A method for post-earthquake landslide susceptibility quantitative evaluation and implicit geotechnical parameter inversion based on KAN and physical main channel collaborative constraint

Abstract

The application discloses a post-earthquake landslide susceptibility quantitative evaluation and implicit rock-soil parameter inversion method based on KAN and physical main channel collaborative constraint, and comprises the following steps: constructing a model input containing multiple source environmental factors and geological lithology coding; inversing the ratio of equivalent cohesion and sliding body thickness and the internal friction angle by KAN under boundary constraint; connecting the ratio of equivalent cohesion and sliding body thickness and the internal friction angle into the physical chain of safety factor, critical acceleration and Newmark permanent displacement to obtain the landslide susceptibility probability of the physical main channel; setting a controlled auxiliary classification channel and one-way consistency constraint, and generating the final landslide susceptibility probability through two-stage frozen main body limited fusion; and combining random cross-validation, spatial partition cross-validation LOBO and repeated sampling uncertainty analysis to model output the susceptibility partition and rock-soil parameter uncertainty interval.

Description

Technical Field

[0001] This invention specifically relates to a method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels. Background Technology

[0002] Earthquake-induced landslides are a common secondary geological hazard in mountainous and steep terrain areas. Strong earthquakes alter the stress state of slopes and, under the combined influence of various factors such as topography, lithology, soil properties, vegetation cover, seismic intensity, and hydrological conditions, induce widespread slope instability. Rapid and reliable post-earthquake assessment of regional-scale landslide susceptibility is crucial for post-disaster emergency response, risk assessment of roads and settlements, prevention and control of secondary disasters, and land space security management.

[0003] Existing methods for assessing post-earthquake landslide susceptibility mainly include empirical statistical methods, physical modeling methods, and data-driven methods. Empirical statistical methods typically establish susceptibility models based on the statistical relationship between landslide inventories and environmental factors. They offer advantages such as simplicity and suitability for regional mapping, but are highly sensitive to sample distribution and feature selection, making it difficult to fully represent the mechanical mechanisms involved in slope instability. Physical modeling methods typically calculate landslide tendency based on slope stability theory, critical acceleration, and Newmark permanent displacement, offering good mechanistic explanation. However, they usually require geotechnical parameters such as cohesion, internal friction angle, sliding mass thickness, and material unit weight as input. In regional post-earthquake scenarios, these parameters often lack densely measured data, making it difficult to directly generalize and apply physical models.

[0004] With the development of remote sensing, geographic information systems, and machine learning technologies, data-driven landslide susceptibility assessment methods have been widely applied. These methods can integrate multi-source data such as topography, seismic motion, soil, geology, and vegetation, and learn the complex relationships between landslides and environmental factors through neural networks, ensemble learning, or other nonlinear models. However, purely data-driven models often suffer from insufficient physical interpretability, and their outputs may not correspond to clear geotechnical meanings. Furthermore, when the training samples are spatially uneven, the post-earthquake landslide inventory is incomplete, or the application is regionally migrated, the model is susceptible to sample bias, leading to insufficient stability and reliability of the assessment results.

[0005] To improve the mechanistic constraints of landslide susceptibility assessment, some studies have attempted to combine machine learning models with physical relationships such as slope stability equations and Newmark displacement models. These methods estimate geotechnical parameters or risk probabilities through neural networks, and then use physical formulas for constraint calculations. While this approach balances data adaptability and physical interpretability to some extent, it still has the following shortcomings: First, conventional fully connected neural networks have limited ability to express the nonlinear mapping between complex environmental factors and implicit geotechnical parameters, and the inverted parameters are prone to values ​​outside the physical boundaries or lacking engineering significance. Second, if there is a lack of reasonable constraints between the physical probability channel and the pure classification probability channel, auxiliary classification information may pull the physical chain in the opposite direction, causing the model to deviate from the slope stability mechanism. Third, when directly fusing physical output and data-driven output, without a restricted fusion mechanism, the final probability may bypass the main physical channel, excessively follow label noise, or produce unstable calibration results. Furthermore, regional-scale post-earthquake landslide assessment not only needs to output landslide susceptibility probabilities but also needs to express the uncertainties of potential geotechnical parameters and assessment results. Due to the spatial heterogeneity of soil and rock parameters, and the potential for errors in post-earthquake landslide samples, seismic inputs, and geological environment data, providing only a single deterministic susceptibility map is insufficient to meet the needs of engineering risk assessment. How to simultaneously obtain physically meaningful implicit soil and rock parameters, stable landslide susceptibility probabilities, and quantifiable uncertainty ranges, in the absence of large-scale measured soil and rock parameters, remains a key technical challenge in post-earthquake landslide regional assessment.

[0006] Therefore, there is an urgent need for a method that can integrate multi-source post-earthquake environmental data, invert implicit geotechnical parameters, maintain the physical chain constraints of slope stability, and improve the stability and interpretability of the model through controlled auxiliary channels and restricted fusion mechanisms for post-earthquake landslide susceptibility assessment and implicit geotechnical parameter inversion. Summary of the Invention

[0007] To address the problems mentioned in the background section, the present invention aims to provide a method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels, comprising the following steps:

[0008] S1. Obtain landslide inventory data, topographic data, seismic motion data, soil property data, and geological lithology data of the target post-earthquake area. Perform spatial registration, sample screening, and feature encoding on all data to generate model input data. The model input data includes numerical features and categorical features. The geological lithology category adopts one-hot encoding with unknown category placeholders.

