A method, device, medium and product for shape response modeling of a magnetically controlled flexible body

Abstract

The present disclosure relates to a morphological response modeling method, device, medium and product of a magnetically controlled flexible body, the method comprising: obtaining a training sample set containing flexible body parameter data and magnet control data of the magnetically controlled flexible body, and obtaining a morphological response model to be trained composed of a KAN network, a physical simulation model and a physical information neural network; performing local load solving on the training sample through the KAN network to obtain end equivalent load of the magnetically controlled flexible body, performing global mapping on the flexible body parameter data and the end equivalent load through the physical simulation model to obtain discrete morphological data, performing continuous field reconstruction on the discrete morphological data through the physical information neural network to obtain continuous morphological data, and completing iterative training of the morphological response model in combination with a reference morphological data set of the training sample set. The present embodiment realizes high-precision, high-efficiency and strong-generalization continuous morphological modeling of the magnetically controlled flexible body, and provides technical support for application and popularization of the magnetically controlled flexible body.

Description

Technical Field

[0001] This disclosure relates to the field of mechanical data processing technology, and in particular to a method, device, medium and product for morphological response modeling of a magnetically controlled flexible body. Background Technology

[0002] Flexible bodies, with their advantages of high compliance, high controllability, and structural continuity, are widely used in minimally invasive procedures, soft robotics, and aerospace. Precisely constructing their nonlinear morphological response characteristics is a crucial prerequisite for achieving high-precision control and intelligent operation.

[0003] Currently, flexible body modeling methods are mainly divided into two categories: physics-driven models and data-driven models. Physics-driven models are constructed based on classical mechanics theory, using material constitutive relations and geometric nonlinear equations to derive the morphological response of flexible bodies; data-driven models, on the other hand, do not require in-depth derivation of complex physical equations, but complete model training by mining the implicit feature patterns and mapping relationships in a large amount of sample data.

[0004] Magnetically controlled flexible bodies, as a special type of flexible body, are subject to the combined influence of complex factors such as differences in magnetic field intensity distribution and dynamic magnetic field disturbances, resulting in stronger nonlinearity and uncertainty in their morphological response. Physically driven models, due to their idealized modeling assumptions, struggle to balance the accuracy and efficiency requirements of morphological response modeling; data-driven models are easily affected by factors such as sample sampling environment and sample coverage, exhibiting significantly insufficient adaptability to complex magnetic field conditions. Therefore, traditional flexible body modeling methods all have significant limitations when applied to magnetically controlled flexible bodies, restricting their application effectiveness and reliability. Summary of the Invention

[0005] This disclosure provides a method, device, medium, and product for modeling the morphological response of magnetically controlled flexible bodies, which addresses the significant performance defects of physical-driven or data-driven models, and facilitates the application and promotion of magnetically controlled flexible bodies.

[0006] This disclosure provides a method for modeling the morphological response of a magnetically controlled flexible body, including: A training sample set and a morphological response model to be trained are obtained. The training sample set includes at least one training sample. The training sample includes flexible body parameter data and magnet control data of a magnetically controlled flexible body. The magnetically controlled flexible body includes a fixed end and an end end distributed along the axial direction. An internal magnet is embedded in the end end. The magnet control data represents the control constraints of an external magnet that provides driving excitation for the magnetically controlled flexible body. The morphological response model includes a Kolmogorov-Arnold network, a physical simulation model, and a physical information neural network. For each training sample, the Kolmogorov-Arnold network is used to calculate the local load based on the training sample, and output the equivalent load at the end of the magnetically controlled flexible body. The physical simulation model is used to perform a global mapping based on the equivalent load at the end and the flexible body parameter data in the training sample to determine discrete morphological data. The physical information neural network is used to reconstruct the continuous field of the discrete morphological data and output the continuous morphological data corresponding to the training sample. Obtain the baseline morphological dataset corresponding to the training sample set, and determine the prediction loss value based on each of the continuous morphological data and the baseline morphological dataset; The network parameters of the Kolmogorov-Arnold network and the physical information neural network are iteratively adjusted based on the predicted loss value until the training termination condition is met.

[0007] Another aspect of this disclosure provides a morphological response modeling apparatus for a magnetically controlled flexible body, comprising: The training sample set acquisition module is used to acquire a training sample set and a morphological response model to be trained. The training sample set includes at least one training sample, which includes flexible body parameter data and magnet control data of a magnetically controlled flexible body. The magnetically controlled flexible body includes a fixed end and an end end distributed along the axial direction. An internal magnet is embedded in the end end. The magnet control data represents the control constraints of an external magnet that provides driving excitation to the magnetically controlled flexible body. The morphological response model includes a Kolmogorov-Arnold network, a physical simulation model, and a physical information neural network. The continuous morphology data determination module is used to, for each training sample, perform local load calculation based on the training sample through the Kolmogorov-Arnold network, output the end equivalent load of the magnetically controlled flexible body, perform global mapping based on the end equivalent load and the flexible body parameter data in the training sample through the physical simulation model, determine discrete morphology data, and perform continuous field reconstruction on the discrete morphology data through the physical information neural network, outputting the continuous morphology data corresponding to the training sample. The prediction loss value determination module is used to obtain the baseline morphological dataset corresponding to the training sample set, and determine the prediction loss value based on each of the continuous morphological data and the baseline morphological dataset. The morphological response model iteration module is used to iteratively adjust the network parameters of the Kolmogorov-Arnold network and the physical information neural network based on the predicted loss value until the training termination condition is met.

[0008] Another aspect of this disclosure provides an electronic device, comprising: At least one processor; A memory that is communicatively connected to the at least one processor; The memory stores a computer program that can be executed by the at least one processor, which is then executed by the at least one processor to enable the at least one processor to perform the morphological response modeling method for a magnetically controlled flexible body according to any embodiment of this disclosure.

[0009] Another aspect of this disclosure provides a computer-readable storage medium storing computer instructions for causing a processor to execute and implement the morphological response modeling method for a magnetically controlled flexible body according to any embodiment of this disclosure.

[0010] Another aspect of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the morphological response modeling method for a magnetically controlled flexible body as described in any embodiment of this disclosure.

[0011] The technical solution of this disclosure captures the local and nonlinear load response of a magnetically controlled flexible body through a Kolmogorov-Arnold network, embeds a physical simulation model in the forward inference process to solve the global morphological response of the magnetically controlled flexible body, and then uses a physical information neural network to reconstruct the continuous field, obtaining continuous morphological data of the magnetically controlled flexible body. Combined with a benchmark morphological dataset, the morphological response model is iteratively trained, solving the problem of significant performance defects in physical-driven or data-driven models, and achieving at least the following technical effects: 1. This embodiment divides the traditional flexible body modeling process into three modeling stages: magnetic field-local load, local load-discrete form, and offline form to continuous form. It simplifies the complex global coupling evolution process into multiple independent mapping links that progress layer by layer, ensuring the continuous modeling accuracy of the overall magnetically controlled flexible body, thereby improving the reliability of the magnetically controlled flexible body in practical application scenarios.

