59 results about "Approximation error" patented technology

The invention discloses a free-form surface three-axis ball-end cutter equal approximation error finish machining tool path generation method which comprises the following steps: firstly, importing a free-form surface model to be machined, and setting data such as the radius, the line spacing, the approximation error maximum allowable value and the precision of a ball-end cutter; secondly, a group of section planes are planned according to the row spacing to intersect with the curved surface, the intersecting line serves as a cutter contact curve, and an equal-bow-height-error cutter contact iterative search method for driving cutter contact adjustment through the geometric distance is provided for the cutter contact curve on the section planes; the maximum distance between a cutter cutting envelope surface and a cutter contact track line is used as an approximation error, and an adaptive discrete method is adopted to carry out approximation error calculation; and finally, the cutter location points of the equal-bow-height-error cutter contact points serve as initial values, an equal-error cutter location point calculation method of step length self-adaptive adjustment iteration is provided, approximation errors between the cutter location points are all within an allowable range, and therefore the free-form surface three-axis ball-end cutter equal approximation error finish machining cutter path is obtained.

The invention relates to the field of nonlinear system control, and provides a preset time reinforcement learning method and system of a continuous nonlinear system, and an electronic device, and the method comprises the steps: constructing a zero-sum game framework based on a kinetic model and a performance index of the nonlinear system; determining a value function and a Hamiltonian function based on a zero-sum game framework; applying a preset neural network model to carry out approximation on the value function, and determining an approximation error; based on the Hamiltonian function and the approximation error, an approximate optimal control strategy and a worst interference strategy are determined; constructing a Lyapunov function based on the value function and the weight error of the value function; and based on a Lyapunov function, an approximate optimal control strategy and a worst interference strategy, a reinforcement learning result is verified. The method and the device are used for overcoming the defects that convergence time cannot be dynamically adjusted, parameter complexity is high and robustness is insufficient in the prior art, and the scheme of the invention can meet dual requirements of a continuous nonlinear system on dynamic convergence and anti-interference performance.

Methods and systems for performing an operation on at least one homomorphically encrypted ciphertext, the method include determining, by a computing device, a value that is an initial approximation of a result of the operation on the at least one homomorphically encrypted ciphertext; and iteratively improving, by the computing device, the value using a recurrence relation wherein a number of iterations is determined based on a predetermined accuracy to minimize an approximation error.

The embodiment of the invention discloses a harmonic compensation method for an angle error of a magnetic encoder, and the method comprises the steps: enabling the magnetic encoder to rotate at a constant speed in a setting mode, collecting sine and cosine signals outputted by the magnetic encoder, and carrying out the calculation through CORDIC, thereby obtaining an initial angle sequence containing a fundamental wave error and a harmonic wave error; extracting each harmonic component through an adaptive wave trap, constructing a harmonic compensation polynomial, and storing each coefficient; in an application mode, a magnetic encoder signal is collected in real time, a current initial angle value is solved, a harmonic compensation amount is calculated according to a current fundamental wave angular frequency and a stored coefficient, and an accurate angle value is obtained by subtracting the compensation amount from the initial angle value. According to the method, external reference signals and a large amount of storage space are not needed, each harmonic error is directly eliminated through a harmonic compensation polynomial, and approximate errors caused by traditional linear interpolation are avoided; and the compensation precision can be improved only by increasing polynomial terms, and the storage requirement is not obviously increased.

The invention discloses an air-space-ground Internet of Things performance analysis method and system based on SWIPT and NOMA, and belongs to the technical field of air-space-ground integrated Internet of Things. Comprising the following steps: constructing an air-space-ground Internet of Things system model comprising an LEO satellite, an unmanned aerial vehicle relay and a ground user, and considering heterogeneous channel characteristics and node dynamics; deducing a closed-form solution of the outage probability of the system through joint transformation of a moment generation function and a characteristic function of a random variable; a high-order Taylor expansion and moment matching method is adopted to carry out approximation on the closed-form solution, a first-order approximate solution and a second-order approximate solution are obtained, and an upper bound of an approximate error is deduced. According to the method, the problem of accurate modeling of the outage probability under heterogeneous link coupling in the air-space-ground Internet of Things is solved, theoretical preciseness and engineering practicability are both achieved, and an effective tool is provided for network reliability analysis and optimization.