[0009] S2. Input the model input data into the Kolmogorov-Arnold network (KAN) subject with geotechnical boundary constraints to invert the implicit geotechnical parameters characterizing the geotechnical properties of the target area; the implicit geotechnical parameters include the ratio of cohesion to sliding body thickness q, and the internal friction angle. Where q = c_eff / t, c_eff represents the scenario-equivalent cohesion, and t represents the equivalent sliding body thickness;

[0010] S3. Integrate the implicit soil and rock parameters obtained in S2 into the slope stability physical chain, and calculate the safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn. Based on Dn, obtain the landslide susceptibility probability P_phys of the physical main channel.

[0011] S4. Based on the shared representation of the KAN subject, build an auxiliary classification channel to output the auxiliary landslide susceptibility probability P_cls; set a one-way consistency constraint to make P_cls follow P_phys after the gradient stops, and block the gradient of the auxiliary classification channel from interfering with the slope stability physical chain.

[0012] S5. A two-stage training and frozen main body restricted fusion strategy is adopted to fuse P_phys and P_cls to generate the final landslide susceptibility probability P_final. The first stage trains the KAN main body, soil and rock parameter output channels, physical chain, and auxiliary classification channels. The second stage freezes all main structures and only trains the fusion head.

[0013] S6. Based on the trained model, perform full spatial unit reasoning on the target post-earthquake area, output landslide susceptibility assessment results, and simultaneously output the spatial distribution grid of implicit soil and rock parameters, safety factor, critical acceleration and Newmark permanent displacement.

[0014] S7. Through random cross-validation, spatial partitioned cross-validation (LOBO), and repeated sampling uncertainty analysis, the uncertainty range of implicit geotechnical parameters and the final landslide probability is determined.

[0015] Preferably, the ratio of cohesion to sliding body thickness q in step S2 is related to the internal friction angle. The acquisition includes the unconstrained intermediate variable u_q output by the KAN network and Perform sigmoid boundary mapping; the corresponding expression is:

[0016] ;

[0017] ;

[0018] Where q_min and q_max represent the minimum and maximum values ​​of the ratio q of cohesion to sliding body thickness, respectively. Angle of internal friction is the maximum value.

[0019] Preferably, the calculating the safety factor Fs, the critical acceleration a_c, and the Newmark permanent displacement Dn in step S3, and converting based on Dn to obtain the physical main channel landslide susceptibility probability P_phys comprises:

[0020] ; where β represents the slope angle, represents the material unit weight; Fs is used to characterize the relative relationship between the anti-sliding capacity and the downslide effect of the slope body;

[0021] ; where, represents the gravitational acceleration; the ratio of the critical acceleration to the peak ground acceleration is defined , is the peak ground acceleration in international units;

[0022] When r≥1, the Newmark permanent displacement Dn is taken as 0; when 0<r<1, the Jibson-type formula is used to calculate the Newmark permanent displacement Dn, and the expression thereof is: ;

[0023] The calculation formula of the physical main channel landslide susceptibility probability P_phys is:

[0024] ;

[0025] In the formula, epsilon_d is a displacement smoothing constant, and D_0 is a preset instability displacement threshold.

[0026] Preferably, the training phase in step S3 further comprises: adopting a hard forward and soft backward gradient stabilization strategy, wherein the forward inference uses the original ratio r to calculate the real physical displacement, and the back propagation uses the alternative smoothing ratio r_s, whose expression is:

[0027] , where epsilon_r represents the lower limit of the ratio.

[0028] Preferably, the construction mode of the unidirectional consistency constraint loss in step S4 is:

[0029] ; and a scaling coefficient is set for the gradient back-propagated from the auxiliary classification channel to the KAN main body at the same time.

[0030] Preferably, the corresponding expression of the final landslide susceptibility probability P_final in step S5 is:

[0031] ; ; ;

[0032] In the formula, R represents the original residual of the fusion head, s represents the residual scale, G(P_phys) represents the Gaussian gating function, m represents the gating center, and w represents the gating width.

[0033] Preferably, the uncertainty analysis of repeated sampling in step S7 includes: sampling the training samples multiple times with replacement, training a complete model independently for each group of samples; obtaining the cohesion to sliding body thickness ratio, internal friction angle, probability of landslide in the main physical channel, probability of final landslide, safety factor, critical acceleration, and Newmark permanent displacement corresponding to the output of each model; and performing quantile statistics on the output results of multiple model instances to generate the mean, confidence limits, and interval width spatial grid of each index, thereby obtaining the uncertainty interval of implicit soil and rock parameters and landslide probability.

[0034] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the above-described method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channels.

[0035] The present invention also provides a computer-readable storage medium storing a computer program thereon, wherein the program, when run by a processor, executes the method described above for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channels.