[0012] 2. In the modeling stage of the magnetic field-local load, this embodiment employs a Kolmogorov-Arnold network that possesses both linear and nonlinear mapping capabilities. During model training, this network can autonomously learn the implicit mapping characteristics between the magnetic field and the local load. On one hand, its linear and nonlinear mapping capabilities can adaptively handle linear physical laws and complex nonlinear couplings. On the other hand, the Kolmogorov-Arnold network compensates for the shortcomings of simple physics-driven models in characterizing complex nonlinear responses. By relying on the correlation modeling method of local loads, it avoids the complex solutions caused by explicit magnetic force derivations such as complex strong couplings and reliance on magnetic field gradient distribution. This ensures modeling accuracy while improving modeling efficiency in this stage.

[0013] 3. In the modeling stage of local load-discrete form, this embodiment adopts a physical simulation model with physical constitutive constraints. On the one hand, it uses its ability to accurately simulate a wide range of geometric forms from the minimum to the maximum without the need to manually set switching thresholds or establish equations in segments. This achieves global physical consistency in the mapping of local load-discrete form, overcomes the problem of weak generalization ability of data-driven models, and improves the modeling accuracy in this modeling stage.

[0014] On the other hand, the physical simulation model also provides the physical information neural network with global physical prior information that conforms to the laws of flexible body mechanics, which narrows the search range of the physical information neural network in three-dimensional space, thereby accelerating the convergence speed of the morphological response model and ensuring the modeling efficiency of the subsequent modeling stage.

[0015] 4. In the stage from discrete to continuous form, this embodiment adopts a physical information neural network with physical constraint embedding capability, which integrates the data representation features of the magnetic field-local load stage and the physical prior constraints of the local load-discrete form stage, and constructs a data-physical dual-driven model architecture. This breaks through the accuracy bottleneck of traditional modeling methods in continuous field reconstruction, and realizes high-precision modeling at the continuous field level. It simultaneously improves the modeling accuracy, modeling efficiency and generalization ability of magnetically controlled flexible bodies from multiple dimensions such as model architecture dimension and constraint optimization dimension.

[0016] 5. This embodiment provides a differentiable, physically interpretable, and modularly extensible unified dynamic framework. Both the physical simulation model and the physical information neural network in the morphological response model possess excellent physical interpretability, and their internal feature variables have clear and realistic physical meanings. Therefore, in addition to supporting morphological prediction, the morphological response model can also support gradient control, inverse dynamics solving, multi-sensor fusion, online state estimation, adaptive control, and disturbance compensation, and can simultaneously adapt to various application tasks such as modeling analysis, motion control, and state estimation. Furthermore, the morphological response model provided in this embodiment also supports additional physical mechanisms such as friction models, fluid forces, magnetic field disturbances, or material viscoelasticity, possessing modular extensibility potential.

[0017] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this disclosure, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating a morphological response modeling method for a magnetically controlled flexible body according to an embodiment of this disclosure; Figure 2 A network architecture diagram of a specific example of a morphological response model of a magnetically controlled flexible body provided in an embodiment of this disclosure; Figure 3 A flowchart illustrating another morphological response modeling method for a magnetically controlled flexible body provided in one embodiment of this disclosure; Figure 4 A flowchart illustrating a specific example of a method for determining a baseline morphological dataset provided in one embodiment of this disclosure; Figure 5 A schematic diagram of the structure of a morphology response modeling device for a magnetically controlled flexible body provided in an embodiment of this disclosure; Figure 6 A schematic diagram of a specific example of a morphology response modeling device for a magnetically controlled flexible body provided in an embodiment of this disclosure; Figure 7 This is a schematic diagram of the structure of an electronic device provided in one embodiment of the present disclosure. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present disclosure, the technical solutions of the present disclosure will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present disclosure, and not all embodiments. Based on the embodiments of the present disclosure, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present disclosure.

[0021] It should be noted that the terms "training," "benchmark," "prediction," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this disclosure described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0022] Figure 1 This is a flowchart illustrating a morphological response modeling method for a magnetically controlled flexible body according to one embodiment of this disclosure. This embodiment is applicable to modeling the morphological response of magnetically controlled flexible bodies, particularly elongated magnetically controlled flexible bodies, especially sub-millimeter scale magnetically controlled flexible bodies. This method can be executed by a morphological response modeling device for magnetically controlled flexible bodies, which can be implemented in hardware and / or software and can be configured in a terminal device. Figure 1 As shown, the method includes: S110. Obtain the training sample set and the morphological response model to be trained.

[0023] Specifically, the training sample set represents structured, model-recognizable feature information used for supervised learning of the morphological response model. In this embodiment, the training sample set includes at least one training sample, which includes flexible body parameter data and magnetic control data of the magnetically controlled flexible body.

[0024] The magnetically controlled flexible body includes a fixed end and an end distributed along the axial direction. The fixed end is used to constrain the basic spatial pose of the magnetically controlled flexible body, and its position coordinates are immutable. The end has an embedded internal magnet, which is used to receive the driving excitation of the external magnet to generate displacement, thereby causing the flexible structure from the end to the fixed end to undergo continuous deformation.

[0025] For example, the magnetically controlled flexible body can be a magnetically sensitive flexible probe on a flexible sensing device or a magnetically controlled flexible actuator on a precision operating platform, but is not limited to the examples given above.

[0026] In one optional embodiment, the magnetically controlled flexible body is an elongated magnetically controlled flexible body with a diameter-to-length ratio of less than 0.2, and under the action of the magnetic field of the external magnet, it has continuous and nonlinear morphological response characteristics.

[0027] In one specific embodiment, the elongated magnetically controlled flexible body is a sub-millimeter scale magnetically controlled flexible body. A sub-millimeter scale magnetically controlled flexible body is an elongated magnetically controlled flexible body with a radial dimension less than 1 mm, typically ranging from 20 to 500 μm. Compared to general magnetically controlled flexible bodies, sub-millimeter scale magnetically controlled flexible bodies have smaller cross-sectional dimensions, weaker bending stiffness, and stronger disturbance amplification effects. Slight changes in the magnetic field, boundary contact, or manufacturing errors can lead to significant shape deviations. This characteristic significantly increases the solution cost of physics-driven models, making them difficult to use directly as online modeling tools. While data-driven models have faster inference speeds, they lack stable physical priors and have severely insufficient extrapolation capabilities for unseen magnetically controlled conditions and unseen initial forms.

[0028] The flexible body parameter data characterizes the static properties of the magnetically controlled flexible body under the influence of no magnetic field. Specifically, the flexible body parameter data includes initial morphological data, which characterizes the morphological parameter information of the magnetically controlled flexible body under the influence of no magnetic field, such as the shape of the center line, the number of sampling points along the arc length, the sampling step size, the three-dimensional coordinates, curvature, torsion, cross-sectional direction and attitude of each sampling point, etc.

