Civil structure carbon mechanics dual-domain evolution prediction method based on generated physical field reasoning

Abstract

This invention discloses a dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field inference. The steps are as follows: 1. Set an initial boundary condition set B within [0,T]; 2. Construct a bidirectional coupled control equation system P for carbonization diffusion and mechanical response based on B; 3. Construct a generative physics field inference model and embed it into P, achieving coordinated iteration of the concentration field C(x,t) and stress field σ(x,t) through spatiotemporal feature encoding and a dual-domain generation kernel, followed by dynamic feedback correction to convergence via a physical consistency regulator; 4. Construct a joint loss function including data fitting, physical equation residuals, energy constraints, and constitutive consistency, and perform two-stage hybrid optimization training to convergence; 5. Discretize the time domain into N layers, performing dual-domain evolution recursion, latent variable residual self-repair, and multi-scale stability control at each step, outputting field distribution, carbonization depth, and stiffness degradation indices. This invention deeply integrates the generative model with the bidirectional coupled equations, achieving unified convergence of data-driven and physical constraints.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering structure durability analysis and artificial intelligence physical modeling technology, specifically involving a dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field reasoning. Background Technology

[0002] Carbonation in concrete structures is one of the main factors affecting the durability and service life of civil engineering projects. Carbon dioxide diffuses in the pores of concrete and reacts with hydration products, leading to a decrease in material alkalinity, damage to the passivation film of reinforcing steel, and degradation of mechanical properties. Traditional carbonation-mechanical coupling analysis is usually based on a step-by-step calculation method: first, the carbonation diffusion equation is solved by the finite element method or numerical analysis, and then the obtained carbonation depth or concentration field is passed as input parameters to the structural mechanics model to solve for stress and damage distribution. Although this type of method has a certain degree of accuracy in engineering practice, it has significant shortcomings: first, the information transfer between carbonation and the mechanical field is delayed, and the boundary conditions are not updated in a timely manner, leading to the accumulation of cross-domain errors; second, the calculation process requires multiple iterations and mesh reconstruction, resulting in low computational efficiency and making it difficult to apply to large-scale or long-term service analysis.

[0003] In recent years, with the development of deep learning and data-driven modeling, attempts have emerged to predict carbonization based on Physically Informed Neural Networks (PINNs). These methods, by introducing partial differential equation residuals into the loss function to constrain network training, can reduce dependence on experimental data to some extent. However, PINNs still belong to a "passive constraint" approach; physical consistency is penalized only during the training phase, lacking dynamic feedback during inference, which may lead to generated results deviating from physical laws. Furthermore, PINNs exhibit poor adaptability to complex boundaries, heterogeneous materials, and time-varying environments, and suffer from long training times and poor convergence.

[0004] Meanwhile, generative deep models (such as diffusion models and Transformer architectures) have demonstrated powerful distributed learning and global modeling capabilities in fields such as image generation and temporal modeling. However, these models are typically used for data generation tasks and have not yet been deeply integrated with the continuous medium equations. Existing research mostly remains at the level of "data-driven prediction," lacking a systematic framework that couples generative models with the carbonization-mechanical dual-domain control equations, making it difficult to achieve physically interpretable and constraint-consistent field distribution inference.

[0005] In summary, the existing technology mainly has the following problems:

[0006] (1) The decoupled calculation of carbonization diffusion and mechanical response has insufficient cross-domain information interaction, and errors are easy to accumulate;

[0007] (2) Physical constraints are mostly static or passive, and there is a lack of dynamic consistency control in the reasoning stage;

[0008] (3) The model has poor universality and it is difficult to take into account multiple physics fields, multiple working conditions and long-term evolution prediction.

[0009] (4) The computational overhead is large and the convergence speed is slow, which limits its application in structural digital twins and life cycle management.

[0010] Therefore, there is an urgent need for a unified framework that can organically combine generative modeling with physical constraint equations, so that the model can actively maintain physical conservation and inter-domain consistency during the generation process, thereby achieving efficient and interpretable prediction of the carbon-mechanical dual-domain evolution of civil structures. Summary of the Invention

[0011] To address the problems existing in the prior art, this invention provides a method for predicting the carbon-mechanical dual-domain evolution of civil structures based on generative physics field inference. The purpose is to use a generative physics field inference method that deeply integrates generative models (including diffusion and Transformer architectures) with the continuous medium governing equations to achieve spatiotemporal physics field prediction and performance degradation analysis of civil structures during the carbonization-mechanical dual-domain evolution process.

[0012] To achieve the above objectives, the specific solution of the present invention is as follows:

[0013] A dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field reasoning includes the following steps:

[0014] Step 1, Setting the research object and initial boundary conditions: In the structural space domain Within the time domain [0,T], where T represents the total duration of the study or prediction, the initial states of the carbon dioxide concentration field and displacement field are set, and the boundary conditions of the concentration field and the mechanical field are defined. The boundary conditions of the concentration field include the concentration setpoint boundary and the concentration flux boundary, and the boundary conditions of the mechanical field include the displacement constraint boundary and the stress load boundary, forming a standardized set of initial boundary conditions B.

[0015] Step 2, Construction of the carbon mechanical dual-domain coupled control equation system: Based on the initial boundary condition set B in Step 1, establish the chemical subdomain control equation, the mechanical subdomain control equation, and the carbon mechanical coupling mechanism equation, construct the bidirectional coupled control equation system of carbonization diffusion and mechanical response, and output the physical control equation set P;

[0016] Step 3, Generative Physics Field Inference Model Construction and Dual-Domain Coupled Prediction: Based on the set of physical control equations P output in Step 2 and the set of initial boundary conditions B formed in Step 1, a generative physics field inference model is constructed. The bidirectional coupled control equation system of carbonization diffusion and mechanical response is embedded into the generative physics field inference model. Spatial, temporal, and physical constraint embedding features are extracted through spatiotemporal feature encoding. A dual-domain generation kernel is used to realize the collaborative iterative evolution of the carbonization concentration field and stress field in the same generation cycle. The generation process is then corrected by an active physical consistency regulator based on the dynamic feedback of carbonization and mechanical residuals until the residuals converge. Finally, the carbonization concentration field C(x,t) and stress field σ(x,t) that satisfy the set of physical control equations P and the set of initial boundary conditions B are output, forming a carbon mechanics dual-domain coupled evolution prediction.

[0017] Step 4: Based on the generative physics inference model constructed in Step 3, a joint loss function is constructed, which includes data fitting loss, physical equation residual loss, energy constraint loss, and constitutive consistency loss. A two-stage hybrid optimization strategy is used to train the model until convergence. The calculation of the physical equation residual loss, energy constraint loss, and constitutive consistency loss is based on the bidirectional coupled control equation system of carbonization diffusion and mechanical response constructed in Step 2. When the data fitting loss, physical equation residual loss, and energy constraint loss are less than the preset thresholds of data error, physical residual, and energy error, respectively, the training converges, and the optimized model parameter set and loss weight configuration are output.

[0018] Step 5: Based on the optimized model parameter set and loss weight configuration output in Step 4, the time domain [0,T] defined in Step 1 is discretized into N time layers. Within each time step, the dual-domain evolution recursive calculation, the latent variable residual self-repair mechanism, and the multi-scale dynamic stability control are executed sequentially. Finally, the engineering interpretable results are output, which include the complete field distribution, carbonization depth distribution, and stiffness degradation index.

[0019] Furthermore, the formulas for setting the initial states of the carbon dioxide concentration field and displacement field in step 1 are as follows:

[0020] (1),

[0021] (2),

[0022] In the formula: This represents the CO2 concentration field within the pores at time t. This represents the initial CO2 concentration distribution; Represents the displacement field at time t; Indicates the depth of carbonization; Represents spatial coordinates; Indicates displacement; Indicates time;

[0023] The formula for the concentration setpoint boundary is as follows:

[0024] (3),

[0025] In the formula: This represents the CO2 concentration field within the pores at time t. This represents the atmospheric CO2 concentration at time t.

