data-driven models. A four-level data strategy enabled by PIML is shown in Figure 7.

6.1. Physics Guided Data Generation and Enhancement: Building a “Synthetic Data Factory”

When real damage data is scarce or the acquisition cost is too high, PIML can use physical models to generate a large and diverse amount of physically consistent synthetic data for training and enhancing the model.

(1)

Mechanism: Using preliminarily validated finite element models or simplified physical models, simulate the response of structures under various loads, environments, and different damage scenarios. Although there is a gap between these simulated data and real data, they contain correct physical laws.

(2)

Application mode (pre-training and fine-tuning): As described in [48], the network is first pre-trained using low fidelity FE simulation data, and then fine-tuned using limited real high fidelity data, significantly improving the model performance under small samples [33].

(3)

Building a hybrid dataset: For example, in the damage detection of the Z24 bridge [49], real monitoring data is mixed with numerical data generated by the FE model to jointly train a multi-layer perceptron, effectively improving the classification accuracy and robustness of the model.

This method can generate extreme working condition data that is difficult to observe or even dangerous in reality, at low cost (such as severe damage, major earthquakes), greatly expanding the scope and diversity of the training set.

6.2. Small Sample and Zero Sample Learning Under Physical Constraints: Achieving “Learning from One Example to Another”

PIML injects prior knowledge into the model through physical constraints, greatly reducing the model’s dependence on data volume and making small sample learning or even zero sample learning possible.

(1)

Mechanism: Physical equations (such as PDEs) themselves are strong constraints and generalizations of system behavior. Embedding this constraint into the model is equivalent to providing the model with the ability to “self-learn”. Even without training data under certain operating conditions, the model can still provide reasonable predictions by satisfying physical laws.

(2)

Application prospects (zero sample learning): As shown in the research on acoustic field reconstruction in ref. [50], incorporating physics knowledge into dictionary learning can achieve prediction in completely new scenarios without training data. This suggests that PIML may be applied to a new type of bridge in the future without the need for its historical data.

(3)

Few sample learning: Weng et al. [51] demonstrates how physics-informed machine learning significantly improves the performance of wind pressure prediction models with very few data samples. In BHM, this means that only short-term monitoring of the bridge is needed to establish a reliable predictive model.

6.3. Physics-Guided Self-Supervision and Meta-Learning: Mining “Free Labels” from Data

PIML naturally aligns with the self-supervised learning paradigm and can quickly adapt to new tasks through meta learning.

6.3.1. Self-Supervised Learning

(1)

Mechanism: Physical laws themselves can be used to generate “pseudo labels”. For example, any set of predictions that satisfy zero PDE residuals can be considered an effective “self-supervised signal”. Park et al. [52] demonstrated that incorporating physical constraints into self-supervised dual learning can effectively solve complex optimization problems.

(2)

Potential in BHM: A large amount of unlabeled monitoring data can be utilized to pre-train a model by minimizing physical residuals, enabling it to learn the intrinsic physical laws of structural response, and then fine-tune with a small amount of labeled data at hand.

6.3.2. Meta Learning

(1)

Mechanism: Meta learning aims to train the model to “learn how to learn”. A meta learning initialization method for PINN was proposed, which enables the model to quickly adapt to new, unseen structures or load conditions with minimal iterations.

(2)

Value in BHM: For a management department with multiple similar bridges, meta learning can be used to train a universal PIML model that can quickly adapt to each specific bridge, achieving “plug and play” health monitoring and greatly reducing the model development cost for each bridge.

6.4. Physical Consistency Fusion of Multi-Source Heterogeneous Data

The actual BHM system contains heterogeneous data from different sensors (accelerometer, strain gauge, GPS, etc.) and different sources (physical simulation, detection report). PIML provides a unified physical framework for solving multi-source data fusion.

(1)

Mechanism: Data from different sources are unified into a common physical equation. For example, strain data and acceleration data are unified for displacement reconstruction through mechanical relationships [29]. Physical equations serve as a “universal language” for connecting different modal data.

(2)

Application: As described in ref. [53], a bridge degradation prediction model is constructed by structurally embedding multi-source knowledge, such as detection reports, physical equations, and simulation data, into a neural network through ontology. The prediction results are more physically meaningful and robust than models that only use monitoring data.