The invention discloses a roadside multi-mode fusion sensing method. According to the method, an initial 3D view cone tensor with depth information is generated through a depth estimation network, features of pixel points are projected to a coordinate system in combination with internal and external parameter matrixes of a camera, then a three-dimensional space point coordinate set is generated according to projected feature position information, a Gaussian function is adopted to distribute weights of neighborhood grids, and a three-dimensional space point coordinate set is obtained. And finally, inputting the image features and the features into a fusion unit, respectively carrying out uncertainty modeling on the two types of features, automatically generating a fusion weight, and finally, carrying out normalization weighted aggregation on the features in the neighborhood so as to reduce the position approximation error and obtain the calibrated image features, and finally, inputting the image features and the features into the fusion unit, and respectively carrying out uncertainty modeling on the two types of features and automatically generating a fusion weight. And dynamic optimization is carried out according to a self-supervised loss function in the fusion process, so that the stability of multi-modal feature fusion is ensured, the detection accuracy is high, the performance is relatively good, and the problem of global feature dislocation caused by external parameter deviation and depth error can be avoided.

The invention discloses a five-axis numerical control finish machining tool path approximation error calculation method based on an Optuna optimization BiLSTM-TCRA (BiLSTM, Bidirectional Long Short Term Memory Network, a Bidirectional Long Short Term Memory Network, a Temporal-Channel Residual Attention, a Time-Channel Residual Attention mechanism) neural network, and relates to a tool path approximation error calculation method based on an Optuna optimization method of a BiLSTM-TCRA (BiLSTM, Bidirectional Long Short Term Memory Network, a Bidirectional Long Short Term Memory Network, a Time-Channel Residual Attention Mechanism) neural network and a tool path approximation error calculation method based on the BiLSTM-TCRA neural network. The method comprises the following steps: firstly, acquiring core parameters required by calculation of a neural network model, and mapping the parameters to the same scale by using mean variance normalization to eliminate the influence of dimensional difference between different features on the performance of the model; then, each hyper-parameter of the BiLSTM model is optimized by using an Optuna hyper-parameter optimization framework; a TCRA attention mechanism module is introduced to dynamically distribute different time step feature weights, so that the model can pay more attention to effective information which greatly influences an approximation error, the learning ability of the model is enhanced, and the training precision is improved; dropout mechanism sparsity is added to optimize a network structure, and part of neurons are randomly discarded in each iteration process, so that interference of non-core knife contacts on an approximation error value is reduced, and model overfitting is avoided; finally, the effectiveness of the method is verified in combination with actual curved surface model data, and efficient and accurate prediction of the five-axis machining approximation error is achieved.

Diffusion models are machine learning algorithms implemented as neural network-based denoisers that are uniquely trained to generate high-quality data from an input lower-quality data. However, for complex datasets, the samples generated by a diffusion model can still fail to reproduce the quality and diversity of the training data, due to approximation errors made by the finite-capacity network. Diffusion guidance addresses this issue by steering the sampling process away from a less desired model, toward a preferred one. However, current guidance methods rely on a single additional denoiser and manual tuning of guidance weights, which is suboptimal for large, complex models and leads to inefficiencies. The present disclosure employs a mixture of denoisers to guide a diffusion model, which can increase the expressiveness of the guidance and substantially improve sample quality and diversity in the output of the diffusion model.