[0026] The formula for the concentration flux boundary is as follows:

[0027] (4),

[0028] In the formula, Indicates the effective diffusion coefficient; Represents the outward normal vector; Represents the concentration gradient; Indicates the concentration setpoint boundary; Indicates the concentration flux boundary; Represents the stress tensor; This represents the concentration flux boundary value at time t;

[0029] The displacement constraint boundary satisfies (5),

[0030] In the formula: Represents the displacement field at time t; Indicates the displacement constraint boundary;

[0031] The stress load boundary satisfies (6),

[0032] In the formula: The stress tensor represents time t; Indicates the displacement force boundary; The external force at time t;

[0033] The formula for the standardized initial boundary condition set B is as follows:

[0034] (7),

[0035] In the formula: This represents the initial CO2 concentration distribution; This represents the atmospheric CO2 concentration at time t. Indicates the effective diffusion coefficient; This represents the concentration flux boundary value at time t; The external force at time t; Indicates the concentration setpoint boundary; Indicates the concentration flux boundary; Indicates the displacement constraint boundary; This indicates the boundary of the displacement force.

[0036] Furthermore, the governing equations for the chemical subdomains described in step 2 are as follows:

[0037] (8),

[0038] In the formula: This represents a partial derivative operator used to describe the local rate of change of a multivariable physical field function with respect to a certain independent variable; This represents the CO2 concentration field within the pores at time t. Indicates time; Indicates the effective diffusion coefficient of concentration-stress coupling; The term representing the carbonization reaction rate; This indicates the external boundary condition for carbon dioxide concentration. Indicates temperature; Represents the stress tensor; , Representing gradient and divergence operators;

[0039] The governing equations of the mechanical subdomain are defined as follows:

[0040] (9),

[0041] (10)

[0042] In the formula: Represents the stress tensor; Indicates physical density; Represents the elastic stiffness tensor as it evolves with carbonization; Represents the total strain tensor; Indicates carbonization shrinkage strain; Indicates temperature strain;

[0043] The equation for the carbon mechanical coupling mechanism is defined as follows:

[0044] (13)

[0045] In the formula: Indicates the reference diffusion coefficient; Indicates the carbonization inhibition coefficient; Indicates the stress coupling coefficient; This represents the stress trace, i.e., the volume average stress.

[0046] The set of physical governing equations P is: (16)

[0047] In the formula, R diff R represents the carbonization residual, which is the residual of the control equations used in generating the model training; mech This represents the mechanical residual, which is the residual of the governing equations for which physical constraints are imposed during the reasoning stage.

[0048] Furthermore, the construction of the generative physics inference model described in step 3 is formally represented as a mapping relationship:

[0049] (17)

[0050] In the formula, This represents the generation of a physics inference model, with the following parameter set: ; It is a spatial coordinate vector; It is a time variable; For material and environmental parameters; This is the initial set of boundary conditions; It is a set of physical governing equations; and This represents the generated carbonization concentration field and stress field;

[0051] The spatiotemporal encoder is mapped to a unified latent representation:

[0052] (18)

[0053] In the formula, For potential representation; Indicates by parameters Control encoding function;

[0054] The dual-domain generation kernel is implemented using a diffusion model or a Transformer structure. The diffusion model constructs the generation process through random perturbation and denoising inversion.

[0055] (19)

[0056] In the formula: Indicates the first Implicit variable vector; Indicates the time step; This represents the generation and update function, i.e., the neural operator; Spatiotemporal coding features;

[0057] The Transformer architecture employs a self-attention mechanism:

[0058] (20)

[0059] In the formula: , , These are query, key, and value vectors, respectively. It is a constant for the attention dimension; This represents the normalized weight function;

[0060] The active physical consistency controller is embedded in the dual-domain generation kernel. In each generation iteration, it calculates the carbonization residual and mechanical residual based on the current output and dynamically adjusts the latent variable vector. When the residual converges to below the threshold, it outputs the current generation result.

[0061] The formula for the carbonization residual is: (14)

[0062] The formula for the mechanical residual is: (15).

[0063] Furthermore, the final output described in step 3 is:

[0064] (twenty three),

[0065] The final output also includes intermediate variables:

[0066] (twenty four),

[0067] In the formula, For carbonization depth, It serves as a structural stiffness degradation index, used for the construction of joint losses and calculation of engineering indices in subsequent S4.

[0068] Furthermore, the formula for calculating the data fitting loss in step 4 is as follows:

[0069] (26)

[0070] In the formula: , This represents the concentration field and stress field generated by the model; , Indicates a reference value for numerical simulation or experiment; , Represents the 2-norm and the Frobenius norm;

[0071] The formula for calculating the residual loss of the physical equation is as follows: (27)

[0072] The formula for calculating the energy constraint loss is as follows:

[0073] (28)

[0074] In the formula: Represents the stress tensor; Represents the strain tensor; Indicates the boundary surface force; Represents the displacement field; This represents the integral over the volumetric domain, i.e., volumetric energy. This represents the boundary integral, i.e., the external work done.

[0075] The formula for calculating the constitutive consistency loss is as follows: (29)

[0076] In the formula: F represents the Frobenius norm;

[0077] The joint loss function is as follows:

[0078] (25)

[0079] In the formula: This represents the model parameter set, including the encoder, generator kernel, and PCC parameters. , , , This represents the weighting coefficient of each loss term; This represents the data fitting loss; , Represents the carbonization and mechanical equation residuals; Indicates energy constraint loss; This represents the constitutive consistency loss;

[0080] The two-stage hybrid optimization strategy includes an outer optimizer and an inner optimizer. The outer optimizer optimizes the network parameters. Perform weight decay and adaptive learning rate adjustment:

[0081] (30)

[0082] In the formula, For learning rate, Provides a stable weight update mechanism;

[0083] Inner optimizer generates hidden variables Implement adaptive residual update:

[0084] (31),

[0085] In the formula, This is the inner step size; this process is executed once in each generation loop, which can actively correct physical residuals during the training phase and reduce gradient oscillations and overfitting. Represents the latent variable The gradient operator;

[0086] The training convergence requires the following conditions to be met simultaneously:

[0087] (32),

[0088] In the formula, , , These are the preset thresholds for data error, physical residual, and energy error, respectively.

[0089] The optimized model parameter set and loss weight configuration are as follows: (33), where, This represents the optimal set of model parameters after optimization by the joint loss function and satisfaction of the convergence condition.

[0090] Furthermore, the dual-domain evolution recursive calculation described in step 5 is as follows:

[0091] (34),

[0092] (35),

[0093] In the formula: This represents the carbonization concentration field at time k+1; This represents the stress field at time k+1; Let represent the carbonization concentration field at time k; Let represent the stress field at time k; Represents spatiotemporal coding features; Represents the set of parameters for the governing equations; , These are sub-modules for generating the carbonization domain and the mechanical domain, respectively.

[0094] The multi-scale dynamic stability control performs local filtering on the dual-domain field according to the smoothing kernel function formula at each time step. The smoothing kernel function formula is as follows:

[0095] (39)

[0096] In the formula: Represents the smoothing kernel function, with the scaling parameter being... ; This represents the smoothed carbonization concentration field; Represents the smoothing operator;

[0097] The final output project can be interpreted as follows:

[0098] (41),

[0099] In the formula: Represents the carbonization depth distribution, defined as ; The stiffness degradation index is defined as follows: ; , This represents the current and initial elastic modulus.

[0100] Furthermore, the latent variable residual self-repair mechanism described in step 5 is executed according to the following steps:

[0101] Step 51: Calculate the residuals of the governing equations for the chemical subdomain and the governing equations for the mechanical subdomain at the current time.

[0102] The residual formula for the governing equation of the chemical subdomain at the current moment is as follows:

[0103] (36)

[0104] In the formula, Indicates the first The time layer or the first The residual of the chemical subdomain governing equation at time t is used to measure the degree of deviation of the currently generated carbonization concentration field from the chemical subdomain governing equation; This represents the time step between two adjacent discrete time layers;

[0105] The residual formula for the governing equation of the current mechanical subdomain is as follows:

[0106] (37)

[0107] In the formula, Indicates the first At each discrete time step, the residuals of the mechanical equilibrium governing equations are used to quantify the degree of deviation of the generated stress field from the mechanical equilibrium conditions and constitutive relations.

[0108] Step 52: Correct the latent variables based on the magnitude of the residuals. The correction formula is as follows:

[0109] (38),

[0110] In the formula, Adjust the step size for the hidden space; Indicates the first Latent variables corresponding to each discrete time level The gradient operator is used to calculate the direction of change of the residual function with respect to the latent variables, thereby guiding the adaptive correction of the latent space;

[0111] Step 53, when the local residual When the current hidden state is retained as the new prediction baseline, a regeneration process is triggered when the residual exceeds a threshold, and the calculation is repeated. and .