In summary, PIML has systematically resolved the data crisis in the BHM field through four strategies: “physical generation”, “physical constraints”, “physical guidance”, and “physical unification”. It liberates data-driven models from blind dependence on “big data” and leads them towards a new path of learning based on “physical intelligence,” enhanced, more efficient, and economical “small data” and even “zero data”.

7. PIML-Driven Bridge Digital Twin System

Digital twin, as a dynamic mapping of physical entities throughout their entire lifecycle in virtual space, is one of the ultimate visions for bridge health monitoring [54,55]. However, traditional digital twins rely heavily on high-fidelity finite element models, which have bottlenecks in real-time performance, adaptive updates, and predicting prognosis [56]. The introduction of PIML provides a key technological path to address these bottlenecks, evolving it from a static “digital shadow” to a dynamic, intelligent, and predictive “digital twin” (as shown in Figure 8).

7.1. Core Engine: Paradigm Upgrade from “Model-Driven” to “Physics-Informed Data-Driven”

PIML serves as the “brain” of the digital twin system, and its core value lies in providing a paradigm upgrade from “model-driven” to “physics-informed data-driven.” In practice, the PIML model interfaces with traditional FEM in several complementary ways to achieve real-time performance: (1) as a fast surrogate model trained on FEM data, bypassing expensive solves during inference; (2) as a corrector learning the residual between a baseline FEM and real sensor data, enabling adaptive hybrid modeling; and (3) as an inverse solver that identifies physical parameters from live data, which are then used to update the FEM periodically. This flexible integration allows the digital twin to balance real-time operation with high physical fidelity. Key advantages of this PIML-centric core include the following:

(1)

Real-time performance: The trained PIML model (such as PINN) has extremely fast inference speed, which can meet real-time or quasi-real-time simulation requirements, far exceeding traditional FEM [46].

(2)

Data assimilation and model updating: PIML can continuously fuse real-time sensor data with physical laws, dynamically adjust model parameters (such as stiffness and boundary conditions), and keep the digital twin and physical entity evolving synchronously, rather than a static “snapshot”.

(3)

Physical consistency guarantee: It ensures that digital twins behave in accordance with basic physical laws even when data is interrupted or extrapolated, avoiding the absurd results that pure data models may produce.

7.2. Implementation of Key Functions

7.2.1. High Fidelity Real-Time Response Prediction and Virtual Sensing

(1)

Mechanism: By using frameworks such as PINN, sparse sensor data (such as acceleration and strain) can be combined with control equations governing structural behavior, and digital twins can reconstruct the full-field response of unmeasured degrees of freedom.

(2)

Case: Developed a PINN-driven RC bridge digital twin, which can predict the real-time response of the structure under various loads based on sensor inputs. Using a physics-informed Gaussian process model, virtual sensing of wind load estimation and key position response of suspension bridges was achieved, overcoming the limitations of sensor deployment quantity and location.

7.2.2. Multi-Physics Field Coupling and Extreme Operating Condition Simulation

Digital twins need to reflect the multi-field coupling effects that structures experience in real environments (such as wind–vehicle–bridge, water–soil–structure).

Cases:

Wind structure coupling: Using PINN to predict the wind field around the bridge tower provides high-precision input for wind vibration analysis [39].

Water soil structure coupling: The Scour PINN framework combines hydrodynamic equations with Scour depth prediction, enabling digital twins to predict the evolution of key geological hazards such as bridge pier erosion, which is difficult for traditional models to achieve in real time.

7.2.3. Adaptive Prognostic and Pre-Diagnostic Maintenance

This is the highest value manifestation of PIML-driven digital twins. The system can not only describe the current situation but also predict the future.

(1)

Mechanism: The digital twin continuously learns the degradation laws of the structure (such as material performance degradation) through PIML and can simulate the structural behavior under future load scenarios (such as traffic growth, extreme storms), thereby predicting its remaining service life and failure risk.

(2)

Case: In the digital twin of prestressed concrete bridges, predictive models and key performance indicators are integrated to predict structural performance degradation and generate predictive maintenance plans. By embedding the knowledge ontology of structural degradation into neural networks, the predictive ability of digital twins for long-term condition rating of bridge components (such as concrete bridge decks) has been enhanced, providing a basis for developing scientific long-term maintenance plans.