[0029] In an optional embodiment, the flexible body parameter data further includes geometric configuration data and / or material property data. The geometric configuration data describes the spatial topology of the magnetically controlled flexible body, such as length, cross-sectional dimensions, and shape parameters; the material property data describes the intrinsic material properties of the magnetically controlled flexible body, such as elastic modulus, shear modulus, cross-sectional area, interfacial moment of inertia, and density.

[0030] Specifically, the magnet control data characterizes the control constraints of the external magnet that provides the magnetic field to the magnetically controlled flexible body. Specifically, the magnet control data includes relative pose data between the external magnet and the magnetically controlled flexible body. For example, the relative pose data includes, but is not limited to, the spatial pose of the external magnet, its relative position, orientation, and distance from the fixed end or distal end of the magnetically controlled flexible body, the spatial pose of the internal magnet, or other geometric parameters that can describe the spatial pose relationship between the two.

[0031] In one optional embodiment, the magnet control data further includes magnetic field attribute data corresponding to the external magnet and the internal magnet, respectively. Exemplarily, the magnetic field attribute data includes, but is not limited to, at least one of the following: magnet moment, excitation intensity, gradient, magnetic field direction, and dynamic characteristics changing over time.

[0032] Specifically, the training samples are standardized sample data adapted to a unified input space after normalization and coordinate system processing.

[0033] Specifically, the morphological response model is used to predict the nonlinear continuous morphology of a magnetically controlled flexible body under the influence of an external magnetic field. In this embodiment, the morphological response model includes a Kolmogorov-Arnold network, a physical simulation model, and a physical information neural network.

[0034] S120. For each training sample, the Kolmogorov-Arnold network is used to calculate the local load based on the training sample, and output the equivalent load at the end of the magnetically controlled flexible body. The physical simulation model is used to perform a global mapping based on the equivalent load at the end and the flexible body parameter data in the training sample to determine discrete morphological data. The physical information neural network is used to reconstruct the continuous field of the discrete morphological data and output the continuous morphological data corresponding to the training sample.

[0035] Specifically, the end-effector equivalent load is the equivalent representation of the resultant force and resultant torque experienced by the end of the magnetically controlled flexible body under the drive of an external magnetic field.

[0036] The Kolmogorov-Arnold network (KAN) is theoretically based on the Kolmogorov-Arnold representation theorem, which approximates nonlinear mapping relationships in high-dimensional spaces using a multi-layered nested function structure. This theorem rigorously proves mathematically that any continuous multivariable function defined in finite dimensions can be accurately represented by the superposition and composition of a finite number of single-variable functions, without relying on complex iterative optimization of network weights. This provides a solid mathematical interpretability guarantee for the local load response of magnetically controlled flexible bodies. Utilizing the unique function approximation structure and excellent nonlinear fitting capabilities of the KAN network, it accurately and efficiently learns the complex mapping relationship between input data and the equivalent end load through a simple combination of nested functions.

[0037] Compared to MLP (Multi-Layer Perceptron), KAN network not only reduces training costs and improves payload calculation efficiency, but also effectively avoids problems such as overfitting and gradient vanishing that are prone to occur in deep neural networks, thus ensuring the stability of morphological response modeling.

[0038] Specifically, the physical simulation model is a simulation model built based on the theory of continuum mechanics. It is used to take the equivalent load at the end of the magnetically controlled flexible body as the external input load, and combine the flexible body parameter data to numerically solve the global morphological response of the magnetically controlled flexible body, outputting discrete morphological data. Among them, the theory of continuum mechanics provides the physical basis for the morphological response of the magnetically controlled flexible body, and the discrete morphological data includes the morphological parameters at each sampling point on the magnetically controlled flexible body.

[0039] For example, the continuum mechanics theory can be the Cosserat flexible rod theory, the three-dimensional flexible body theory, the geometrically precise beam theory, or the large deformation hyperelastic theory, etc., which can be flexibly selected according to the geometric structure and deformation characteristics of the magnetically controlled flexible body. For example, the Cosserat flexible rod theory can be preferentially used for long and narrow magnetically controlled flexible bodies, while the three-dimensional flexible body theory or the large deformation hyperelastic theory can be selected for short and thick magnetically controlled flexible bodies. For magnetically controlled flexible bodies with large rotation angle and large deflection deformation characteristics, the geometrically precise beam theory is suitable.

[0040] For example, the numerical solution method used in the physical simulation model may be the finite element method (FEM), the finite difference method, or the generalized -α method, but is not limited to the examples given above.

[0041] Among them, Physics-Informed Neural Networks (PINN) is a modeling vehicle that integrates deep learning networks with prior physical knowledge. It embeds known conservation laws of mechanics into the loss function of the neural network in the form of partial differential equations (PDEs), thereby guiding the co-optimization of network parameters and physical constraint residuals during model training, so that the final prediction results strictly follow the corresponding conservation laws of mechanics.

[0042] For example, the network architecture used by the PINN network includes, but is not limited to, fully connected neural networks, feedforward neural networks, residual networks, convolutional neural networks, or graph neural networks, which can be customized according to the spatial topology and shape field distribution characteristics of the magnetically controlled flexible body.

[0043] Specifically, the continuous morphological data includes a morphological field continuously defined along the arc length of the magnetically controlled flexible body. For example, the morphological parameters corresponding to the morphological field can be three-dimensional coordinates, curvature, torsion, cross-sectional direction, and attitude, but are not limited to the given example.

[0044] S130. Obtain the baseline morphological dataset corresponding to the training sample set, and determine the prediction loss value based on each of the continuous morphological data and the baseline morphological dataset.

[0045] Specifically, the baseline morphology dataset includes baseline morphology data corresponding to each training sample.

[0046] In an optional embodiment, the loss function corresponding to the predicted loss value includes two parts: a boundary condition loss function and a data loss function. The boundary condition loss function is used to constrain the magnetically controlled flexible body to meet preset boundary conditions at the endpoints, while the data loss function minimizes the morphological deviation between the continuous deformation data output by the PINN network and the baseline morphological data.

[0047] Specifically, the preset boundary conditions include fixed-end constraint conditions and / or end-effector constraint conditions. The fixed-end constraint conditions require that the displacement and rotation angle of the magnetically controlled flexible body at the fixed end be zero, i.e., consistent with its initial pose under no magnetic field. The end-effector constraint conditions require that the deformation load of the magnetically controlled flexible body at the end be zero.

[0048] In this embodiment, determining the prediction loss value based on each of the continuous morphological data and the reference morphological dataset includes: determining fixed-end constraint terms based on fixed-end constraint conditions and fixed-end morphological parameters in each of the continuous morphological data; performing continuous domain differentiation on each of the continuous morphological data to obtain a deformation load dataset, and obtaining an end deformation load set in the deformation load dataset; determining end constraint terms based on end constraint conditions and the end deformation load set; determining boundary condition loss values ​​based on the fixed-end constraint terms and the end constraint terms; determining data loss values ​​based on each of the continuous morphological data and the reference morphological dataset; and determining the prediction loss value based on the boundary condition loss value and the data loss value.