[0112] A carbon mechanics dual-domain generative inference simulation platform includes:

[0113] The data acquisition and preprocessing module is configured to acquire structural carbonization and mechanical response data and generate standardized input tensors;

[0114] A dual-domain control equation and constraint construction module is built, which embeds carbonization diffusion equation and mechanical equilibrium equation, and generates residual operators based on symbolic automatic differentiation;

[0115] The core engine for generating physical field inference integrates a generative AI model, a physical consistency regulator, a latent variable self-repair mechanism, and a multi-scale filtering operator to perform dual-domain evolution prediction.

[0116] The hybrid optimization and self-healing engine is configured to dynamically adjust the weights of the joint loss function and perform two-layer optimization; and the engineering visualization and digital twin interface is configured to convert the prediction results into three-dimensional field visualization graphics and standard format data output.

[0117] Furthermore, the output of the data acquisition and preprocessing module is connected to the input of the generative physics field inference core engine; the dual-domain control equation and constraint construction module is connected to the generative physics field inference core engine bidirectionally; the generative physics field inference core engine is connected to the hybrid optimization and self-healing engine bidirectionally; and the output of the generative physics field inference core engine is connected to the input of the engineering visualization and digital twin interface.

[0118] Advantages of the present invention

[0119] 1. The present invention proposes a novel “generative model-physical equation fusion” technical path in the field of structural durability prediction based on the dual-domain evolution prediction method of carbon mechanics of civil structures based on generative physical field reasoning. It breaks through many bottlenecks of traditional numerical methods and neural networks in terms of coupled solution, long-term evolution and physical reliability.

[0120] 2. This invention innovatively embeds the carbonization-diffusion equation and the structural mechanics equilibrium equation into a generative model (Diffusion / Transformer). Through a unified latent space representation, it achieves simultaneous generation and constraint optimization of the concentration and stress fields, significantly improving computational accuracy and convergence stability. The deep integration of the generative model and physical equations enables end-to-end dual-domain collaborative prediction. This end-to-end modeling mode eliminates step-by-step calculation errors, forming a physically self-consistent joint prediction framework. It solves the problem that traditional carbonization-mechanics coupled calculations typically employ "step-by-step diffusion-mechanics solution" or "weakly coupled iteration," requiring manual transfer of boundary and material parameters, which easily introduces error accumulation and inconsistency issues.

[0121] 3. This invention introduces a Physical Consistency Controller (PCC) to actively calculate the residuals of the governing equations at each step of the generation process. , Furthermore, it corrects latent variables through gradient feedback, achieving closed-loop physical consistency control of "generation-correction-regeneration". This mechanism ensures the physical credibility of the model during the prediction phase and maintains equation constraints even under unsupervised conditions.

[0122] This solves the problem that existing neural network-based physical constraint methods (such as PINN) typically only penalize residuals during the training phase and cannot correct them in real time during inference.

[0123] 4. This invention introduces a joint loss function during the training phase, integrating data error terms, equation residual terms, energy conservation terms, and constitutive consistency terms, achieving end-to-end optimization through automatic differentiation. This design enables the model to develop a physically consistent convergence trend in the early training stages, significantly improving training stability, physical rationality, and model generalization performance. It solves the problem of traditional neural networks that only pursue data fitting accuracy while neglecting physical conservation, leading to a lack of interpretability in prediction results.

[0124] 5. The Latent Variable Residual Self-Repairing Mechanism (LRSC) proposed in this invention monitors residual changes in real time during the inference phase and automatically corrects the latent space state. When the residual exceeds a threshold, a regeneration process is triggered. Combined with the Multi-Scale Smoothing Operator (MSO), the model can maintain convergence consistency and physical stability over long-term evolution, providing reliable support for structural lifetime prediction. This solves the problem of numerical drift and distortion that easily occur in existing models during long-term time-series predictions.

[0125] 6. The output results of this invention include not only the carbonization concentration field With stress field It also directly generates carbonization depth Stiffness degradation index These are key engineering parameters. These indicators have clear physical meanings and can be directly used for structural durability assessment, carbonization life prediction, and maintenance decisions, significantly improving the engineering usability and interpretability of the model.

[0126] 7. The generative physics field reasoning framework of this invention is based on the general governing equations of continuous media. By replacing diffusion terms, reaction terms, or constitutive equations, it can be rapidly extended to multi-field coupled problems such as chloride ion corrosion-mechanics, temperature and humidity-stress, and freeze-thaw-strain.

[0127] This versatility makes this method applicable not only to concrete carbonation prediction but also to multi-domain modeling of other material-environment coupling processes.

[0128] 8. Compared with the traditional finite element method, the generative model of this invention can maintain high-precision physical consistency while significantly reducing computational costs. The generation and inference time can be reduced from hours to seconds, without the need for complex mesh generation or boundary iteration. This characteristic makes this method highly suitable for application in complex digital twin systems and real-time health monitoring platforms, possessing significant engineering potential and economic value. Attached Figure Description

[0129] Figure 1 This is a flowchart of the dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field reasoning, as described in this invention.

[0130] Figure 2 This is a schematic diagram of the module principle of the simulation platform of the present invention. Detailed Implementation

[0131] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.

[0132] like Figure 1 As shown in the figure, this specific embodiment provides a dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field reasoning, including the following steps:

[0133] Step 1, Setting the research object and initial boundary conditions: In the structural space domain Within the time domain [0,T], where T represents the total duration of the study or prediction, the initial states of the carbon dioxide concentration field and displacement field are set, and the boundary conditions of the concentration field and the mechanical field are defined. The boundary conditions of the concentration field include the concentration setpoint boundary and the concentration flux boundary, and the boundary conditions of the mechanical field include the displacement constraint boundary and the stress load boundary, forming a standardized set of initial boundary conditions B; specifically:

[0134] To achieve unified modeling for dual-domain generation prediction in carbon mechanics, the geometric, material, and environmental conditions of civil structures are first standardized and defined to form an input set that can be used by both the control equations and the generation model. By uniformly describing the geometric domain, time domain, and their initial and boundary conditions, the physical consistency and repeatability of subsequent equation solving and generation model inference are ensured.

[0135] (1) Initial conditions setting

[0136] In the structural space domain With time domain [0, [Inside, among which,] Represents the set of real numbers. Representing three-dimensional real space, The total duration of the study or prediction is indicated by the initial states of the carbon dioxide concentration field and displacement field as follows:

[0137] (1),

[0138] (2),

[0139] In the formula: This represents the CO2 concentration field within the pores at time t. This represents the initial CO2 concentration distribution; Represents the displacement field at time t; Indicates the depth of carbonization; Represents spatial coordinates; Indicates displacement; Indicates time.

[0140] The formula for the concentration setpoint boundary is as follows:

[0141] (3),

[0142] In the formula: This represents the CO2 concentration field within the pores at time t. This represents the atmospheric CO2 concentration at time t.

[0143] The formula for the concentration flux boundary is as follows:

[0144] (4),

[0145] In the formula, Indicates the effective diffusion coefficient; Represents the outward normal vector; Represents the concentration gradient; Indicates the concentration setpoint boundary; Indicates the concentration flux boundary; Represents the stress tensor; This represents the concentration flux boundary value at time t;

[0146] ② Boundary conditions of the mechanical field

[0147] The stress and constraint conditions of the structure are as follows:

[0148] The displacement constraint boundary satisfies (5),

[0149] In the formula: Represents the displacement field at time t; Indicates the displacement constraint boundary;

[0150] The stress load boundary satisfies (6),

[0151] In the formula: The stress tensor represents time t; Indicates the displacement force boundary; The external force at time t;

[0152] (3) Output and logic connection

[0153] The formula for the standardized initial boundary condition set B is as follows:

[0154] (7),

[0155] In the formula: This represents the initial CO2 concentration distribution; This represents the atmospheric CO2 concentration at time t. Indicates the effective diffusion coefficient; This represents the concentration flux boundary value at time t; The external force at time t; Indicates the concentration setpoint boundary; Indicates the concentration flux boundary; Indicates the displacement constraint boundary; This indicates the boundary of the displacement force.