This invention discloses a floating-point-fractional hybrid anchoring method and computational system for suppressing iteration errors, belonging to the field of high-precision numerical computation technology. It solves the technical problems of pseudo-chaos caused by the accumulation of iteration errors in pure floating-point calculations, the computational power explosion in pure high-precision fractional calculations, and the inability to simultaneously achieve both computational power and precision. This invention completes high-speed iterative computations of nonlinear systems using a general floating-point format. After each floating-point calculation, an optimal rational number approximation algorithm is used to convert the calculation result into a simplified rational number with a denominator not exceeding a preset threshold, eliminating the original errors introduced by floating-point truncation and rounding. The purified rational number is then converted back to floating-point format to participate in the next iteration, relying on a bounded rational number anchoring mechanism to progressively block the error amplification chain. The denominator threshold is set to 10¹²~10¹ based on the effective number of bits of the floating-point number. 5 This invention can adaptively adjust to various scenarios such as embedded terminals, supercomputing, and industrial control, and optimizes the continued fraction algorithm to achieve the globally optimal rational approximation under a given upper limit of the denominator. It requires no dedicated large number hardware and combines the advantages of high-speed, low-load floating-point operations with zero approximation error in rational numbers. It can be stably used in nonlinear computing scenarios that are sensitive to initial values ​​and require long-term stable iterations, such as chaotic simulation, vehicle trajectory prediction, industrial PID closed-loop control, 5G / 6G communication channel simulation, microscale meteorological simulation, and large-scale number theory zero-point verification. It effectively eliminates numerical trajectory drift, reduces equipment computing power consumption, and minimizes the workload of manual calibration and data screening, possessing extremely high engineering and academic application value.

The invention belongs to the technical field of laser interference precision measurement, and provides a full geometric error displacement calculation method based on non-approximate simplification of a light beam track. All optical machine geometric errors can be completely calculated, the real refraction condition can be completely calculated, no approximate error is introduced in the simplification process, and the displacement calculation process conforms to the real light beam track condition; according to the method provided by the invention, all reflection phenomena in the interferometer are simplified, parameter integration is carried out on a reflecting surface and a receiving surface of a reflected light beam, an originally complicated multi-beam calculation process is optimized, the number of parameter items required for completely describing geometric errors is reduced, and the calculation efficiency is improved. And meanwhile, the light beams which do not influence the calculation of the total optical path difference are deleted, so that the calculation efficiency is high.

The invention discloses a large model similar channel sharing weight lightening method and device, and belongs to the field of artificial intelligence. The method comprises the steps of performing K-Means clustering on a Q / K projector weight matrix of a self-attention layer of a Transform architecture large model according to columns, and generating a cluster representative vector and a cluster label list to replace an original weight matrix to complete compression; restoring the approximate weight matrix based on the representative vector and the cluster label, and constructing an error matrix of the original matrix and the approximate matrix; performing singular value decomposition on the error matrix and retaining a key singular value to obtain two low-dimensional matrixes; during reasoning, multiplying the two low-dimensional matrixes to obtain an approximate error matrix, and adding the approximate error matrix with the approximate weight matrix to obtain a final reasoning weight; the total storage size after compression is calculated through a unified formula, and accurate quantification of storage overhead is achieved. According to the method, the performance degradation under low-bit compression is effectively relieved, the resource demand of model deployment is reduced, and the method is adaptive to various mainstream large models and different-dimension weight matrixes.

The invention discloses a chromatin contact atlas-based topological correlation domain division method, which comprises the following steps of: acquiring and preprocessing chromatin contact atlas data, and constructing a normalized contact matrix; according to the normalized contact matrix, calculating single-segment Infomap entropy values of all possible division intervals; solving an Infomap entropy value of a minimum part in each state through dynamic programming recursion, and calculating a complete Infomap entropy value under each step number according to the Infomap entropy value of the minimum part in each state; selecting the step number corresponding to the minimum integral Infomap entropy value, and obtaining the optimal topological correlation structure domain division through backtracking; an approximation error of the partition structure is calculated to assess partition accuracy. According to the method, a machine learning model does not need to be trained, whole genome chromatin contact information can be fully utilized, optimal division of TAD is automatically achieved, the division accuracy and repeatability are improved, meanwhile, the calculation complexity and cost are reduced, and an efficient and reliable tool is provided for chromatin three-dimensional structure and gene regulation and control research.