[0049] The fixed end morphological parameters include the displacement and rotation angle of the fixed end. The deformation load data in the deformation load dataset represents the distribution information of the deformation load corresponding to the magnetically controlled flexible body, including the deformation load of the magnetically controlled flexible body at multiple sampling points. The deformation load includes internal force and internal moment. The end deformation load in the end deformation load set includes the internal force and internal moment of the end.

[0050] For example, boundary condition loss value Satisfy the following formula: in, This represents the predicted three-dimensional coordinates of the fixed end. Indicates the initial three-dimensional coordinates of the fixed end. Indicates the predicted attitude of the fixed end. This indicates the initial attitude of the fixed end. Indicates the internal force at the end. This represents the internal torque at the end. Indicates the fixed-end constraint term. This represents the terminal constraint term.

[0051] By adding a penalty term for boundary conditions to the overall loss, the model training process continuously satisfies the pose constraints of the fixed end and the mechanical balance constraints of the end, avoiding drift, morphological instability, or unreasonable non-physical morphology of the magnetically controlled flexible body, and further improving the accuracy and reliability of morphological response modeling.

[0052] In an optional embodiment, the loss function corresponding to the predicted loss value further includes a constraint loss function, which includes a physical loss function and / or a smoothing loss function. The physical loss function is used to constrain the continuous deformation data output by the PINN network to satisfy the minimization of the residuals of the mechanical equilibrium equation, and the smoothing loss function is used to constrain the continuous deformation data output by the PINN network to satisfy the continuous deformation transition between adjacent regions and the absence of local distortion jumps.

[0053] In this embodiment, determining the predicted loss value based on the boundary condition loss value and the data loss value includes: determining constraint loss data based on each of the continuous morphological data, wherein the constraint loss data includes physical loss value and / or smoothing loss value; and determining the predicted loss value based on the constraint loss data, the boundary condition loss value, and the data loss value.

[0054] Specifically, for each continuous deformation data, the driving load data of the external magnet corresponding to the continuous deformation data is obtained. Using the static equilibrium equation, the partial differential residual value corresponding to the continuous deformation data is determined based on the deformation load data and the driving load data. Based on each partial differential residual value, the physical loss value is determined.

[0055] In one specific embodiment, the magnetically controlled flexible body is a narrow magnetically controlled flexible body based on the Cosserat continuum theory, and the mechanical equilibrium equation is the static equilibrium equation of the deformation load of the narrow magnetically controlled flexible body under static equilibrium conditions.

[0056] Specifically, the physical loss value is the sum of the partial differential residuals, and the driving load data characterizes the distribution information of the driving load applied by the external magnet to the elongated magnetically controlled flexible body, including the driving load applied by the external magnet to the elongated magnetically controlled flexible body at each sampling point, and the driving load includes magnetic force and magnetic torque.

[0057] For example, the static equilibrium equation can be expressed as: in, Indicates internal force. Indicates internal torque. This represents the magnetic force per unit arc length. This represents the magnetic torque per unit arc length. This represents the arc length parameter.

[0058] The operator form corresponding to the above static equilibrium equations can be expressed as: in, Represents a nonlinear differential operator. This indicates the position of the elongated magnetically controlled flexible body at the arc length position. The morphological parameters at that location This indicates the position of the external magnet at the corresponding arc length. The applied magnetic force and magnetic torque.

[0059] Specifically, the partial differential residual value represents the degree of deviation between continuous deformation data and the static mechanical equilibrium equations. For example, the partial differential residual value... Satisfy the following formula: in, This indicates the length of the elongated, magnetically controlled flexible body.

[0060] S140. The network parameters of the Kolmogorov-Arnold network and the physical information neural network are iteratively adjusted according to the predicted loss value until the training termination condition is met.

[0061] Specifically, the network parameters of the KAN network include the interpolation coefficients of the network nodes and the basis function fitting parameters, while the network parameters of the PINN network include the weight parameters and the bias parameters. The network parameters of the KAN and PINN networks are updated by backpropagation based on the calculated predicted loss value until the training termination condition is met, thus obtaining the trained morphological response model.

[0062] The training termination condition is used to determine whether the morphological response model has converged. For example, the training termination condition includes, but is not limited to, the predicted loss value being less than a preset threshold, the number of iterations reaching the upper limit, and the loss curve not showing a significant downward trend for a preset number of consecutive rounds.

[0063] Figure 2 This is a network architecture diagram of a specific example of a morphological response model of a magnetically controlled flexible body provided in an embodiment of this disclosure. Specifically, the input data of the morphological response model are flexible body parameter data and magnet control data. The flexible body parameter data includes geometric configuration data, material property data, initial morphological data, and arc length sampling information corresponding to the initial morphological data. The magnet control data includes relative pose data and magnetic field property data.

[0064] Specifically, learnable activation functions are deployed on the connection edges of the network topology using a KAN network, and parameterized modeling of each connection edge is completed using spline functions. Figure 2In the illustrated KAN network, the squares between two connecting lines represent spline functions, and the circles represent nodes. These nodes are used to aggregate and transfer data from the feature vectors processed by the spline functions of the previous layer's connecting edges. Each node itself has no parameters or activation transformations. Training samples are sequentially transformed by spline functions in each layer and aggregated and transferred by nodes to complete the nonlinear mapping. The final node outputs the terminal equivalent load. A node can be a neuron.

[0065] Specifically, the equivalent load at the end is mapped to globally discrete morphological parameters using a finite element simulation model. Figure 2 Taking a morphological parameter consisting of four morphological parameters as an example, these four morphological parameters can be curvature, three-dimensional coordinates, cross-sectional orientation, and attitude. Finally, the discrete morphological parameters are reconstructed into a continuous morphological field by a PINN network with a fully connected network architecture. The morphological field includes a position field, curvature field, orientation field, and attitude field that are continuously defined along the arc length.

[0066] Based on the above embodiments, the method may optionally further include: performing performance testing on the trained morphological response model according to a test sample set. Exemplarily, the performance testing includes morphological prediction error, end-effector position error, prediction accuracy, generalization ability testing under different magnet control data, and inference time testing.

[0067] For example, test samples are generated in batches under conditions such as multiple sets of magnet spatial poses, different initial shapes and differentiated material parameters. Generalization tests are carried out using test samples under magnetic field conditions not covered in the training sample set. The morphological response model obtained by modeling in the embodiments of this disclosure is compared and verified horizontally with the pure simulation model, the pure FBG data-driven model and the single-output discrete regression model.

[0068] The benefit of setting up a performance testing mechanism is that it verifies the application effectiveness of the morphological response model under real magnetic field conditions, thereby providing a reliable basis for the actual deployment of magnetically controlled flexible bodies.