[0156] The standardized initial boundary condition set B serves as the boundary constraint input for the carbon-mechanical dual-domain governing equations in step 2. In step 3, it serves as the condition input for generating the physics inference model. In step 5, it is used for physical and energy consistency verification of the results. This standardization process ensures complete consistency of the model inputs at the spatiotemporal, boundary, and physical constraint levels, eliminating the problem of incomplete physics field closure caused by inconsistent data interfaces at its source.

[0157] Step 2, Construction of the carbon mechanical dual-domain coupled control equation system: Based on the initial boundary condition set B in Step 1, establish the chemical subdomain control equation, the mechanical subdomain control equation, and the carbon mechanical coupling mechanism equation, construct the bidirectional coupled control equation system of carbonization diffusion and mechanical response, and output the physical control equation set P;

[0158] In the standardized structural space domain With time domain [0, To simultaneously characterize the coupling relationship between carbonation diffusion reaction and mechanical response in concrete structures, a dual-domain governing equation system is established.

[0159] The carbonization process alters the porosity and basicity of materials, leading to a degradation of the diffusion coefficient and stiffness; conversely, the structural stress state also affects the diffusion path. To achieve this two-way coupling, physical constraint equations need to be defined before generating the physical field inference model to ensure that the model output conforms to physical conservation and mechanical equilibrium.

[0160] (2) Carbonization-diffusion reaction equation (chemical subdomain)

[0161] The carbonization process follows a coupling law between diffusion and chemical reaction, and the governing equations of the chemical subdomains are as follows:

[0162] (8),

[0163] In the formula: This represents a partial derivative operator used to describe the local rate of change of a multivariable physical field function with respect to a certain independent variable; This represents the CO2 concentration field within the pores at time t. Indicates time; Indicates the effective diffusion coefficient of concentration-stress coupling; The term representing the carbonization reaction rate; This indicates the external boundary condition for carbon dioxide concentration. Indicates temperature; Represents the stress tensor; , Representing gradient and divergence operators;

[0164] The governing equation of this chemical subdomain indicates that at any given time... Below this, the rate of change of CO2 within the pores is equal to the difference between the divergence of the diffusion flux and the consumption term of the chemical reaction. Wherein... The changes in concentration and stress reflect the influence of mechanical state on the diffusion channel.

[0165] (3) Equilibrium equations and constitutive relations (mechanical subdomains)

[0166] Considering the equilibrium conditions of the material under the combined effects of carbonization, temperature, and external load, the governing equations of the mechanical subdomain are defined as follows:

[0167] (9),

[0168] (10)

[0169] In the formula: Represents the stress tensor; Indicates the density of body force (gravity or external load); Represents the elastic stiffness tensor as it evolves with carbonization; Represents the total strain tensor; Indicates carbonization shrinkage strain; This indicates temperature strain.

[0170] Carbonization shrinkage strain is expressed as:

[0171] (11),

[0172] in The carbonization shrinkage coefficient, It is a unit tensor.

[0173] Stiffness Tensor It can be defined as:

[0174] (12)

[0175] in Stiffness when not carbonized; The carbonization stiffness degradation coefficient; This represents the saturated carbonization concentration.

[0176] (4) Carbon-mechanical coupling mechanism

[0177] To describe the inverse effect of stress on the diffusion coefficient, the carbon mechanical coupling mechanism equation is defined as follows:

[0178] (13)

[0179] In the formula: Indicates the reference diffusion coefficient; Indicates the carbonization inhibition coefficient; Indicates the stress coupling coefficient; This represents the stress trace, i.e., the volume average stress.

[0180] When the structure is under compressive stress ( The diffusion coefficient decreases; in the tensile stress region ( The diffusion coefficient increases, thus demonstrating the promoting effect of pore microcracks on the carbonization rate.

[0181] (5) Definition of physical constraint residuals (for subsequent model embedding)

[0182] To impose physical constraints during the training and inference phases of the generative model, two types of governing equation residuals are defined:

[0183] The formula for the carbonization residual is: (14)

[0184] The formula for the mechanical residual is: (15).

[0185] These two residuals measure the degree to which the current concentration field and stress field deviate from the control equations, respectively. In the physical field inference model generated in step 3, they serve as the input feedback signal of the "Physical Consistency Controller (PCC)" to correct the model output in real time, so that the generated result satisfies the conservation and equilibrium conditions.

[0186] (6) Logical continuity

[0187] Based on the above derivation, this step outputs a complete set of physical governing equations that can be directly used by the generated model. The set of physical governing equations P is as follows:

[0188] (16)

[0189] In the formula, R diff R represents the carbonization residual, which is the residual of the control equations used in generating the model training; mech This represents the mechanical residual, which is the residual of the governing equations for which physical constraints are imposed during the reasoning stage.

[0190] This set will be embedded inside the generation kernel (DiffusionTransformer) in step 3 during the construction of the physical field inference model, to implement an active physical consistency loop of "generation-constraint-regeneration".

[0191] Step 3, Generative Physics Field Inference Model Construction and Dual-Domain Coupled Prediction: Based on the set of physical control equations P output in Step 2 and the set of initial boundary conditions B formed in Step 1, a generative physics field inference model is constructed. The bidirectional coupled control equation system of carbonization diffusion and mechanical response is embedded into the generative physics field inference model. Spatial, temporal, and physical constraint embedding features are extracted through spatiotemporal feature encoding to capture the multi-timescale features of carbonization mechanical evolution. A dual-domain generation kernel is used to realize the coordinated iterative evolution of the carbonization concentration field and stress field in the same generation cycle. The generation process is then corrected by an active physical consistency regulator based on the dynamic feedback of carbonization and mechanical residuals until the residuals converge. Finally, the carbonization concentration field C(x,t) and stress field σ(x,t) satisfying the set of physical control equations P and the set of initial boundary conditions B are output, forming a dual-domain coupled evolution prediction of carbon mechanics; specifically:

[0192] (1) Design motivation and overall idea

[0193] Traditional carbon-mechanical coupling analysis typically employs stepwise numerical calculations, first solving for carbonization and diffusion, and then applying the results for mechanical analysis. This stepwise method is prone to inconsistencies between boundary error propagation and time step, leading to decreased prediction accuracy.

[0194] To achieve a unified integration of physical constraints and data-driven approaches, this embodiment proposes a Generative Physical Field Reasoning Model (GPFRM).

[0195] The generative physics inference model directly embeds the carbon-mechanical dual-domain control equation established in step 2 into the generative model, enabling the carbonization concentration field and stress field to evolve collaboratively in the same generation cycle, thus achieving proactive physical consistency inference of "generation-correction-regeneration".

[0196] (2) Overall structure of the model

[0197] Generative physics inference models can be formally represented as mapping relationships:

[0198] (17)

[0199] In the formula: This represents the generation of a physics inference model, with the following parameter set: ; It is a spatial coordinate vector; It is a time variable; For material and environmental parameters; For the initial set of boundary conditions (from step 1); The set of parameters for the governing equations (from step 2); and This represents the generated carbonization concentration field and stress field.

[0200] The model is constructed by combining a multi-scale spatiotemporal feature encoder with a dual-domain generator kernel. The encoder extracts the spatial-temporal-physical constraint embedding of the input features, while the generator kernel is responsible for the iterative generation of the dual-domain coupled field.

[0201] (3) Spatiotemporal feature coding and conditional embedding

[0202] To accurately capture the multi-timescale features of carbonization-mechanical evolution, the input is first mapped to unified latent features by a spatiotemporal encoder:

[0203] (18)

[0204] In the formula, This is a latent representation. Indicates by parameters The control encoding function.

[0205] The encoder employs a three-channel convolutional and temporal position encoding structure, which can retain conditional information such as boundary, load, and material parameters, ensuring the spatiotemporal consistency of the generation process.

[0206] (4) Dual-domain generating kernel structure

[0207] Based on the latent features output by the encoder, the Dual-domain Generator Core (DGC) is responsible for generating the field distributions of the carbonization and mechanical domains. The DGC is implemented using a diffusion model or a Transformer structure, as detailed below:

[0208] (a) Generation based on the diffusion model

[0209] The diffusion model constructs the generation process through random perturbation and denoising inversion:

[0210] (19)

[0211] In the formula: Indicates the first Latent variable vector; Indicates the time step; This represents the generation and update function, i.e., the neural operator; These are spatiotemporal coding features.