An apparatus for computing functions using polynomial-based approximation, comprising one or more processing circuitries configured for computing a polynomial-based approximant approximating a function by executing one or more iterations. Each iteration comprising computing the polynomial-based approximant using scaled fixed-point unit(s) according to a constructed set of coefficients, minimizing an approximation error of the computed polynomial-based approximant compared to the function while complying with one or more constraints selected from a group comprising at least: an accuracy, a compute graph size, a computation complexity, and a hardware utilization of the processing circuitry(s), adjusting one or more of the coefficients in case the approximation error is incompliant with the constraint(s) and initiating another iteration. The polynomial-based approximant and its adjusted set of coefficients for which the computed polynomial-based approximant complies with the constraint(s) may be output to one or more processing circuitries configured to approximate the function by computing the polynomial-based approximant.

The invention belongs to the field of computational electromagnetism numerical simulation, and particularly relates to a non-uniform conformal FDTD method based on a sub-grid technology. According to the method, non-uniform conformal geometric correction is introduced into the sub-grids, so that high-precision fitting of a curved surface boundary is realized, step approximation errors are reduced, and the calculation precision of field quantities near the boundary is improved; according to the method, bidirectional coupling transfer which simultaneously meets line integral conservation and flux conservation is established on a main-sub grid interface, and a conservation relation required by a non-uniform conformal FDTD method is prevented from being damaged, so that interface numerical value reflection is effectively inhibited, energy non-physical errors are reduced, and long-term stability is improved; and fine grids are only adopted in the local fine structure neighborhood and are matched with time sub-cycle propulsion, so that global grid encryption and limitation of global time step length to a minimum unit are avoided, and the storage and calculation time overhead is remarkably reduced while the precision is ensured. According to the method, geometric modeling precision, interface stability and calculation efficiency are considered, and the method has high engineering application value.

This invention discloses a method, system, and electronic device for preparing stable substates based on graph states. The method includes: acquiring and preprocessing stable substate generators to obtain complete stable substate generators; generating an initial parity-check matrix based on the complete stable substate generators; converting the initial parity-check matrix into a graph state parity-check matrix and recording the conversion operations performed during the conversion; constructing a graph state preparation circuit based on the graph state parity-check matrix; constructing a stable substate reduction circuit based on the conversion operations; merging the graph state preparation circuit and the stable substate reduction circuit into a total circuit; acquiring an initial quantum state and executing the total circuit with the initial quantum state to obtain a stable substate. This invention uses graph states as an intermediary, reducing the complexity of circuit design and improving computational efficiency, making it suitable for large-scale quantum systems. Furthermore, the precise mapping relationship between stable substates and graph states avoids approximation errors.

To provide an information processing device, information processing method, and program that can reduce the scale of computations and improve the uniformity of approximation error of a square root of an input value.SOLUTION: An information processing device 1 includes a determination unit configured to calculate the largest integer n that satisfies the expression [1] for an input numerical value x, and a first calculation unit configured to output a numerical value y obtained by performing, on the numerical value x, a computation that includes a term of the expression [2], in which a numerical value α is a predetermined constant. The numerical value α is a predetermined constant close to 1 / 3. The numerical value y obtained in this manner is an approximation of the square root of the numerical value x (i.e., √x).SELECTED DRAWING: Figure 2

The application provides a real-time security evaluation method and device. The method comprises the following steps: acquiring a monitoring data stream, and extracting security level information corresponding to each time point of all data blocks from the monitoring data stream; updating the weight change of the security index based on the security level information through a KernelSHAP method; incrementally updating an evaluation model by using the updated security index and weight, and predicting a security evaluation result by using the updated evaluation model; and determining a security evaluation result according to a preset decision threshold and the security evaluation result. By using the KernelSHAP method, the importance of the newly collected monitoring data stream is determined based on a wide learning system structure, the negative influence caused by the approximation error is reduced, the drift detection is combined with the adaptive and generated explanation ranking preference, and therefore the result of the real-time security evaluation task can be better predicted.