[0036] The present invention also provides a computer program product comprising a computer program or computer-executable instructions, wherein when the program or instructions run on an electronic device processor, they execute the above-described method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channels.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] First, this invention uses the boundary-constrained Kolmogorov-Arnold network (KAN) to invert the ratio of cohesion to landslide thickness and internal friction angle, enabling multi-source environmental factors to be mapped into implicit parameters with geotechnical significance. Compared to purely data-driven methods that directly output landslide probabilities, this invention avoids parameters without engineering significance; it does not require extensive borehole data, relying solely on remote sensing, topographic, and publicly available seismic raster data to invert continuous spatial geotechnical parameters; and it provides stronger physical interpretability. Compared to traditional physical models that rely on measured geotechnical parameters, this invention is more suitable for regional-scale post-earthquake assessment scenarios lacking dense measured geotechnical data.

[0039] Second, this invention integrates the implicit soil and rock parameters obtained by inversion into the slope stability physical chain composed of safety factor, critical acceleration and Newmark permanent displacement, and uses the landslide susceptibility probability of the physical main channel as the main evaluation channel. This makes the landslide susceptibility probability of the physical main channel constrained by the classical soil and rock slope instability mechanism, rather than simply fitting sample labels, thus reducing the problem of insufficient physical interpretation caused by simply relying on statistical correlation or label fitting.

[0040] Third, this invention sets up an auxiliary classification channel and adopts a one-way consistency constraint, enabling the auxiliary classification channel to absorb the data discrimination information from the landslide inventory labels, while preventing it from inversely undermining the stability mechanism expressed by the main physical channel. Thus, this invention can establish a synergistic relationship between physical constraints and data adaptability, improving the model's robustness in complex post-earthquake environments, achieving synergistic gains between physical mechanisms and statistical data information, and enhancing prediction accuracy.

[0041] Fourth, this invention employs a two-stage training and frozen subject-based restricted fusion strategy, enabling the final landslide susceptibility probability to undergo limited correction while preserving the main physical channel structure. This restricted fusion method can suppress the problem of the final output bypassing the physical chain or excessively following label noise. The final landslide probability will not excessively follow sample noise, significantly improving the probability calibration accuracy and contributing to improved ranking ability, calibration performance, and engineering reliability of landslide susceptibility probabilities.

[0042] Fifth, this invention comprehensively evaluates the model's discriminative ability, spatial generalization ability, and implicit geotechnical parameter stability through random cross-validation, spatial partitioned cross-validation (LOBO), and repeated sampling uncertainty analysis. It also outputs landslide susceptibility zoning results and geotechnical parameter uncertainty intervals. This not only classifies landslide susceptibility levels but also provides a reference for analyzing slope instability control factors. This mechanism can provide richer decision-making basis for post-earthquake emergency assessment, regional risk investigation, and subsequent engineering treatment.

[0043] Sixth, this invention can simultaneously output spatial distribution results such as landslide susceptibility probability, cohesion to sliding body thickness ratio, internal friction angle, safety factor, critical acceleration, and Newmark permanent displacement. This allows the assessment results to not only reflect the tendency of landslides to occur, but also reveal the spatial differences in potential soil and rock parameters and slope stability, thereby improving the interpretability and application value of post-earthquake landslide susceptibility assessment results. Attached Figure Description

[0044] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0045] Figure 1A schematic diagram of the overall process of the quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion method based on the collaborative constraints of KAN and physical master channel provided in the embodiments of the present invention;

[0046] Figure 2 This is a schematic diagram of the process of inputting data into the multi-source post-earthquake environmental data construction model in an embodiment of the present invention; Figure 3 This is a schematic diagram of the Kolmogorov-Arnold network KAN main body inversion of implicit soil and rock parameters under boundary constraints in an embodiment of the present invention.

[0047] Figure 4 This is a schematic diagram of the process of integrating implicit soil and rock parameters into the slope stability physical chain and generating the physical main channel for landslide susceptibility in an embodiment of the present invention.

[0048] Figure 5 This is a schematic diagram of the structure of the auxiliary classification channel, unidirectional consistency constraint and physical main channel collaborative training in an embodiment of the present invention;

[0049] Figure 6 This is a flowchart illustrating the two-stage training and freezing of the subject-restricted fusion strategy in an embodiment of the present invention.

[0050] Figure 7 This is a schematic diagram of the evaluation process for random cross-validation and spatial partitioning cross-validation in embodiments of the present invention;

[0051] Figure 8 This is a schematic diagram of the process for analyzing the uncertainty of repeated sampling and outputting the uncertainty interval of implicit geotechnical parameters in an embodiment of the present invention.

[0052] Figure 9 is a schematic diagram of the spatial distribution of the landslide susceptibility assessment results of the target post-earthquake area in an embodiment of the present invention.