7.3. System Architecture and Workflow

A typical PIML-driven digital twin system includes the following closed loops:

(1)

Perception layer: A sensor network deployed on physical bridges continuously collects data.

(2)

Model layer: The PIML core model serves as the computing engine for the digital twin.

(3)

Data physical fusion: Real-time data is input into the PIML model, which performs state estimation and parameter updates through its embedded physical constraints to ensure synchronization between digital twins and physical entities.

(4)

Simulation and prediction: The updated digital twin is used to run “What if” scenarios, predicting the structural response under future loads or damage propagation.

(5)

Decision and feedback: Predictive results and diagnostic information are provided to managers to guide inspections, maintenance, or traffic control. The resulting decision actions then have a feedback effect on physical entities, forming a closed loop.

In summary, PIML injects soul into bridge digital twins by seamlessly integrating physical laws with real-time data. It solves the pain points of traditional simulation models being inaccurate, unpleasant, and ineffective, and promotes the upgrade of digital twins from a beautiful static visualization model to a collaborative intelligent agent that can perceive, learn, evolve, and foresee the future in real time. Ultimately, it provides a revolutionary technological platform for achieving the safety, economy, and longevity of bridge infrastructure.

8. Challenges and Future Directions

Despite the disruptive potential of PIML in bridge health monitoring, there are still a series of serious challenges on its path from academic research to mature engineering applications. Identifying these challenges and planning future research directions based on them is crucial for the healthy development of this field (as shown in Figure 9).

8.1. Current Core Challenges

8.1.1. Inherent Challenges at the Data Level

The data environment for bridge health monitoring is extremely challenging. Sensor failures, transmission packet loss, environmental noise, and other factors often lead to data loss, heterogeneity, and high noise. Although PIML has lower requirements for data volume than pure data-driven methods, its performance still depends on the quality and representativeness of the data. Effective extraction of physical laws from low-signal-to-noise ratio measurements and integrating data of different qualities and sources (such as sensors, detection reports, images) is an unsolved problem.

8.1.2. Complexity and Computational Burden of Physical Constraints

The expression and solution of complex PDEs: Many bridge dynamics problems involve high-dimensional, nonlinear, and even coupled partial differential equations (such as fluid–structure coupling). Accurately embedding these complex PDEs into neural networks and ensuring their stable and efficient training is both theoretically and practically challenging [57,58].

Multiscale problem: Bridge structures span a huge spatiotemporal scale, from macroscopic overall vibration to minor local damage. A single PIML model is difficult to accurately capture physical phenomena at all scales simultaneously and is prone to becoming stuck in local optima or scale confusion during training.

8.1.3. The Art of Balancing Multi-Objective Loss Functions

The loss function of PIML is usually the multi-objective weighted sum of the data fitting term and the physical regularization term. How to automatically and adaptively balance the weights of these loss terms (as in the formula) λ, avoiding one dominant training process from causing another to fail, is a critical and yet to be standardized issue [59]. Inappropriate weighting can lead to the model either overfitting noisy data or degenerating into a purely physical solver that ignores measured information.

The ultimate pursuit of model generalization and interpretability.

Although the “gray box” feature of PIML improves interpretability, its core neural network components are still complex nonlinear functions. How to extract human-understandable damage mechanics mechanisms from thousands of network parameters (such as identifying specific damage constitutive relationships), rather than just providing a black box prediction result, is the key to winning the complete trust of bridge engineers. In addition, how to generalize a PIML model trained on a specific bridge to other bridges with different structural forms, materials, or boundary conditions, that is, to achieve cross-structure transfer, remains a huge challenge.

8.2. Future Research Directions

8.2.1. Intelligent Data Strategy and Physical Guided Active Learning

Future research will focus more on developing smarter methods for utilizing data:

(1)

Physics-Informed Active Learning (PIAL): PIAL can be implemented by a PIML model that quantifies its own predictive uncertainty. An acquisition function, guided by physical principles (e.g., stress concentrations, modal sensitivities), would then identify the most valuable actions—such as where to place a new sensor, which location to inspect with non-destructive testing, or what diagnostic load configuration to apply—to maximally reduce model uncertainty about critical parameters [60]. This creates a closed-loop, resource-optimized monitoring strategy.