[0212] The process involves gradually denoising and reconstructing the physical field distribution using random perturbation vectors.

[0213] After each generation step, the carbonization and mechanical residuals are calculated. , Then, the hidden variables are corrected by feedback to achieve physically consistent diffusion generation.

[0214] (b) Transformer-based generation

[0215] When long-range spatiotemporal dependencies need to be captured, the kernel generation adopts a self-attention mechanism:

[0216] (20)

[0217] In the formula: , , These are query, key, and value vectors, respectively. It is a constant for the attention dimension; This represents the normalized weight function. The Transformer structure can capture nonlocal dependencies across time steps, enabling global modeling of high-dimensional coupled fields.

[0218] (5) Active Physical Consistency Regulator (PCC)

[0219] To ensure that the output during the generation phase conforms to physical constraints, this embodiment embeds a Physical Consistency Controller (PCC) within the dual-domain generation kernel. In each generation iteration, the carbonization residual and mechanical residual are calculated based on the current output, and the latent variable vector is dynamically adjusted. The current generation result is output when the residual converges to below a threshold. Its working mechanism is as follows:

[0220] a. In each generation iteration, based on the current output , Calculate the residual , ;

[0221] The residual The formula is as follows:

[0222]

[0223] In the formula: This represents the CO2 concentration field within the pore at time t and spatial location x. The gradient of the concentration field represents the direction and intensity of the change in carbon dioxide concentration in the pores within space. The effective diffusion coefficient describes the ability of carbon dioxide to diffuse through pores. This coefficient may vary with the concentration of carbon dioxide. The change in concentration reflects the influence of concentration on the diffusion rate. The carbonization reaction rate term represents the rate at which carbon dioxide reacts with hydration products; it is typically a rate dependent on concentration. Functions related to other environmental factors such as possible temperature or humidity; Let be the partial derivative of the concentration field with respect to time, representing time . The rate of change of carbon dioxide concentration in the pores over time reflects the concentration change during the carbonization process. The divergence operator is used to describe the spatial variation of a physical field. In the formula, the divergence operator is applied to the diffusion term to indicate the direction and rate of concentration change. It is a carbonation diffusion term, representing the diffusion process of carbon dioxide concentration field. It describes the propagation of carbon dioxide in concrete over time and space.

[0224] The residual The formula is as follows:

[0225]

[0226] In the formula: Let be the stress tensor, at time When, it indicates the position of the structure. Stress state at the location; It is a divergence operator used to describe the spatial variation of a physical field; The divergence of the stress tensor represents the distribution and variation of stress in space; External force density represents the external forces acting on the structure. It can be gravity, external loads, etc., and occurs at time [time]. Acting on position External force density.

[0227] b..PCC dynamically adjusts implicit variables based on the residual magnitude:

[0228] (twenty two),

[0229] in To adjust the step size; Indicates the current moment Hidden variables under Find the gradient;

[0230] c. When the residual converges to the threshold The following outputs the current generated result. Through PCC, active residual feedback control in the generation stage is achieved, significantly improving the physical reliability and stability of the model.

[0231] (6) Model output and logical connection

[0232] Final generated model output:

[0233] (twenty three),

[0234] The generated results simultaneously satisfy the physical equations of step 2 and the boundary conditions of step 1, forming a carbon-mechanical dual-domain coupled prediction. The output also includes intermediate variables: (24), where, For carbonization depth, It serves as a structural stiffness degradation index, used for the construction of joint losses and calculation of engineering indices in subsequent S4.

[0235] Step 4: Based on the generative physics inference model constructed in Step 3, a joint loss function is constructed, including data fitting loss, physical equation residual loss, energy constraint loss, and constitutive consistency loss. A two-stage hybrid optimization strategy is used to train the model until convergence. The calculation of the physical equation residual loss, energy constraint loss, and constitutive consistency loss is based on the bidirectional coupled control equation system of carbonization diffusion and mechanical response constructed in Step 2. When the data fitting loss, physical equation residual loss, and energy constraint loss are less than preset thresholds for data error, physical residual, and energy error, respectively, the training converges, and the optimized model parameter set and loss weight configuration are output. Specifically:

[0236] In the generative physics inference model of step 3, the carbonization domain and the mechanical domain evolve simultaneously through the same generation cycle. However, if the model is trained solely using a data-driven approach, physical conservation and equation consistency will be ignored, resulting in a lack of physical interpretability in the generated results. Therefore, this embodiment introduces a joint loss function during the training phase to unify observation data errors, equation residual errors, and energy constraint errors into a single optimization objective. This hybrid optimization strategy achieves triple consistency between "data, physics, and energy."

[0237] (1) Construction of joint loss function

[0238] The joint loss function for the generative physics inference model is defined as:

[0239] (25)

[0240] In the formula: This represents the model parameter set, including the encoder, generator kernel, and PCC parameters. , , , This represents the weighting coefficient of each loss term; This represents the data fitting loss; , Represents the carbonization and mechanical equation residuals; Indicates energy constraint loss; This represents the constitutive consistency loss.

[0241] (2) Definition and physical meaning of various losses

[0242] (a) Data fitting loss

[0243] The data fitting loss is calculated using the following formula to constrain the consistency between the generated field and high-precision simulation or experimental data:

[0244] (26)

[0245] In the formula: , This represents the concentration field and stress field generated by the model; , Indicates a reference value for numerical simulation or experiment; , This represents the 2-norm and the Frobenius norm.

[0246] Data fitting loss enables the generated physics inference model to statistically approximate real observations.

[0247] (b) Physical equation residual loss

[0248] The residual loss of the physical equation is minimized by minimizing the squared residual of the equation in step 2 to ensure that the generated result satisfies conservation and balance. The formula is as follows:

[0249] (27)

[0250] This item reflects the degree of agreement between the generated physical field and the governing equations, and measures physical consistency in real time.

[0251] (c) Energy confinement loss

[0252] The energy constraint loss is used to ensure the consistency of energy conservation and transfer in the carbon-mechanical dual-domain system. The formula for calculating the energy constraint loss is as follows:

[0253] (28)

[0254] In the formula: Represents the stress tensor; Represents the strain tensor; Indicates the boundary surface force; Represents the displacement field; This represents the integral over the volumetric domain, i.e., volumetric energy. This represents the boundary integral, i.e., the external work done.

[0255] This ensures that the generated stress field satisfies the principle of energy balance, thus maintaining physical plausibility even in the absence of monitoring data.

[0256] (d) Constitutive consistency loss

[0257] The constrained stress field is consistent with the material constitutive relation, and the formula for calculating the constitutive consistency loss is:

[0258] (29)

[0259] In the formula: F represents the Frobenius norm;

[0260] Constitutive consistency loss is used to prevent the generative physics inference model from producing non-physical stress-strain distributions during training.

[0261] (4) Hybrid optimization strategy

[0262] To improve convergence speed and stability, this embodiment employs a two-stage hybrid optimization strategy: the two-stage hybrid optimization strategy includes an outer optimizer and an inner optimizer, the outer optimizer optimizes the network parameters... Weight decay and adaptive learning rate adjustment are performed. Details are as follows:

[0263] (a) Outer optimizer (AdamW-based global parameter update)

[0264] Outer optimizer for network parameters Perform weight decay and adaptive learning rate adjustment:

[0265] (30)

[0266] in For learning rate, Provides a stable weight update mechanism.

[0267] (b) Inner optimizer (based on automatic differentiation for residual correction)

[0268] Generate latent variables Implement adaptive residual update:

[0269] (31),

[0270] in Inner layer step size; Represents the latent variable The gradient operator is executed once in each generation loop, which can actively correct physical residuals during the training phase and reduce gradient oscillations and overfitting.

[0271] (5) Multi-stage convergence criterion

[0272] Model training converges when all of the following conditions are met:

[0273] (32),

[0274] in , , These are the thresholds for data error, physical residual, and energy error, respectively.

[0275] Once the convergence criterion is met, the model enters the inference phase (corresponding to S5) for long-term evolution prediction.

[0276] (6) Logical connection and output

[0277] Step 4: Output the final optimized model parameter set. And the corresponding loss weight configuration:

[0278] (33),

[0279] In the formula, This represents a partial derivative operator used to describe the local rate of change of a multivariable physical field function with respect to a certain independent variable.