[0053] Figure 10 (a) is a schematic diagram of the spatial distribution of cohesion and sliding body thickness ratio in an embodiment of the present invention;

[0054] Figure 10 (b) is a schematic diagram of the spatial distribution of the internal friction angle in an embodiment of the present invention;

[0055] Figure 10 (c) is a schematic diagram of the spatial distribution of the safety factor in an embodiment of the present invention;

[0056] Figure 10 (d) is a schematic diagram of the spatial distribution of critical acceleration in an embodiment of the present invention;

[0057] Figure 10 (e) is a schematic diagram of the spatial distribution of the Newmark permanent displacement Dn in an embodiment of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0059] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the structures and / or processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted. Specific implementation method one:

[0061] This embodiment provides only a preferred implementation method: a method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of the Kolmogorov-Arnold network (KAN) and physical master channels. This method uses post-earthquake regional spatial units as evaluation objects, inputs multi-source environmental factors into the boundary-constrained KAN body, inverts the ratio of cohesion to sliding body thickness and internal friction angle, generates the landslide susceptibility probability of the physical master channel through the slope stability physical chain, and then obtains the final landslide susceptibility probability through the fusion of a controlled auxiliary classification channel and a two-stage frozen body. Specifically, it includes the following steps:

[0062] S1. Obtain landslide inventory data, topographic data, seismic motion data, soil property data, and geological lithology data for the target post-earthquake area. Perform spatial registration, sample screening, and feature coding on all data. Label the landslide-occurring samples and non-occurring samples with binary labels to generate model input data. For spatial units whose slope does not meet the conditions for slope stability analysis, screening can be performed to avoid instability in physical formula calculations due to extremely small slopes. The model input data includes numerical features and categorical features. The geological lithology category uses unique thermal coding with unknown category placeholders.

[0063] This invention provides a preferred embodiment where the model input vector consists of 15 numerical features and a 10-dimensional geological lithology category code, with an input dimension of 25. The numerical features include elevation, topographic relief, horizontal curvature, vertical curvature, slope, precipitation, vegetation index, peak ground acceleration, sand content, silt content, clay content, soil bulk density, slope standard deviation, elevation statistics, and peak ground velocity. In a specific data table, the 15 numerical features are assigned the fields Est_m, Nrt_m, HC_m, VC_m, Slp_m, Prc_m, NDVI_m, PGA_Usgs, Sand_m, Silt_m, Clay_m, Bdod_m, Slp_s, Ele_m, and PGV_Usgs in a fixed order. The geological lithology categories are represented using one-hot encoding, and placeholders for unknown categories are set to handle geological categories not seen during the training phase that may occur in the inference region. When standardizing numerical features, the standardized parameters are calculated only from the training samples and applied to both validation and inference samples; when encoding geological lithology categories, the category vocabulary is determined only from the training samples. These methods avoid information leakage during the validation and inference phases, allowing the model evaluation results to better reflect true generalization ability.

[0064] S2. Input the model input data into the Kolmogorov-Arnold network (KAN) subject with geotechnical boundary constraints to invert the implicit geotechnical parameters characterizing the geotechnical properties of the target area; the implicit geotechnical parameters include the ratio of cohesion to sliding body thickness q, and the internal friction angle. Wherein, the ratio q of cohesion to sliding body thickness represents the ratio of the scenario-based equivalent cohesion c_eff to the given sliding body thickness t, i.e., q = c_eff / t. This embodiment does not directly invert the independently measured cohesion, but rather inverts the ratio q of cohesion to sliding body thickness; when the subsequent engineering scenario analysis gives a sliding body thickness t, the scenario-based equivalent cohesion can be derived from c_eff = q × t; the sliding body thickness t is the equivalent sliding body thickness that matches the slope stability formula used under the given scenario. This setting is applicable to post-earthquake landslide assessment scenarios where continuous measured sliding body thickness data is lacking at the regional scale. The KAN adopts a learnable activation structure based on a restricted B-spline function to express the nonlinear mapping relationship between multi-source environmental factors and implicit geotechnical parameters. Preferably, the KAN body adopts a cubic B-spline function, with 8 grid intervals, a grid range of [-3,3], a hidden layer width of 64, 13 hidden layers, and the SiLU function as the basic activation function.

[0065] S3. Integrate the implicit soil and rock parameters obtained in S2 into the slope stability physical chain; let the slope angle, material unit weight, gravitational acceleration, and peak ground acceleration converted to m / s² be denoted as follows: And PGA_ms. Material density It can be determined by the material density Calculated, i.e. Preferably, It is permissible, but not limited to, taking 2300 kg / m³. Take 9.81 m / s², The value is approximately 22.563 kN / m³. The safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn are calculated, and the landslide susceptibility probability P_phys of the main physical channel is obtained based on the transformation of Dn.

[0066] S4. Based on the shared representation of the KAN subject, an auxiliary classification channel is built to output the auxiliary landslide susceptibility probability P_cls; a one-way consistency constraint is set so that P_cls follows P_phys after the gradient stops. This auxiliary channel uses the landslide inventory label as a supervision signal to absorb data-driven discrimination information and block the gradient of the auxiliary classification channel from interfering with the slope stability physical chain. Preferably, the auxiliary classification channel includes a hidden layer with a width of 16 and the activation function is the SiLU function.