(2)

Self-supervision and meta learning: As shown in ref. [61], using physical laws to create pre-training tasks from unlabeled data, or training meta-models that can quickly adapt to new bridges, will be the key to solving small-sample and cross-structure generalization problems.

8.2.2. Innovation in Advanced Model Architecture and Optimization Algorithms

(1)

A novel network for handling complex PDEs: Developing specialized architectures that can naturally handle multi-scale, long-term dependencies (such as combining graph neural networks with PINNs for complex topological structures) to overcome the limitations of traditional PINNs in complex dynamical systems.

(2)

Adaptive loss balancing technology: Promote multi-task loss weighting algorithms based on homoscedastic uncertainty, to dynamically adjust the contributions of different loss terms in PIML, achieving more stable and efficient training.

8.2.3. Deep Integration with Cutting-Edge Information Technology

(1)

Edge computing and IoT integration: With the help of IoT technology trends pointed out by ref. [62] and others, lightweight PIML models are deployed on edge computing nodes to achieve real-time intelligent diagnosis on the end side and reduce the pressure on data transmission and cloud computing.

(2)

Visualization and explainable AI: Developing advanced visualization tools to visually correlate PIML prediction results (such as damage location and degree) with physical parameters (such as stress and mode) and using attribution analysis and other techniques to explain the decision-making basis of the model, enhancing its credibility in practical engineering.

8.2.4. Standardization and Verification for Engineering Practice

Promote the establishment of a benchmark dataset, standard validation process, and performance evaluation indicators for PIML in bridge engineering. Through a large number of real bridge case studies, systematically verify the reliability, robustness, and economy of the PIML method in long-term monitoring, paving the way for its eventual inclusion in industry norms and standards.

In summary, PIML’s journey in bridge health monitoring is flourishing. The future development requires deep collaboration among mathematicians, computer scientists, and bridge engineers to jointly overcome the layers of barriers from theoretical algorithms to engineering practice. Through continuous innovation, PIML is expected to evolve from an advanced analytical tool to a core enabling technology that supports the safe, intelligent, and resilient operation and maintenance of future bridge infrastructure.

9. Conclusions

Bridge health monitoring is evolving from a “skill” that relies on experience and regular inspections to a “science” based on deep integration of data and physics. This article systematically reviews and looks forward to the core driving force of this evolution process: PIML.

In traditional methods, the interpretability of physical models in the “white box” and the powerful learning ability of data-driven models in the “black box” have long been separated. The emergence of PIML creatively constructs a “gray box” fusion paradigm by embedding physical laws into machine learning models in the form of constraints, priors, residuals, or discovery targets. This paradigm not only effectively alleviates real-world challenges such as data scarcity and noise interference but also fundamentally improves the model’s generalization ability, physical consistency, and result credibility. From high-fidelity simulation in the design phase, to precise damage diagnosis during operation, and to performance prognosis in the maintenance phase, PIML runs through the entire lifecycle of bridges, promoting the transformation of health management from passive and reactive detection to a proactive and predictive intelligent maintenance paradigm.

However, the path towards comprehensive intelligent monitoring still requires overcoming many challenges. The precise modeling of complex physical systems, balancing multi-objective losses, improving cross-structural generalization ability, and ultimately gaining complete trust in interpretability in engineering practice are all key issues that urgently need to be overcome. Future breakthroughs will rely on deep interdisciplinary collaboration: mathematicians, computer scientists, and bridge engineers who must work closely together to develop stronger algorithms, more efficient architectures, and more rigorous validation standards. At the same time, the integration with the Internet of Things, edge computing, and visualization technology will enable the PIML-driven digital twin to move from a research concept to an engineering system with wide coverage, fast response, and accurate decision-making.

In short, PIML is not just a new algorithm tool; it represents a core methodology that integrates physical mechanisms and data intelligence, providing a new technological path for ensuring the longevity and resilience improvement of bridge infrastructure. With the deepening of theoretical research and the accumulation of engineering practice, PIML is expected to become an indispensable intelligent core in future smart infrastructure management, ultimately achieving the grand goal of “preventing problems before they happen”.