The invention provides a variable-rate collaborative reaching law nonsingular fast integral terminal sliding mode control method. The method comprises the following steps: designing a disturbance observer, a nominal controller and a compensation controller; the interference observer constructs an observer through the intermediate state vector and the adjustable gain matrix in combination with a smooth gain function to obtain a lumped interference observation value; an improved command filter technology is introduced into the nominal controller, and signal smoothing processing is achieved by dynamically adjusting a weight factor; then, a filtering error compensation mechanism is designed to counteract a filtering error; in the compensation controller, a non-singular fast integral terminal sliding mode surface is constructed through a sliding mode surface function, a fusion tracking error, an error integral term and a smoothing function tanh; designing adaptive estimation; based on adaptive estimation, an adaptive variable rate cooperative reaching law is updated, so that the observation error of the observer is disturbed, and the approximation error of the saturation model is compensated. According to the method, the dynamic response speed and the steady-state precision of trajectory tracking control can be remarkably improved.

This application belongs to the field of delay differential equation modeling, specifically disclosing a delay differential equation modeling method based on Bayesian optimization and neural networks. The method includes: generating multiple trajectory data of the system; searching for the optimal delay term using a Bayesian optimization algorithm, where the delay term to be solved is the optimization variable, and the error based on neural network simulation is the objective function, obtaining the optimal delay term through iterative optimization using a surrogate model; constructing a state matrix and a delay matrix from the trajectory data based on the optimal delay term, using the concatenated matrix as input to a neural network to construct a neural network for approximating a nonlinear function; integrating a linear multi-step method into the loss function of the neural network, training the neural network using the trajectory data to obtain a nonlinear function approximation model; and separating the numerical discretization error and the neural network approximation error based on this model to construct a total error bound. This application can achieve high-precision, high-efficiency delay differential equation modeling with quantization error guarantee.

This invention discloses a track smoothness adjustment method based on 3D coordinates and multi-wavelength technology, aiming to solve the problems of accumulated adjustment errors caused by reliance on approximate models in existing technologies, and low efficiency due to the inability to simultaneously handle long and short wave irregularities caused by the single wavelength. The method includes: acquiring the designed and measured three-dimensional coordinates of the track; directly calculating the lateral and vertical versine deviations for each wavelength based on the three-dimensional coordinates using the moving string method according to a preset wavelength list; directly correcting the three-dimensional coordinates using a predetermined proportion of these deviations as a correction amount; completing a single-round adjustment by traversing the wavelength list, and performing multiple rounds of iterative optimization based on the updated coordinates to achieve multi-wavelength gradient smoothness of the track's three-dimensional curve. This invention eliminates approximation errors at their source, significantly improving adjustment accuracy and linear continuity; it can simultaneously correct long and short wave irregularities in one go, greatly improving operational efficiency; and through iteration, it converges the deviations, meeting millimeter-level high smoothness standards, and has strong versatility.

The invention provides an exponential function calculation method, circuit and device and electronic equipment, and the method comprises the steps: receiving an exponential function calculation instruction, analyzing a first operand from the exponential function calculation instruction, and enabling the first operand to be an input value of a to-be-calculated exponential function; performing a * y + (b-c) operation by the floating point multiply-add unit, where a is a parameter related to the base of the exponential function; y is the first operand; b is a floating point number representation corresponding to the index offset value of the floating point data format; c is a parameter for indicating an approximate error; and performing bit extraction and combination on an output result of the floating point multiplication and addition unit through a normalization shift unit according to an exponential bit width and a mantissa bit width of a floating point data format to generate a floating point number conforming to the floating point data format, and outputting the floating point number as an exponential function approximate value of the input value y.