[0067] S5. A two-stage training and frozen subject-constrained fusion strategy is adopted to fuse P_phys and P_cls to generate the final landslide susceptibility probability P_final. The first stage trains the KAN subject, implicit soil parameter output channel, slope stability physical chain, and auxiliary classification channel, using the validation index of the physical master channel P_phys as the basis for selecting the subject model. The loss function of the first stage includes the binary cross-entropy loss of the physical master channel landslide susceptibility probability P_phys, the auxiliary binary cross-entropy loss of the auxiliary landslide susceptibility probability P_cls, and the one-way consistency loss, where P_phys serves as the main supervised channel and P_cls as the controlled auxiliary channel. The second stage loads the model weights obtained in the first stage, freezes the KAN subject, implicit soil parameter output channel, slope stability physical chain, P_phys channel, and P_cls channel, and trains only the final fusion head. The input of the final fusion head includes the physical master channel landslide susceptibility probability P_phys after gradient stopping, the auxiliary landslide susceptibility probability P_cls, their log odds values, and the difference between them. Since the gradient is not backpropagated to the main network in the second stage, the final fusion will not change the implicit soil and rock parameter inversion results and the physical main channel structure.

[0068] S6. Based on the trained model, infer the landslide susceptibility of the entire spatial unit of the target post-earthquake area and output the landslide susceptibility assessment results. The input data of each spatial unit of the target post-earthquake area is fed into the trained model to obtain the final landslide susceptibility probability P_final. The model can also simultaneously output the landslide susceptibility probability of the main physical channel P_phys, the auxiliary landslide susceptibility probability P_cls, and the ratio of cohesion to sliding body thickness. internal friction angle The following parameters are used: safety factor Fs, critical acceleration a_c, ratio of critical acceleration to peak ground acceleration r, and Newmark permanent displacement Dn. Based on the above outputs, a landslide susceptibility zoning map, a spatial map of cohesion to sliding body thickness ratio, a spatial map of internal friction angle, a spatial map of safety factor, a spatial map of critical acceleration, and a spatial map of Newmark permanent displacement can be generated for the target area.

[0069] S7. Determine the uncertainty intervals between implicit geotechnical parameters and the final landslide probability through random cross-validation, spatial partitioned cross-validation (LOBO), and repeated sampling uncertainty analysis. Conduct model stability evaluation and uncertainty analysis. Use random cross-validation to evaluate the model's overall discriminative ability under random sample partitioning conditions, and use spatial partitioned cross-validation (LOBO) to evaluate the model's generalization ability under spatial migration conditions. Evaluation metrics may include, but are not limited to, one or more of the following: ROC-AUC, PR-AUC, equilibrium accuracy, F1 score, Brier score, and confusion matrix.

[0070] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One; the ratio of cohesion to sliding body thickness q in step S2 and the internal friction angle The acquisition includes the unconstrained intermediate variable u_q output by the KAN network and Perform sigmoid boundary mapping; the corresponding expression is:

[0071] ;

[0072] ;

[0073] Where q_min and q_max represent the minimum and maximum values ​​of the ratio q of cohesion to sliding body thickness, respectively. Angle of internal friction The maximum value. Preferably, q_min is 5 kPa / m and q_max is 40 kPa / m. The angle is 60°. Through the above transformation, the network output is limited to a range that is meaningful in geotechnical mechanics; the contents not mentioned in this embodiment are the same as in specific embodiment one.

[0074] Specific Implementation Method Three: This implementation method is a further limitation of Specific Implementation Method One or Two; Step S3, which involves calculating the safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn, and then converting Dn to obtain the probability of landslide susceptibility P_phys of the physical main channel, includes:

[0075] In the formula, β represents the slope angle. represents the unit weight of the material; Fs is used to characterize the relative relationship between the anti-sliding capacity and the sliding effect of the slope, and a larger Fs indicates higher slope stability.

[0076] ; where in the formula, represents the gravitational acceleration, and a_c represents the critical seismic acceleration required for the slope to start generating permanent displacement. When Fs is less than or close to 1, a_c is small, and the slope is more prone to generate permanent displacement under the action of ground motion; when Fs is large, a_c increases, and the slope stability is relatively improved. The ratio of the critical acceleration to the peak ground acceleration is further defined , is the peak ground acceleration in international units;

[0077] When r ≥ 1, it means that the critical acceleration is not lower than the ground motion intensity, and the Newmark permanent displacement Dn is 0; when 0 < r < 1, the Jibson-type formula is used to calculate the Newmark permanent displacement Dn, and its expression is: ; where in the formula, Dn is the Newmark permanent displacement, with the unit of cm. To ensure numerical stability, but not limited to, a very small positive lower limit can be set for r, and r is restricted to the open interval (0,1) for logarithmic calculation.

[0078] The preferred calculation formula for the physical main channel landslide susceptibility probability P_phys is:

[0079] ;

[0080] where in the formula, epsilon_d is the displacement smoothing constant, and D_0 is the preset instability displacement threshold, preferably 5 cm. Preferably, epsilon_d can be 0.001 cm, and D_0 can be 5 cm. Through logarithmic displacement probability processing, the impact of permanent displacement spanning multiple orders of magnitude on the stability of probability output can be reduced; the content not mentioned in this embodiment is the same as that in the first or second specific embodiment.

[0081] Fourth specific embodiment: This embodiment is a further limitation of the first, second or third specific embodiment; the training phase in step S3 further includes: adopting a hard forward and soft backward gradient stabilization strategy, wherein the forward reasoning uses the original ratio r to calculate the real physical displacement, and the back propagation uses the alternative smoothing ratio r_s, whose expression is:

[0082] , where in the formula, epsilon_r represents the lower limit of the ratio; the alternative Newmark displacement is calculated based on r_s to provide stable gradients; finally, P_phys maintains the hard physical result in terms of numerical forward direction, and uses the soft alternative result for training in gradient propagation; the content not mentioned in this embodiment is the same as that in the first, second or third specific embodiment.