[0280] This output serves as the input for the dual-domain evolution prediction and adaptive correction in step 5, enabling physically reliable high-precision predictions during the inference phase.

[0281] Step 5: Based on the optimized model parameter set and loss weight configuration output in Step 4, the time domain [0, T] defined in Step 1 is discretized into N time layers. Within each time step, dual-domain evolutionary recursive calculation, latent variable residual self-repair mechanism, and multi-scale dynamic stability control are executed sequentially. The final output is an engineering-interpretable result, which includes the complete field distribution, carbonization depth distribution, and stiffness degradation index. The stiffness degradation index... From the current elastic modulus With initial elastic modulus The ratio is defined for assessing structural performance degradation. Specifically:

[0282] The model after optimization by the joint loss function Building upon this foundation, the problems of error accumulation and physical drift in long-term prediction still need to be addressed. Traditional neural network inference stages operate on a "static generation" model, meaning the input-output mapping is a one-time process, lacking temporal self-correction capabilities. To address this, this embodiment proposes an Adaptive Dual-domain Evolution and Residual Self-correction Mechanism (ADERSM), which achieves stable prediction of the carbon-mechanical dual-domain field during long-term evolution through time-step recursion and dynamic updates of the latent space.

[0283] (1) Dual-domain evolutionary recursive mechanism

[0284] In the time domain Internally, the generation process is discretized into Time layer Each step takes 1 hour. .

[0285] The two-domain evolutionary recursion of the model during the inference phase is recursively performed as follows:

[0286] (34),

[0287] (35),

[0288] In the formula: This represents the carbonization concentration field at time k+1; This represents the stress field at time k+1; Let represent the carbonization concentration field at time k; Let represent the stress field at time k; Represents spatiotemporal coding features; Represents the set of parameters for the governing equations; , These are sub-modules for generating the carbonization domain and the mechanical domain, respectively.

[0289] The dual-domain evolution recursion is used to realize the feedforward influence of the carbonization domain results on the mechanical domain, and the reverse feedback of the stress field on the diffusion path. Within each time step, the updated carbonization concentration is immediately fed back to the mechanical generation submodule to ensure that the dual-domain fields evolve synchronously in time.

[0290] (3) Self-repair mechanism of latent variable residuals (core innovation)

[0291] In long-term inference, small residuals accumulate over time, causing carbonization depth drift or stress imbalance.

[0292] To prevent this problem, this embodiment introduces a latent residual self-correction (LRSC) mechanism, which monitors the residuals and automatically adjusts the latent space variables to achieve model self-stabilization.

[0293] Its working principle is as follows:

[0294] The latent variable residual self-repair mechanism described in step 5 is executed according to the following steps:

[0295] Step 51: Calculate the residuals of the governing equations for the chemical subdomain and the governing equations for the mechanical subdomain at the current time.

[0296] The residual formula for the governing equation of the chemical subdomain at the current moment is as follows:

[0297] (36)

[0298] In the formula, Indicates the first At each discrete time step, the residuals of the mechanical equilibrium governing equations are used to quantify the degree of deviation of the generated stress field from the mechanical equilibrium conditions and constitutive relations.

[0299] The residual formula for the governing equation of the current mechanical subdomain is as follows:

[0300] (37)

[0301] In the formula, Indicates the first At each discrete time step, the residuals of the mechanical equilibrium governing equations are used to quantify the degree of deviation of the generated stress field from the mechanical equilibrium conditions and constitutive relations.

[0302] Step 52: Correct the latent variables based on the magnitude of the residuals. The correction formula is as follows:

[0303] (38),

[0304] In the formula, Adjust the step size for the hidden space; Indicates the first Latent variables corresponding to each discrete time level The gradient operator is used to calculate the direction of change of the residual function with respect to the latent variables, thereby guiding the adaptive correction of the latent space;

[0305] Step 53, when the local residual If the current hidden state is retained as the new prediction baseline, and the residual exceeds the threshold, a regeneration process is triggered, and the model recalculates the result. .

[0306] This mechanism ensures that predictions automatically correct drift over long periods of time, achieving stable convergence of the generated physical field.

[0307] (4) Multi-scale dynamic stability control

[0308] To prevent local oscillations, this embodiment introduces a multi-scale smoothing operator (MSO) in the prediction stage to achieve multi-scale dynamic stability control. Local filtering of the dual-domain field is performed at each time step according to the smoothing kernel function formula, which is as follows:

[0309] (39)

[0310] In the formula: Represents the smoothing kernel function, with the scaling parameter being... ; This represents the smoothed carbonization concentration field; This represents the smoothing operator.

[0311] The smoothing operator performs local filtering after each self-repair to avoid micro-scale oscillations affecting the stability of global prediction.

[0312] Similarly, the corresponding stress field also performs... (40),

[0313] (5) Prediction results and physical output

[0314] After completing time recursion and residual self-healing, the model outputs the following engineering-interpretable results:

[0315] (41),

[0316] In the formula: Represents the carbonization depth distribution, defined as ; The stiffness degradation index is defined as follows: ; , This represents the current and initial elastic modulus.

[0317] The engineering-interpretable results include both the complete field distribution and engineering metrics that can be directly used for durability assessment. This dual-layer output ensures the interpretability and engineering usability of the model results.

[0318] The above method forms a complete closed-loop process from data input → physical reasoning → optimization training → stability prediction → engineering output. The generated results can be output as spatiotemporal visualization data of carbonization concentration field, stress field, and carbonization depth, and can be interfaced with Building Information Modeling (BIM) systems via a digital twin interface to achieve structural health assessment.

[0319] Existing structural carbonization prediction methods using the finite element method suffer from low computational efficiency, while purely data-driven methods lack physical interpretability. The technical problem this embodiment aims to solve is: how to deeply embed the bidirectional coupling control equations of carbonization diffusion and mechanical response into a generative AI model to achieve efficient computation and engineering reliability for dual-domain evolution prediction under physical constraints. To address this technical problem, this embodiment also provides a carbon mechanics dual-domain generative inference simulation platform, such as... Figure 2 As shown, the carbon mechanics dual-domain generative inference simulation platform includes a data acquisition and preprocessing module, a dual-domain control equation and constraint construction module, a generative physics field inference core engine, and a hybrid optimization and self-repair engine.

[0320] The data acquisition and preprocessing module is configured to acquire structural carbonization and mechanical response data and generate standardized input tensors;

[0321] The data acquisition and preprocessing module is responsible for extracting the carbonization and mechanical data required for model training from experimental, field monitoring, and finite element results, including:

[0322] A. Carbonization data: CO2 concentration field distribution, carbonization depth test values;

[0323] B. Mechanical data: stress-strain measurement points, structural reactions, displacement fields;

[0324] C. Environmental data: temperature, humidity, CO2 concentration, and boundary conditions.

[0325] After normalization, interpolation, and noise filtering, the data is converted into a standardized input tensor:

[0326] (42),

[0327] In the formula, This represents the number of samples.

[0328] The output of the data acquisition and preprocessing module is connected to the input of the core engine for generating physical field inference, which facilitates end-to-end training.

[0329] The dual-domain control equation and constraint construction module is bidirectionally connected to the core engine for generating physical field inference. The dual-domain control equation and constraint construction module embeds carbonization diffusion equation and mechanical equilibrium equation, and generates residual operators based on symbolic automatic differentiation.

[0330] The dual-domain governing equations and constraint construction module embeds the carbonization diffusion equations and mechanical equilibrium equations from step 2, and automatically generates residual operators:

[0331] , (43),

[0332] Users can customize material properties, boundary conditions, and loading methods. The system calculates the residual gradient in real time through automatic differentiation, providing the basic operators for the joint loss function in step 4 and the self-healing mechanism in step 5. This design ensures the universality and scalability of the model's physical constraints.

[0333] The core engine for generating physical field inference is bidirectionally connected to the hybrid optimization and self-repair engine. The core engine for generating physical field inference integrates a generative AI model, a physical consistency regulator, a latent variable self-repair mechanism, and a multi-scale filtering operator to perform dual-domain evolution prediction.