[0069] The technical solution of this embodiment captures the local and nonlinear load response of the magnetically controlled flexible body through a Kolmogorov-Arnold network, embeds a physical simulation model in the forward inference process to complete the global morphological response solution of the magnetically controlled flexible body, and then realizes continuous field reconstruction through a physical information neural network to obtain continuous morphological data of the magnetically controlled flexible body. Combined with the benchmark morphological dataset, the morphological response model is iteratively trained, which solves the problem of significant performance defects of physical-driven models or data-driven models, and takes into account the modeling accuracy, modeling efficiency and generalization ability of the magnetically controlled flexible body.

[0070] Figure 3This is a flowchart illustrating another method for modeling the morphological response of a magnetically controlled flexible body according to an embodiment of this disclosure. This embodiment further refines the step of "obtaining the baseline morphological dataset corresponding to the training sample set" in the above embodiment. Figure 3 As shown, the method includes: S210. Obtain the training sample set and the morphological response model to be trained.

[0071] S220. For each training sample, the Kolmogorov-Arnold network is used to calculate the local load based on the training sample, and output the equivalent load at the end of the magnetically controlled flexible body. The physical simulation model is used to perform a global mapping based on the equivalent load at the end and the flexible body parameter data in the training sample to determine discrete morphological data. The physical information neural network is used to reconstruct the continuous field of the discrete morphological data and output the continuous morphological data corresponding to the training sample.

[0072] S210-S220 in this embodiment are the same as those in the above embodiment. Figure 1 The S110-S120 shown are the same or similar, and will not be described again here.

[0073] S230. Obtain the simulation morphology dataset and / or the measured morphology dataset corresponding to the training sample set.

[0074] In this embodiment, the benchmark morphology dataset includes a simulated morphology dataset and / or a measured morphology dataset. In an optional embodiment, obtaining the benchmark morphology dataset corresponding to the training sample set includes: obtaining the simulated morphology dataset corresponding to the training sample set, or obtaining the measured morphology dataset corresponding to the training sample set.

[0075] The simulated morphology dataset includes simulated morphology data for each training sample, representing the morphology data of the magnetically controlled flexible body under given assumptions, and serves as the physical supervision basis for morphology response modeling; the measured morphology dataset includes measured morphology data for each training sample, representing the morphology data of the magnetically controlled flexible body in a real magnetic field environment, and serves as the data supervision basis for morphology response modeling.

[0076] In another optional embodiment, obtaining the benchmark morphological dataset corresponding to the training sample set includes: obtaining the simulated morphological dataset corresponding to the training sample set, and obtaining the measured morphological dataset corresponding to the training sample set, converting the simulated morphological dataset and the measured morphological dataset into a unified morphological representation space to obtain the benchmark morphological dataset corresponding to the training sample set.

[0077] In an optional embodiment, obtaining the simulation morphology dataset corresponding to the training sample set includes: inputting each training sample in the training sample set into the physical information proxy model to obtain the output simulation morphology dataset, wherein the physical information proxy model is trained based on high-fidelity morphology data as the label.

[0078] In another optional embodiment, obtaining the simulation morphology dataset corresponding to the training sample set includes: performing physical simulation based on the training sample set using a physical simulation engine to determine the simulation morphology dataset.

[0079] Specifically, the physical simulation engine is a high-fidelity simulation platform built on the theory of continuum mechanics and magnetoelastic coupling. The engine fully considers the stress-strain transmission law of magnetically controlled flexible bodies, the material morphology response characteristics under the action of magnetic field, and the mutual coupling and constraint relationship between field quantities, so as to completely restore the whole-domain physical evolution process of magnetic field excitation - material stress - structural morphology.

[0080] In this embodiment, the simulation accuracy of the physical simulation engine is higher than that of the physical simulation model, so as to ensure that the output is a continuous morphological field that better conforms to the real physical laws.

[0081] In one optional embodiment, obtaining the measured morphology dataset corresponding to the training sample set includes: obtaining the measured point cloud dataset corresponding to the training sample set; and performing gridded reconstruction on each measured point cloud data in the measured point cloud dataset to obtain the measured morphology dataset corresponding to the training sample set. For example, the point cloud acquisition device can be a LiDAR device or a depth camera, etc.

[0082] In another optional embodiment, obtaining the measured morphological dataset corresponding to the training sample set includes: obtaining the measured ultrasound echo set corresponding to the training sample set; performing inversion calculation and reconstruction on each measured echo signal in the measured ultrasound echo set to obtain the measured morphological dataset corresponding to the training sample set.

[0083] In another optional embodiment, obtaining the measured morphological dataset corresponding to the training sample set includes: obtaining the measured strain dataset corresponding to the training sample set; and performing morphological reconstruction on the strain parameter sequence corresponding to each training sample to determine the measured morphological dataset.

[0084] In this embodiment, the measured strain dataset includes a strain parameter sequence for each training sample at multiple acquisition points on the magnetically controlled flexible body, and the strain parameter sequence includes strain data for each acquisition point.

[0085] For example, the strain acquisition device for the strain parameter sequence can be a fiber optic grating (FBG) demodulator, a distributed fiber optic sensor acquisition device, a strain gauge acquisition system, a vision acquisition device, etc., and the morphological reconstruction method can be a strain interpolation reconstruction algorithm, a finite element inverse morphological solution method, a field quantity smooth fitting reconstruction method, a multi-point strain inversion reconstruction method, etc., but is not limited to the examples listed above.

[0086] Based on the above embodiments, optionally, the step of converting the simulated morphology dataset and the measured morphology dataset into a unified morphological representation space to obtain the benchmark morphological dataset corresponding to the training sample set includes: for each training sample, obtaining the simulated morphological data and measured morphological data corresponding to the training sample in the simulated morphology dataset and the measured morphological dataset respectively; performing coordinate system alignment processing and arc length normalization processing on the simulated morphological data and the measured morphological data to obtain preprocessed simulated morphological data and measured morphological data; filtering the preprocessed simulated morphological data and the preprocessed measured morphological data in the sampling dimension to obtain simulated morphological sequences and measured morphological sequences; and determining the benchmark morphological dataset in the unified morphological representation space based on each simulated morphological sequence and each measured morphological sequence.

[0087] Specifically, the simulated morphological data is constrained by the modeling boundaries, discretization methods, and numerical solution rules of the physical simulation engine. Its coordinate system is a locally customized coordinate system built into the physical simulation engine, with no unified calibration standard for the origin position, axial reference, and spatial orientation. The arc length exhibits a non-uniform discrete distribution depending on the mesh density of the flexible body and the simulation sampling step size. The measured morphological data is constrained by the deployment location of the strain acquisition equipment, the sensor sampling accuracy, and the fitting interpolation rules of the morphological reconstruction method. Its coordinate system is the equipment observation coordinate system in the actual measurement scenario, which has origin offset, attitude deflection, and reference misalignment with the simulated local coordinate system. The measured arc length sampling is affected by the sensor deployment spacing and reconstruction interpolation strategy, resulting in inconsistencies with the simulated arc length sampling in terms of the number of sampling points and discrete intervals.