[0083] Specific Implementation Method Five: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, or Four; in step S4, to prevent the auxiliary classification channel from inverting and destroying the physical main channel, the gradient of the auxiliary channel is scaled, and a one-way consistency constraint is set. Preferably, the gradient scaling factor of the auxiliary channel returning the KAN shared representation can be selected as 0.05; at the same time, P_cls is made to follow P_phys after the gradient stops in the log-odds space, and its consistency loss can be expressed as:

[0084] Simultaneously, a scaling factor is set for the gradient propagated back from the auxiliary classification channel to the KAN main body. Preferably, the consistency loss weight can be 0.03. With this setting, P_cls can learn a risk representation consistent with P_phys, but will not pull the physical chain away from the slope stability mechanism. Content not mentioned in this embodiment is the same as in specific embodiments one, two, three, or four.

[0085] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, or Five; the final fusion head in step S5 adopts a gated residual fusion structure with the physical main channel as the initial approximation, which can be expressed as:

[0086] ; ; ;

[0087] In the formula, R represents the original residual of the fusion head, s represents the residual scale, G(P_phys) represents the Gaussian gating function, m represents the gating center, and w represents the gating width. Preferably, but not limited to, s can be 0.25, m can be 0.5, and w can be 0.25. This structure allows the final landslide susceptibility probability P_final to start from the physical main channel landslide susceptibility probability P_phys, and allows limited correction only when P_phys is close to the uncertainty probability interval; when P_phys is close to the high confidence stable or high confidence unstable region, the residual correction is suppressed; the contents not mentioned in this embodiment are the same as those in specific embodiments one, two, three, four, or five.

[0088] Specific Implementation Method Seven: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, or Six; the uncertainty analysis of repeated sampling in step S7 includes: sampling the training samples multiple times with replacement, training the complete model independently for each group of samples; constructing multiple model instances; and saving the final landslide susceptibility probability P_final, the physical main channel landslide susceptibility probability P_phys, the auxiliary landslide susceptibility probability P_cls, and the ratio of cohesion to sliding body thickness output by each model instance. internal friction angle The parameters include the safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn. Quantile statistics are performed on the output results of multiple model instances to generate the mean, confidence limits, and interval width spatial grids for each indicator, obtaining the uncertainty intervals of implicit soil parameters and landslide susceptibility probability. This can express the parameter uncertainty and probability uncertainty caused by sample perturbation and the model training process. Content not mentioned in this embodiment is the same as in specific embodiments one, two, three, four, five, or six.

[0089] Specific Implementation Method Eight: This implementation method provides a specific application example, applying the method of the present invention to post-earthquake landslide sample data. After slope screening, the total number of spatial units participating in training, validation, and regional inference is 14925. Under random hold-out validation conditions, the final landslide susceptibility probability P_final has a ROC-AUC of approximately 0.8802, a PR-AUC of approximately 0.6993, a balance accuracy of approximately 0.7808, an F1 score of approximately 0.6322, and a Brier score of approximately 0.1202. These results indicate that under these data and partitioning conditions, the method of the present invention has good landslide discrimination ability and probability calibration performance.

[0090] In randomized cross-validation, the mean ROC-AUC of the final landslide susceptibility probability P_final across multiple random folds was approximately 0.8783, the mean PR-AUC was approximately 0.6794, the mean balance accuracy was approximately 0.7834, the mean F1 score was approximately 0.6417, and the mean Brier score was approximately 0.1328. These results demonstrate that the method of this invention possesses relatively stable overall evaluation capability under random sample partitioning conditions.

[0091] In spatial partition cross-validation (LOBO), the mean ROC-AUC of the final landslide susceptibility probability P_final across multiple spatial partitions is approximately 0.7988. Due to differences in the proportion of landslide samples, topographic and geological conditions, and seismic input across different spatial partitions, the PR-AUC and F1 values ​​fluctuate between different spatial partitions. These results demonstrate that the method of this invention can maintain a certain level of discriminative ability under spatial migration conditions, while also revealing the model's applicability boundaries and regional generalization uncertainties through spatial partition cross-validation.

[0092] In the uncertainty analysis of repeated sampling, 50 iterations of Bootstrap modeling can be used to output the ratio of cohesion to sliding body thickness q and the internal friction angle, respectively. The spatial distribution results of the landslide susceptibility probability P_phys (main physical channel), P_cls (auxiliary landslide susceptibility probability), P_final (final landslide susceptibility probability), safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn are used to generate quantile and interval width plots. This uncertainty expression can reflect the stability of implicit soil and rock parameters and landslide susceptibility probabilities under different training sample disturbance conditions, providing auxiliary basis for post-earthquake risk assessment and priority classification of engineering treatment.