[0334] The core engine for generating physics field inference is the technological heart, integrating the key mechanisms described in steps 3 to 5:

[0335] Generation core (Diffusion / Transformer): Supports dual-domain generation under different scales and scenarios;

[0336] Physical Consistency Controller (PCC): Calculates residuals in real time and provides feedback for correction;

[0337] Latent variable self-repair mechanism (LRSC): dynamic stability adjustment in long-term evolution;

[0338] Multiscale filtering operator (MSO): Prevents numerical oscillations and non-physical solutions.

[0339] It adopts a modular interface design, supports GPU parallel inference and cross-domain deployment (hybrid implementation of Python / C++ / TensorRT), and achieves efficient generation of physically reliable data.

[0340] The hybrid optimization and self-healing engine automatically assigns and dynamically adjusts the joint loss function in the training phase of step 4.

[0341] The outer AdamW global optimizer and the inner global optimizer residual corrector are run in parallel to form a two-layer closed loop:

[0342] The outer global optimizer is responsible for parameter learning and gradient updates;

[0343] The inner optimizer is responsible for minimizing physical residuals and adjusting the latent space.

[0344] The output of the core engine for generating physical field inference is connected to the input of the engineering visualization and digital twin interface. The hybrid optimization and self-healing engine is configured to dynamically adjust the weights of the joint loss function and perform two-layer optimization. The engineering visualization and digital twin interface is configured to convert the prediction results into three-dimensional field visualization graphics and standard format data output.

[0345] The engineering visualization and digital twin interface will generate results such as carbonization concentration fields. Stress field carbonization depth Stiffness degradation index Transform it into visual graphics and digital twin data interfaces.

[0346] System support:

[0347] 3D field visualization: Automatically generates concentration isosurfaces, stress cloud maps, and dynamic evolution animations of the carbonization front;

[0348] Digital twin integration: Outputs standard format data (JSON / HDF5) for integration with BIM or structural monitoring systems;

[0349] Intelligent assessment report: Automatically generates "carbonization risk map" and "residual life prediction report", which can be directly used for engineering durability decision-making.

[0350] These interfaces enable a closed loop from theoretical modeling to digital prediction to engineering decision-making.

[0351] The simulation platform can automatically monitor during training. , , The convergence state is determined, and the weights are adaptively adjusted. , , , To ensure optimal balance.

[0352] The simulation platform achieves fully automated integration of the entire process from physical modeling, model training, predictive inference to visualization of engineering results.

[0353] The simulation platform is a dedicated device for implementing a dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field inference. Each module has a one-to-one execution relationship with the steps of the method. Specifically: the data acquisition and preprocessing module performs the data preparation function in step 1; the dual-domain control equation module solidifies the physical constraints in step 2; the generative inference core engine implements model inference and training in steps 3-4; the hybrid optimization engine executes the optimization strategy in step 4; and the visualization interface outputs the prediction results in step 5. Those skilled in the art should understand that although the method can be implemented on general-purpose computing devices, the platform significantly improves engineering implementation efficiency and the automated embedding capability of physical constraints through modular integration.

[0354] This simulation platform architecture is based on the general continuum governing equations and can be extended to other coupled field problems by modifying the physical constraint terms, for example:

[0355] Chloride ion corrosion – mechanical coupling, only the carburization diffusion term needs to be replaced. ;

[0356] Temperature and humidity-stress coupling is addressed by introducing a humidity diffusion equation and a temperature strain term.

[0357] Freeze-thaw degradation prediction is improved by adding latent heat of phase change and stress expansion constraints.

[0358] This scalability gives the invention long-term application potential and industrial transformation value.

[0359] (8) Logical connection and output of results

[0360] Thus, this embodiment completes the entire unified system from step 2, physical equation construction, step 3, model design, step 4, optimization training, step 5, inference prediction, to step 6, engineering implementation.

[0361] The final output includes:

[0362] Physics field prediction model:

[0363] Software platform: GPSP

[0364] Engineering application results: (41),

[0365] The above simulation can not only automatically generate carbon-mechanical dual-domain evolution prediction results, but can also be directly used for structural life assessment and durability design, significantly improving prediction efficiency and engineering reliability.

Claims

1. A dual-domain evolution prediction method for carbon mechanics of civil structures based on generative physics field reasoning, characterized in that, Includes the following steps: Step 1, Setting the research object and initial boundary conditions: In the structural space domain Within the time domain [0,T], where T represents the total duration of the study or prediction, the initial states of the carbon dioxide concentration field and displacement field are set, and the boundary conditions of the concentration field and the mechanical field are defined. The boundary conditions of the concentration field include the concentration setpoint boundary and the concentration flux boundary, and the boundary conditions of the mechanical field include the displacement constraint boundary and the stress load boundary, forming a standardized set of initial boundary conditions B. Step 2, Construction of the carbon mechanical dual-domain coupled control equation system: Based on the initial boundary condition set B in Step 1, establish the chemical subdomain control equation, the mechanical subdomain control equation, and the carbon mechanical coupling mechanism equation, construct the bidirectional coupled control equation system of carbonization diffusion and mechanical response, and output the physical control equation set P; Step 3, Generative Physics Field Inference Model Construction and Dual-Domain Coupled Prediction: Based on the set of physical control equations P output in Step 2 and the set of initial boundary conditions B formed in Step 1, a generative physics field inference model is constructed. The bidirectional coupled control equation system of carbonization diffusion and mechanical response is embedded into the generative physics field inference model. Spatial, temporal, and physical constraint embedding features are extracted through spatiotemporal feature encoding. A dual-domain generation kernel is used to realize the collaborative iterative evolution of the carbonization concentration field and stress field in the same generation cycle. The generation process is then corrected by an active physical consistency regulator based on the dynamic feedback of carbonization and mechanical residuals until the residuals converge. Finally, the carbonization concentration field C(x,t) and stress field σ(x,t) that satisfy the set of physical control equations P and the set of initial boundary conditions B are output, forming a carbon mechanics dual-domain coupled evolution prediction. Step 4: Based on the generative physics inference model constructed in Step 3, a joint loss function is constructed, which includes data fitting loss, physical equation residual loss, energy constraint loss, and constitutive consistency loss. A two-stage hybrid optimization strategy is used to train the model until convergence. The calculation of the physical equation residual loss, energy constraint loss, and constitutive consistency loss is based on the bidirectional coupled control equation system of carbonization diffusion and mechanical response constructed in Step 2. When the data fitting loss, physical equation residual loss, and energy constraint loss are less than the preset thresholds of data error, physical residual, and energy error, respectively, the training converges, and the optimized model parameter set and loss weight configuration are output. Step 5: Based on the optimized model parameter set and loss weight configuration output in Step 4, the time domain [0,T] defined in Step 1 is discretized into N time layers. Within each time step, the dual-domain evolution recursive calculation, the latent variable residual self-repair mechanism, and the multi-scale dynamic stability control are executed sequentially. Finally, the engineering interpretable results are output, which include the complete field distribution, carbonization depth distribution, and stiffness degradation index.

2. The method according to claim 1, characterized in that, The formulas for setting the initial states of the carbon dioxide concentration field and displacement field in step 1 are as follows: （1）， （2）， In the formula: This represents the CO2 concentration field within the pores at time t. This represents the initial CO2 concentration distribution; Represents the displacement field at time t; Indicates the depth of carbonization; Represents spatial coordinates; Indicates displacement; Indicates time; The formula for the concentration setpoint boundary is as follows: （3）， In the formula: This represents the CO2 concentration field within the pores at time t. This represents the atmospheric CO2 concentration at time t. The formula for the concentration flux boundary is as follows: （4）， In the formula, Indicates the effective diffusion coefficient; Represents the outward normal vector; Represents the concentration gradient; Indicates the concentration setpoint boundary; Indicates the concentration flux boundary; Represents the stress tensor; This represents the concentration flux boundary value at time t; The displacement constraint boundary satisfies (5), In the formula: Represents the displacement field at time t; Indicates the displacement constraint boundary; The stress load boundary satisfies (6), In the formula: The stress tensor represents time t; Indicates the displacement force boundary; The external force at time t; The formula for the standardized initial boundary condition set B is as follows: （7）， In the formula: This represents the initial CO2 concentration distribution; This represents the atmospheric CO2 concentration at time t. Indicates the effective diffusion coefficient; This represents the concentration flux boundary value at time t; The external force at time t; Indicates the concentration setpoint boundary; Indicates the concentration flux boundary; Indicates the displacement constraint boundary; This indicates the boundary of the displacement force.