[0088] Specifically, coordinate system alignment processing refers to registering the simulated morphological data with the measured morphological data at the origin, correcting the spatial attitude, and unifying the axial reference, eliminating positional and orientation deviations caused by differences in coordinate system references between the two types of data. Arc length normalization processing refers to using the actual total extension arc length of the magnetically controlled flexible body as a unified reference, and proportionally mapping and normalizing the discrete arc length coordinates of the two types of morphological data, eliminating differences in arc length scale and discrete interval caused by mesh partitioning and sensor sampling. The preprocessed simulated and measured morphological data achieve dimensional alignment and feature matching in spatial coordinate reference, arc length scale, and discrete sampling dimension, providing standardized input conditions for subsequent morphological representation fusion and network model training.

[0089] In this embodiment, the simulated morphological sequence and the measured morphological sequence use the same sampling point distribution. Specifically, based on the sampling point sequence corresponding to the preprocessed simulated morphological data, for each sampling point, if the preprocessed measured morphological data contains the measured morphological parameters corresponding to the sampling point, the simulated morphological parameters corresponding to the sampling point are added to the simulated morphological sequence, and the measured morphological parameters corresponding to the sampling point are added to the measured morphological sequence.

[0090] Figure 4 This is a flowchart illustrating a specific example of a method for determining a baseline morphological dataset provided in one embodiment of this disclosure. Specifically, using a Cosserat rod simulation engine or a continuous medium simulation engine, the initial morphological data of the elongated magnetically controlled flexible body is represented by discrete nodes or shapes, and simulated morphological data is output, serving as the first supervisory data. The strain parameter sequence acquired by the FBG demodulator on the elongated magnetically controlled flexible body is demodulated and morphologically reconstructed, outputting measured morphological data, which is then used as the second supervisory data. The simulated and measured morphological data are aligned to a coordinate system and normalized to arc length. By using a unified sampling point method, simulated and measured morphological sequences in a unified morphological representation space are obtained. The two morphological sequences use a unified arc length parameter space, specifically including a three-dimensional coordinate sequence, a curvature sequence, and an attitude sequence. , They represent the first The sampling point and the first One sampling point, Indicates curvature. To express a gesture.

[0091] This embodiment unifies the morphological representation of two types of morphological data and supervises the same continuous morphological data, forming a consistent training mechanism between simulation and actual measurement. This avoids deviation conflicts caused by inconsistent formats of the two types of data and improves the stability of morphological response modeling.

[0092] S240. Determine the prediction loss value based on the continuous morphological data and the baseline morphological dataset.

[0093] In one optional embodiment, the baseline morphology dataset is a simulated morphology dataset, and the step of determining the data loss value based on each of the continuous morphology data and the baseline morphology dataset includes: determining a first loss value based on the difference between each of the continuous morphology data and the simulated morphology dataset, and using the first loss value as the data loss value.

[0094] In another optional embodiment, the baseline morphological dataset is a measured morphological dataset, and the step of determining the data loss value based on each of the continuous morphological data and the baseline morphological dataset includes: determining a second loss value based on the difference between each of the continuous morphological data and the measured morphological dataset, and using the second loss value as the data loss value.

[0095] In another optional embodiment, the baseline morphological dataset includes a simulated morphological dataset and a measured morphological dataset in a unified morphological representation space. The step of determining the data loss value based on each of the continuous morphological data and the baseline morphological dataset includes: determining a first loss value based on the difference between each of the continuous morphological data and the simulated morphological dataset in the unified morphological representation space; determining a second loss value based on the difference between each of the continuous morphological data and the measured morphological dataset in the unified morphological representation space; and using the weighted sum of the first loss value and the second loss value as the data loss value.

[0096] For example, the first loss value Satisfy the following formula: in, This indicates the number of samples in the training sample set. Indicates the first Continuous deformation data corresponding to each training sample Indicates the first Simulated deformation sequences in a unified morphological representation space corresponding to each training sample.

[0097] For example, the second loss value Satisfy the following formula: in, This indicates the number of samples in the training sample set. Indicates the first Continuous deformation data corresponding to each training sample Indicates the first The measurement deformation sequence under the unified morphological representation space corresponding to each training sample.

[0098] For example, data loss value Satisfy the following formula: in, and These represent the weighting coefficients for the first and second loss values, respectively. .

[0099] Based on the above embodiments, the loss value is predicted, exemplarily. Satisfy the following formula: in, , , , These represent the physical loss values. Data loss value, boundary condition loss value, and smoothing loss value The corresponding weighting coefficients.

[0100] S250. The network parameters of the Kolmogorov-Arnold network and the physical information neural network are iteratively adjusted according to the predicted loss value until the training termination condition is met.

[0101] S250 in this embodiment is the same as in the above embodiment. Figure 1 The S140 shown is the same or similar, and will not be described again here.

[0102] The technical solution of this embodiment sets simulated morphological data and measured morphological data as the data supervision basis for the model, realizing the complementary advantages between the virtual simulation system and the real measurement system. Together, they serve as the basis for supervising and optimizing continuous morphological data. Among them, measured morphological data can specifically compensate for the training bias of the morphological response model under small sample conditions and correct the prediction distortion between the morphological response model and reality. Simulated morphological data, based on its underlying physical mechanism, can provide global continuous morphological prior constraints for morphological response modeling, standardize the solution space and avoid non-physical solution divergence, enabling the morphological response model to adapt to more real-world scenarios and ensuring that the model's converged solution can strictly follow physical laws while maintaining the authenticity of the morphological response.

[0103] The physical-data dual-driven supervision system provided in this embodiment reduces invalid iterations during model training. It further superimposes a data supervision dimension on the physical-data dual-driven dimension of the above embodiment, thereby improving the modeling accuracy, response efficiency, and generalization ability of the magnetically controlled flexible body from three dimensions of physical-data dual-driven mechanism.

[0104] The following are embodiments of the morphological response modeling device for magnetically controlled flexible bodies provided in this disclosure. This device and the morphological response modeling method for magnetically controlled flexible bodies described in the above embodiments belong to the same inventive concept. For details not described in detail in the embodiments of the morphological response modeling device for magnetically controlled flexible bodies, please refer to the content of the morphological response modeling method for magnetically controlled flexible bodies in the above embodiments.

[0105] Figure 5 This is a schematic diagram of the structure of a morphology response modeling device for a magnetically controlled flexible body provided in one embodiment of this disclosure. Figure 5As shown, the device includes: a training sample set acquisition module 310, a continuous morphological data determination module 320, a prediction loss value determination module 330, and a morphological response model iteration module 340.