[0093] To verify that this invention is not a mechanical parallel combination of KAN network, slope stability physical chain, and classification channel, multiple comparative models were set up for ablation verification under the same sample division, input features, training settings, and evaluation criteria. These comparative models include: Comparative Model 1, a model using a fully connected neural network with a Dense backbone and a logarithmic displacement activation physical chain; Comparative Model 2, a physical chain model introducing a hard forward-soft backward stabilization strategy but without employing the KAN main body and the frozen main body restricted fusion strategy; Comparative Model 3, a model using the KAN main body and physical main channel but without setting a controlled auxiliary classification channel and a final fusion head; Comparative Model 4, a model using the KAN main body, physical main channel, and controlled auxiliary classification channel but without performing a second-stage frozen main body restricted fusion; and the complete model of this embodiment, using the KAN main body, physical main channel, controlled auxiliary classification channel, and frozen main body restricted fusion. The evaluation results of each model under random hold-out verification conditions are shown in Table 1.

[0094] Table 1 Comparison of random hold-out validation metrics for different models

[0095]

[0096] In Table 1, higher ROC-AUC, PR-AUC, balance accuracy, and F1 scores indicate better performance for the corresponding metrics, while lower Brier scores indicate better performance for probability calibration.

[0097] As shown in Table 1, the ROC-AUC, PR-AUC, and Brier scores of the embodiments of the present invention are approximately 0.8802, 0.6993, and 0.1202, respectively, achieving superior or optimal performance among multiple comparative examples, especially in probabilistic calibration. Although some comparative examples have local advantages in threshold-related indicators such as balanced accuracy, the embodiments of the present invention achieve a better overall balance between ranking ability, probabilistic calibration performance, and interpretability of the physical main channel. The above results indicate that the present invention, through controlled auxiliary classification channels, unidirectional consistency constraints, and frozen subject constraint fusion, does not simply add model components, but improves the overall evaluation effect of the final landslide susceptibility probability while maintaining the physical main channel constraints. Furthermore, to verify that the final fusion head did not bypass the physical chain of slope stability and that the auxiliary classification channel did not replace the physical main channel, an internal comparative analysis was conducted within the KAN main body, physical main channel, controlled auxiliary classification channel, and frozen main body restricted fusion architecture used in this embodiment of the invention to evaluate the final landslide susceptibility probability P_final, the physical main channel landslide susceptibility probability P_phys, and the auxiliary landslide susceptibility probability P_cls. The evaluation results for each channel are shown in Table 2.

[0098] Table 2 Comparison of internal evaluation indicators of the three channels in the embodiments of the present invention

[0099]

[0100] In Table 2, higher ROC-AUC, PR-AUC, balance accuracy, and F1 scores indicate better performance for the corresponding metrics, while lower Brier scores indicate better probabilistic calibration performance. Table 2 shows that the ROC-AUCs of P_final, P_phys, and P_cls are approximately 0.8802, 0.8797, and 0.8380, respectively, and the Brier scores are approximately 0.1202, 0.1267, and 0.1863, respectively. Simultaneously, the average probability difference between P_final and P_phys is approximately 0.0167, and the correlation coefficient is approximately 0.9981. These results indicate that the auxiliary classification channel does not replace the physical main channel, but rather provides controlled discriminative information under unidirectional consistency constraints. The final fusion head also does not circumvent the slope stability physical chain, but rather performs limited corrections to the physical main channel output based on the frozen main body, thereby improving the discriminative ability and calibration stability of the final output while maintaining physical interpretability.

[0101] Through the above implementation methods, this invention can invert physically meaningful implicit geotechnical parameters from multi-source environmental data in the absence of regional-scale measured geotechnical parameters, and generate landslide susceptibility probabilities through a physical chain composed of safety factors, critical acceleration, and Newmark permanent displacement. Compared with purely data-driven models, the output results of this invention have a clearer geotechnical mechanical interpretation; compared with traditional physical models that rely on dense measured parameters, this invention is more suitable for rapid post-earthquake regional-scale assessment. This invention, through controlled auxiliary classification channels and one-way consistency constraints, enables the model to absorb data discrimination information from landslide inventory labels while maintaining the dominant role of the physical main channel; through two-stage frozen main body restricted fusion, the final probability is subject to limited correction without bypassing the physical chain, thereby improving the top-level probability ranking and probability calibration performance, maintaining good classification and recognition capabilities under specific threshold conditions, and reducing the risk of overfitting landslide inventory label noise.

[0102] Specific Implementation Method Nine: This implementation method is an electronic device, including a processor and a memory. The memory stores a computer program. When the computer program is executed by the processor, it implements the above-mentioned method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channel.

[0103] Specific Implementation Method Ten: This implementation method is a computer-readable storage medium storing a computer program. When the program is executed by a processor, it performs the aforementioned method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channels. The storage medium described in this implementation method includes, but is not limited to, hard disks, USB flash drives, embedded system storage instruction sets, etc., supporting real-time data processing and parameter updates.

[0104] Specific Implementation Method Eleven: This implementation method is a computer program product, which includes a computer program or computer executable instructions. When the program or instructions run on the processor of an electronic device, they execute the above-mentioned method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channel.