3. The method according to claim 1, characterized in that, The governing equations for the chemical subdomains described in step 2 are as follows: （8）， In the formula: This represents a partial derivative operator used to describe the local rate of change of a multivariable physical field function with respect to a certain independent variable; This represents the CO2 concentration field within the pores at time t. Indicates time; Indicates the effective diffusion coefficient of concentration-stress coupling; The term representing the carbonization reaction rate; This indicates the external boundary condition for carbon dioxide concentration. Indicates temperature; Represents the stress tensor; , Representing gradient and divergence operators; The governing equations of the mechanical subdomain are defined as follows: （9）， （10）， In the formula: Represents the stress tensor; Indicates physical density; Represents the elastic stiffness tensor as it evolves with carbonization; Represents the total strain tensor; Indicates carbonization shrinkage strain; Indicates temperature strain; The equation for the carbon mechanical coupling mechanism is defined as follows: （13）， In the formula: Indicates the reference diffusion coefficient; Indicates the carbonization inhibition coefficient; Indicates the stress coupling coefficient; This represents the stress trace, i.e., the volume average stress. The set of physical governing equations P is: (16) In the formula, R diff R represents the carbonization residual, which is the residual of the control equations used in generating the model training; mech This represents the mechanical residual, which is the residual of the governing equations for which physical constraints are imposed during the reasoning stage.

4. The method according to claim 1, characterized in that, Step 3, which involves constructing the generative physics inference model, is formally represented as a mapping relationship: （17）， In the formula, This represents the generation of a physics inference model, with the following parameter set: ; It is a spatial coordinate vector; It is a time variable; For material and environmental parameters; This is the initial set of boundary conditions; It is a set of physical governing equations; and This represents the generated carbonization concentration field and stress field; The spatiotemporal encoder is mapped to a unified latent representation: （18）， In the formula, For potential representation; Indicates by parameters Control encoding function; The dual-domain generation kernel is implemented using a diffusion model or a Transformer structure. The diffusion model constructs the generation process through random perturbation and denoising inversion. （19）， In the formula: Indicates the first Implicit variable vector; Indicates the time step; This represents the generation and update function, i.e., the neural operator; Spatiotemporal coding features; The Transformer architecture employs a self-attention mechanism: （20）， In the formula: , , These are query, key, and value vectors, respectively. It is a constant for the attention dimension; This represents the normalized weight function; The active physical consistency controller is embedded in the dual-domain generation kernel. In each generation iteration, it calculates the carbonization residual and mechanical residual based on the current output and dynamically adjusts the latent variable vector. When the residual converges to below the threshold, it outputs the current generation result. The formula for the carbonization residual is: (14) The formula for the mechanical residual is: (15).

5. The method according to claim 1, characterized in that, The final output described in step 3 is: （23）， The final output also includes intermediate variables: （24）， In the formula, For carbonization depth, It is a structural stiffness degradation index used for joint loss construction and engineering index calculation.

6. The method according to claim 1, characterized in that, The formula for calculating the data fitting loss in step 4 is as follows: （26）， In the formula: , This represents the concentration field and stress field generated by the model; , Indicates a reference value for numerical simulation or experiment; , Represents the 2-norm and the Frobenius norm; The formula for calculating the residual loss of the physical equation is as follows: (27) The formula for calculating the energy constraint loss is as follows: （28）， In the formula: Represents the stress tensor; Represents the strain tensor; Indicates the boundary surface force; Represents the displacement field; This represents the integral over the volumetric domain, i.e., volumetric energy. This represents the boundary integral, i.e., the external work done. The formula for calculating the constitutive consistency loss is as follows: (29) In the formula: F represents the Frobenius norm; The joint loss function is as follows: （25）， In the formula: This represents the model parameter set, including the encoder, generator kernel, and PCC parameters. , , , This represents the weighting coefficient of each loss term; This represents the data fitting loss; , Represents the carbonization and mechanical equation residuals; Indicates energy constraint loss; This represents the constitutive consistency loss; The two-stage hybrid optimization strategy includes an outer optimizer and an inner optimizer. The outer optimizer optimizes the network parameters. Perform weight decay and adaptive learning rate adjustment: （30）， In the formula, For learning rate, Provides a stable weight update mechanism; Inner optimizer generates hidden variables Implement adaptive residual update: （31）， In the formula, This is the inner step size; this process is executed once in each generation loop, which can actively correct physical residuals during the training phase and reduce gradient oscillations and overfitting. Represents the latent variable The gradient operator; The training model must simultaneously satisfy the following conditions until it converges: （32）， In the formula, , , These are the preset thresholds for data error, physical residual, and energy error, respectively. The optimized model parameter set and loss weight configuration are as follows: (33), where, This represents the optimal set of model parameters after optimization by the joint loss function and satisfaction of the convergence condition.

7. The method according to claim 1, characterized in that, The bi-domain evolution recursive calculation described in step 5 is as follows: （34）， （35）， In the formula: This represents the carbonization concentration field at time k+1; This represents the stress field at time k+1; Let represent the carbonization concentration field at time k; Let represent the stress field at time k; Represents spatiotemporal coding features; Represents the set of parameters for the governing equations; , These are sub-modules for generating the carbonization domain and the mechanical domain, respectively. The multi-scale dynamic stability control performs local filtering on the dual-domain field according to the smoothing kernel function formula at each time step. The smoothing kernel function formula is as follows: （39）， In the formula: Represents the smoothing kernel function, with the scaling parameter being... ; This represents the smoothed carbonization concentration field; Represents the smoothing operator; The final output project can be interpreted as follows: （41）， In the formula: Represents the carbonization depth distribution, defined as ; The stiffness degradation index is defined as follows: ; , This represents the current and initial elastic modulus.

8. The method according to claim 1, characterized in that, The latent variable residual self-repair mechanism described in step 5 is executed according to the following steps: Step 51: Calculate the residuals of the governing equations for the chemical subdomain and the governing equations for the mechanical subdomain at the current time. The residual formula for the governing equation of the chemical subdomain at the current moment is as follows: （36）， In the formula, Indicates the first The time layer or the first The residual of the chemical subdomain governing equation at time t is used to measure the degree of deviation of the currently generated carbonization concentration field from the chemical subdomain governing equation; This represents the time step between two adjacent discrete time layers; The residual formula for the governing equation of the current mechanical subdomain is as follows: （37）， In the formula, Indicates the first At each discrete time step, the residuals of the mechanical equilibrium governing equations are used to quantify the degree of deviation of the generated stress field from the mechanical equilibrium conditions and constitutive relations. Step 52: Correct the latent variables based on the magnitude of the residuals. The correction formula is as follows: （38）， In the formula, Adjust the step size for the hidden space; Indicates the first Latent variables corresponding to each discrete time level The gradient operator is used to calculate the direction of change of the residual function with respect to the latent variables, thereby guiding the adaptive correction of the latent space; Step 53, when the local residual When the current hidden state is retained as the new prediction baseline, a regeneration process is triggered when the residual exceeds a threshold, and the calculation is repeated. and .

9. A carbon mechanics dual-domain generative inference simulation platform for implementing the method of any one of claims 1 to 8, characterized in that, include: The data acquisition and preprocessing module is configured to acquire structural carbonization and mechanical response data and generate standardized input tensors; A dual-domain control equation and constraint construction module is built, which embeds carbonization diffusion equation and mechanical equilibrium equation, and generates residual operators based on symbolic automatic differentiation; The core engine for generating physical field inference integrates a generative AI model, a physical consistency regulator, a latent variable self-repair mechanism, and a multi-scale filtering operator to perform dual-domain evolution prediction. The hybrid optimization and self-healing engine is configured to dynamically adjust the weights of the joint loss function and perform two-layer optimization; and the engineering visualization and digital twin interface is configured to convert the prediction results into three-dimensional field visualization graphics and standard format data output.

10. The platform as described in claim 9, characterized in that, The output of the data acquisition and preprocessing module is connected to the input of the generative physics field inference core engine. The dual-domain control equation and constraint construction module is bidirectionally connected to the generative physics field inference core engine. The generative physics field inference core engine is bidirectionally connected to the hybrid optimization and self-healing engine. The output of the generative physics field inference core engine is connected to the input of the engineering visualization and digital twin interface.

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