[0106] The training sample set acquisition module 310 is used to acquire a training sample set and a morphological response model to be trained. The training sample set includes at least one training sample, which includes flexible body parameter data and magnet control data of a magnetically controlled flexible body. The magnetically controlled flexible body includes a fixed end and an end end distributed along the axial direction. An internal magnet is embedded in the end end. The magnet control data represents the control constraint conditions of an external magnet that provides driving excitation for the magnetically controlled flexible body. The morphological response model includes a Kolmogorov-Arnold network, a physical simulation model, and a physical information neural network. The continuous morphological data determination module 320 is used to, for each training sample, perform local load calculation based on the training sample through the Kolmogorov-Arnold network, output the end equivalent load of the magnetically controlled flexible body, perform global mapping based on the end equivalent load and the flexible body parameter data in the training sample through the physical simulation model, determine discrete morphological data, and perform continuous field reconstruction on the discrete morphological data through the physical information neural network, outputting the continuous morphological data corresponding to the training sample. The prediction loss value determination module 330 is used to obtain the baseline morphological dataset corresponding to the training sample set, and determine the prediction loss value based on each of the continuous morphological data and the baseline morphological dataset. The morphological response model iteration module 340 is used to iteratively adjust the network parameters of the Kolmogorov-Arnold network and the physical information neural network according to the predicted loss value until the training termination condition is met.

[0107] The technical solution of this embodiment captures the local and nonlinear load response of the magnetically controlled flexible body through a Kolmogorov-Arnold network, embeds a physical simulation model in the forward inference process to complete the global morphological response solution of the magnetically controlled flexible body, and then realizes continuous field reconstruction through a physical information neural network to obtain continuous morphological data of the magnetically controlled flexible body. Combined with the benchmark morphological dataset, the morphological response model is iteratively trained, which solves the problem of significant performance defects of physical-driven models or data-driven models, and takes into account the modeling accuracy, modeling efficiency and generalization ability of the magnetically controlled flexible body.

[0108] In an optional embodiment, the prediction loss value determination module 330 includes: The simulation morphology dataset acquisition unit is used to acquire the simulation morphology dataset corresponding to the training sample set and the measured morphology dataset corresponding to the training sample set. The simulation morphology dataset includes the simulation morphology data of each training sample, and the measured morphology dataset includes the measured morphology data of each training sample. The baseline morphology dataset determination unit is used to transform the simulated morphology dataset and the measured morphology dataset into a unified morphology representation space to obtain the baseline morphology dataset corresponding to the training sample set.

[0109] In one optional embodiment, the simulation morphology dataset acquisition unit includes: The simulation morphology dataset is a sub-unit used to determine the simulation morphology dataset by performing physical simulation based on the training sample set through a physical simulation engine. The simulation accuracy of the physical simulation engine is higher than that of the physical simulation model.

[0110] In one optional embodiment, the simulation morphology dataset acquisition unit includes: The measured morphology dataset is used to determine the sub-unit, which is used to obtain the measured strain dataset corresponding to the training sample set. The measured strain dataset includes the strain parameter sequence of each training sample at multiple acquisition points of the magnetically controlled flexible body. Morphological reconstruction is performed on the strain parameter sequence corresponding to each training sample to determine the measured morphological dataset.

[0111] In one optional embodiment, the baseline morphology dataset determination unit is specifically used for: For each training sample, the simulation morphology dataset and the measured morphology dataset are obtained respectively corresponding to the training sample. The simulation morphology data and the measured morphology data are then subjected to coordinate system alignment and arc length normalization to obtain preprocessed simulation morphology data and measured morphology data. The preprocessed simulation morphology data and the preprocessed measured morphology data are then filtered in terms of sampling dimension to obtain simulation morphology sequence and measured morphology sequence. The simulation morphology sequence and the measured morphology sequence use the same sampling point distribution. Based on the simulated morphological sequences and the measured morphological sequences, a benchmark morphological dataset in the unified morphological representation space is determined.

[0112] In an optional embodiment, the prediction loss value determination module 330 includes: The fixed-end constraint term determination unit is used to determine the fixed-end constraint term based on the fixed-end constraint conditions and the fixed-end morphological parameters in each of the continuous morphological data. The end constraint term determination unit is used to perform continuous domain differentiation on each of the continuous morphological data to obtain the deformation load dataset, and to obtain the end deformation load set in the deformation load dataset, and to determine the end constraint term according to the end constraint condition and the end deformation load set; The data loss value determination unit is used to determine the boundary condition loss value based on the fixed end constraint term and the end constraint term, and to determine the data loss value based on each of the continuous morphological data and the reference morphological dataset. The prediction loss value determination unit is used to determine the prediction loss value based on the boundary condition loss value and the data loss value; The deformation load data in the deformation load dataset represents the distribution information of the deformation load corresponding to the magnetically controlled flexible body.

[0113] In one optional embodiment, the prediction loss value determination unit is specifically used for: Based on the continuous morphological data, constraint loss data is determined, which includes physical loss value and / or smoothing loss value; The predicted loss value is determined based on the constraint loss data, the boundary condition loss value, and the data loss value.

[0114] In one optional embodiment, the magnetically controlled flexible body is an elongated magnetically controlled flexible body with a diameter-to-length ratio of less than 0.2, and under the action of the magnetic field of the external magnet, it has continuous and nonlinear morphological response characteristics.

[0115] Figure 6 This is a schematic diagram illustrating a specific example of a morphology response modeling device for a magnetically controlled flexible body provided in one embodiment of this disclosure. Figure 6 Taking a narrow magnetically controlled optical fiber as an example of a magnetically controlled flexible body, the device specifically includes an input data module, a physical simulation engine, an FBG reconstruction module, a PINN main network model, a loss optimization module, and an evaluation and verification module.

[0116] The input data module receives user-inputted magnetically controlled fiber attribute sets, material properties, and magnetic control parameters to determine the training sample set. For example, the magnetically controlled fiber attribute set includes geometric configuration data and initial morphological data corresponding to each narrow magnetically controlled fiber, and there are multiple narrow magnetically controlled fibers. The physical simulation engine is pre-built based on Cosserat flexible body theory and is used to determine the simulation morphological data corresponding to the training samples, supporting offline simulation under various magnetic field conditions. The data input module also receives strain parameter sequences collected by the FBG demodulator on the narrow magnetically controlled fibers. The FBG reconstruction module demodulates and reconstructs the strain parameter sequences to obtain measured morphological data. The simulated morphological data and measured morphological data are converted into a unified morphological representation space to obtain baseline morphological data for model supervision.

[0117] The PINN main network module loads the KAN network, FEM model, and PINN network. It outputs continuous morphological data for each training sample based on the training sample set. Specifically, a physical loss function is constructed using Cosserat flexible body theory. The total loss value corresponding to the PINN main network module is determined based on the physical loss value, smoothing loss value, boundary condition loss value, simulation loss value, and measured loss value. The KAN network and PINN network are then iteratively trained based on this total loss value. The resulting morphological response model is evaluated and validated, such as in terms of accuracy and generalization ability, providing a reliable basis for engineering applications.

[0118] The morphological response modeling device for magnetically controlled flexible bodies provided in this disclosure can execute the morphological response modeling method for magnetically controlled flexible bodies provided in any embodiment of this disclosure, and has the corresponding functional modules and beneficial effects of the method.