[0105] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels, characterized in that, comprising the following steps: S1. Obtain landslide inventory data, topographic and geomorphic data, ground motion data, soil property data and geological lithology data of the target post-earthquake area, perform spatial registration, sample screening and feature encoding on all the data to generate model input data; the model input data includes numerical features and categorical features, and the geological lithology categories adopt one-hot encoding with an unknown category placeholder; S2. Input the model input data into the Kolmogorov-Arnold network (KAN) subject with geotechnical boundary constraints to invert the implicit geotechnical parameters characterizing the geotechnical properties of the target area; the implicit geotechnical parameters include the ratio of cohesion to sliding body thickness q, and the internal friction angle. Where q = c_eff / t, c_eff represents the scenario-equivalent cohesion, and t represents the equivalent sliding body thickness; S3. Access the implicit geotechnical parameters obtained in S2 to the slope stability physical chain, calculate the safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn, and convert based on Dn to obtain the landslide susceptibility probability P_phys of the physical main channel; S4. Build an auxiliary classification channel on the basis of the shared representation of the KAN backbone to output the auxiliary landslide susceptibility probability P_cls; set a one-way consistency constraint to make P_cls follow P_phys after gradient stopping, so as to block the gradient of the auxiliary classification channel from reversely interfering with the slope stability physical chain; S5. Adopt a two-stage training and backbone-freezing restricted fusion strategy to fuse P_phys and P_cls to generate the final landslide susceptibility probability P_final; wherein, in the first stage, the KAN backbone, the geotechnical parameter output channel, the physical chain and the auxiliary classification channel are trained; in the second stage, all backbone structures are frozen, and only the fusion head is trained; S6. Perform inference on all spatial units in the target post-earthquake area based on the trained model, output the landslide susceptibility assessment result, and synchronously output the spatial distribution rasters of the implicit geotechnical parameters, safety factor, critical acceleration and Newmark permanent displacement; S7. Determine the uncertainty intervals of the implicit geotechnical parameters and the final landslide probability through random cross-validation, spatially partitioned cross-validation LOBO and repeated sampling uncertainty analysis.

2. The method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels as described in claim 1, is characterized in that... The ratio of cohesion to sliding body thickness q in step S2 and the internal friction angle The acquisition includes the unconstrained intermediate variable u_q output by the KAN network and Perform sigmoid boundary mapping; the corresponding expression is: ； ； Where q_min and q_max represent the minimum and maximum values ​​of the ratio q of cohesion to sliding body thickness, respectively. Angle of internal friction The maximum value.

3. The method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels as described in claim 1, is characterized in that... The calculation of the safety factor Fs, critical acceleration a_c, and Newmark permanent displacement Dn described in step S3, and the conversion based on Dn to obtain the landslide susceptibility probability P_phys of the physical main channel includes: In the formula, β represents the slope angle. The unit weight of the material is indicated; Fs is used to characterize the relative relationship between the slope's anti-sliding capacity and the sliding force. In the formula, Represents gravitational acceleration; defines the ratio of critical acceleration to peak ground acceleration. , Peak ground acceleration is expressed in international units. When r≥1, the Newmark permanent displacement Dn is set to 0; when 0<r<1, the Jibson formula is used to calculate the Newmark permanent displacement Dn, and its expression is: ； The calculation formula of the landslide susceptibility probability P_phys of the physical main channel is: ； where epsilon_d is the displacement smoothing constant, and D_0 is the preset instability displacement threshold.

4. The method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels as described in claim 3, is characterized in that... The training phase in step S3 further includes: adopting a hard forward and soft reverse gradient stabilization strategy, wherein the forward inference uses the original ratio r to calculate the real physical displacement, and the back propagation uses the alternative smoothing ratio r_s, whose expression is: In the formula, epsilon_r represents the lower limit of the ratio.

5. The method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels as described in claim 4, is characterized in that... The construction method of the one-way consistency constraint loss in step S4 is: Simultaneously, a scaling factor is set for the gradient transmitted back from the auxiliary classification channel to the KAN main body.

6. The method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels as described in claim 5, is characterized in that... The corresponding expression of the final landslide susceptibility probability P_final in step S5 is: ； ； ； where R represents the original residual of the fusion head, s represents the residual scale, G(P_phys) represents the Gaussian gating function, m represents the gating center, and w represents the gating width.

7. The method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the synergistic constraints of KAN and physical master channels as described in claim 6, is characterized in that... The uncertainty analysis of repeated sampling in step S7 includes: sampling the training samples multiple times with replacement, training a complete model independently for each group of samples; obtaining the cohesion to sliding body thickness ratio, internal friction angle, probability of landslide in the main physical channel, probability of final landslide, safety factor, critical acceleration, and Newmark permanent displacement of the corresponding outputs of each model; performing quantile statistics on the output results of multiple model instances; generating the mean, upper and lower confidence limits, and interval width spatial grids of each index; and obtaining the uncertainty intervals of implicit soil and rock parameters and landslide probability.

8. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channel as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program thereon, characterized in that, When the program is run by the processor, it executes the method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channel as described in any one of claims 1 to 7.

10. A computer program product comprising a computer program or computer-executable instructions, characterized in that, When the program or instruction runs on the processor of an electronic device, it executes the method for quantitative assessment of post-earthquake landslide susceptibility and implicit geotechnical parameter inversion based on the collaborative constraints of KAN and physical master channels as described in any one of claims 1 to 7.

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