[0119] Figure 7 This is a schematic diagram of an electronic device provided according to one embodiment of the present disclosure. The electronic device 10 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices (such as helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0120] like Figure 7As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor 11. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0121] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information or data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0122] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as the morphological response modeling method for magnetically controlled flexible bodies provided in the above embodiments.

[0123] In some embodiments, the morphological response modeling method for magnetically controlled flexible bodies provided in the above embodiments can be implemented as a computer program, which is tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the morphological response modeling method for magnetically controlled flexible bodies described above can be performed. Alternatively, in other embodiments, processor 11 can be configured to perform the morphological response modeling method for magnetically controlled flexible bodies by any other suitable means (e.g., by means of firmware).

[0124] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication unit 19, or installed from storage unit 18, or installed from ROM 12. When the computer program is executed by processor 11, it performs the functions defined in the methods of embodiments of this disclosure.

[0125] Various embodiments of the systems and techniques described above can be implemented in the following systems or combinations thereof: digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard parts (ASSPs), system-on-chips (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0126] Computer programs used to implement the morphological response modeling method for magnetically controlled flexible bodies of this disclosure can be written in any combination of one or more programming languages. These computer programs can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The computer programs can be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0127] In the context of this application, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. Alternatively, a computer-readable storage medium can be a machine-readable storage medium. Examples of machine-readable storage media include, based on an electrical connection of at least one wire, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0128] To provide interaction with a user, the systems and techniques described herein can be implemented on a terminal device having: a display device for displaying information to the user (e.g., a cathode-ray tube (CRT) or liquid crystal display (LCD) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the terminal device. Other types of devices can also provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0129] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0130] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and Virtual Private Server (VPS) services, such as high management difficulty and weak business scalability.

[0131] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this disclosure can be achieved, and this is not limited herein.

[0132] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for modeling the morphological response of a magnetically controlled flexible body, characterized in that, include: A training sample set and a morphological response model to be trained are obtained. The training sample set includes at least one training sample. The training sample includes flexible body parameter data and magnet control data of a magnetically controlled flexible body. The magnetically controlled flexible body includes a fixed end and an end end distributed along the axial direction. An internal magnet is embedded in the end end. The magnet control data represents the control constraints of an external magnet that provides driving excitation for the magnetically controlled flexible body. The morphological response model includes a Kolmogorov-Arnold network, a physical simulation model, and a physical information neural network. For each training sample, the Kolmogorov-Arnold network is used to calculate the local load based on the training sample, and output the equivalent load at the end of the magnetically controlled flexible body. The physical simulation model is used to perform a global mapping based on the equivalent load at the end and the flexible body parameter data in the training sample to determine discrete morphological data. The physical information neural network is used to reconstruct the continuous field of the discrete morphological data and output the continuous morphological data corresponding to the training sample. Obtain the baseline morphological dataset corresponding to the training sample set, and determine the prediction loss value based on each of the continuous morphological data and the baseline morphological dataset; The network parameters of the Kolmogorov-Arnold network and the physical information neural network are iteratively adjusted according to the predicted loss value until the training termination condition is met. Wherein, obtaining the benchmark morphological dataset corresponding to the training sample set includes: Obtain the simulation morphology dataset corresponding to the training sample set, and obtain the actual morphology dataset corresponding to the training sample set. The simulation morphology dataset includes the simulation morphology data of each training sample, and the actual morphology dataset includes the actual morphology data of each training sample. The simulated morphology dataset and the measured morphology dataset are transformed into a unified morphology representation space to obtain the benchmark morphology dataset corresponding to the training sample set. The step of determining the prediction loss value based on each of the continuous morphological data and the baseline morphological dataset includes: The fixed-end constraint terms are determined based on the fixed-end constraint conditions and the fixed-end morphological parameters in each of the continuous morphological data. The deformation load dataset is obtained by performing continuous domain differentiation on each of the continuous morphological data, and the end deformation load set in the deformation load dataset is obtained. The end constraint term is determined according to the end constraint condition and the end deformation load set. Based on the fixed-end constraint term and the end constraint term, the boundary condition loss value is determined, and based on each of the continuous morphological data and the baseline morphological dataset, the data loss value is determined; The predicted loss value is determined based on the boundary condition loss value and the data loss value; The deformation load data in the deformation load dataset represents the distribution information of the deformation load corresponding to the magnetically controlled flexible body.

2. The method according to claim 1, characterized in that, The step of obtaining the simulation morphology dataset corresponding to the training sample set includes: Using a physics simulation engine, physical simulations are performed based on the training sample set to determine the simulation morphology dataset. The simulation accuracy of the physical simulation engine is higher than that of the physical simulation model.

3. The method according to claim 1, characterized in that, The step of obtaining the measured morphology dataset corresponding to the training sample set includes: Obtain the measured strain dataset corresponding to the training sample set, wherein the measured strain dataset includes the strain parameter sequence of each training sample at multiple acquisition points of the magnetically controlled flexible body; Morphological reconstruction is performed on the strain parameter sequence corresponding to each training sample to determine the measured morphological dataset.

4. The method according to claim 1, characterized in that, The step of converting the simulated morphological dataset and the measured morphological dataset into a unified morphological representation space to obtain the benchmark morphological dataset corresponding to the training sample set includes: For each training sample, the simulation morphology dataset and the measured morphology dataset are obtained respectively corresponding to the training sample. The simulation morphology data and the measured morphology data are then subjected to coordinate system alignment and arc length normalization to obtain preprocessed simulation morphology data and measured morphology data. The preprocessed simulation morphology data and the preprocessed measured morphology data are then filtered in terms of sampling dimension to obtain simulation morphology sequence and measured morphology sequence. The simulation morphology sequence and the measured morphology sequence use the same sampling point distribution. Based on the simulated morphological sequences and the measured morphological sequences, a benchmark morphological dataset in the unified morphological representation space is determined.

5. The method according to claim 1, characterized in that, The step of determining the predicted loss value based on the boundary condition loss value and the data loss value includes: Based on the continuous morphological data, constraint loss data is determined, which includes physical loss value and / or smoothing loss value; The predicted loss value is determined based on the constraint loss data, the boundary condition loss value, and the data loss value.

6. The method according to claim 1, characterized in that, The magnetically controlled flexible body is a narrow and elongated magnetically controlled flexible body with a diameter-to-length ratio of less than 0.

2. Under the action of the magnetic field of the external magnet, it has continuous and nonlinear morphological response characteristics.

7. An electronic device, characterized in that, The electronic device includes: At least one processor; A memory that is communicatively connected to the at least one processor; The memory stores a computer program that can be executed by the at least one processor, which is then executed by the at least one processor to enable the at least one processor to perform the morphological response modeling method for the magnetically controlled flexible body according to any one of claims 1-6.

8. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the morphological response modeling method for a magnetically controlled flexible body according to any one of claims 1-6.

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