The invention provides a high-dimensional fan blade reliability optimization method based on sparse orthogonal lattice points, and relates to the technical field of high-dimensional fan blades, and the method comprises the following steps: S1, building a finite element model; s2, generating sparse orthogonal lattice points; s3, evaluating the response quantity of each performance index, and judging whether a reliability requirement is met or not; s4, quantitative sensitivity analysis; and S5, modifying the dispersibility of the key material parameters to carry out reliability evaluation. The invention provides a new uncertainty quantification method for a high-dimensional problem, a sampling error of sampling simulation and an approximate error of an agent model are avoided by directly substituting a design sample into the model for calculation, quantification of the high-dimensional problem is realized through sparse orthogonal lattice points, information loss caused by dimension reduction processing of a sensitivity analysis method is avoided, and the method is suitable for large-scale popularization and application. And when a reliability evaluation result does not meet a design requirement, an intermediate calculation result can be fully utilized to carry out sensitivity analysis, and a specific solution is provided for reliability optimization design.

The application discloses a linear path global smoothing and curvature optimization method based on a PH curve, and relates to the technical field of numerical control machining. The method comprises the following steps: acquiring an original tool path comprising three continuous straight line segments; constructing an 11th order PH curve to replace a local polyline path comprising a middle second straight line segment and two end corners; determining a bias distance satisfying a preset upper limit of an approximate error according to an internal angle bisector of the two corners, and determining an entry point and an exit point on adjacent straight line segments; calculating four initial complex coefficients according to first and second derivative continuity constraints; establishing a tangent parallel constraint and a distance constraint at a middle parameter point; and solving two to-be-solved complex coefficients based on displacement continuity constraints, the tangent parallel constraint and the distance constraint to generate a complete curve. The method can eliminate interference between adjacent transition curves, reduce curvature peaks, and improve machine tool transition speed and cutting efficiency.

The application provides a kind of neural network enhanced mechanical arm safety control method and system, the application constructs safety function for joint and workspace obstacle;Robust compensation term is designed by combining network weight error and inherent approximation error, and high-order safety constraint is converted into robust differential inequality;Single integrator auxiliary system and auxiliary barrier constraint are configured for each safety constraint channel, to maintain the feasibility of quadratic programming solution;According to stability driving item and safety driving, weight update law is constructed;And nominal joint torque, auxiliary reference input is used as optimization goal to construct quadratic programming problem, different working modes are switched by mode selection switch and solved, and the optimal control is obtained.The application can compensate system uncertainty, suppress various network errors and external disturbances, maximize trajectory tracking accuracy under the premise of ensuring that the joints of the robot arm do not exceed the limit and the body does not collide, effectively improve the robustness, stability and comprehensive performance of the control system.

The present invention makes it possible to detect an approximation error amount in approximating and encoding axis-dependent data that depends on the coordinate value of each axis of an industrial machine. An approximation error detection device 1 comprises an approximation error amount detection unit 11 that detects an approximation error amount with an absolute value greater than or equal to a predetermined threshold among approximation error amounts in performing model approximation encoding of axis-dependent data on the basis of a part of the axis-dependent data that depends on the coordinate value of each axis of an industrial machine, and on a linear combination model that approximates the axis-dependent data as a linear combination of data on each axis of the industrial machine.

This invention discloses a method and system for stabilizing a robotic arm based on fractional-order sliding mode adaptive compensation. The method includes: constructing a unified dynamic model incorporating time-varying delays, nonlinear disturbances, and neural network approximation errors; defining the sliding mode function using Caputo fractional derivatives, establishing an improved trend law based on the improved Fal function and hyperbolic tangent function, and obtaining a control law based on the error-driven dynamic model and the improved approach law; constructing a dynamic adaptive compensator linked to time-delay gradient information to address the residual errors of the radial basis function and the unknown nonlinear terms in the neural network approximation, and dynamically adjusting the compensation gain based on the dynamic adaptive compensator; constructing a Lyapunov functional adapted to the fractional-order system, deriving the exponential stability criterion for the closed-loop system using Young's inequality and Halany's inequality, and determining the quantitative correlation between the fractional-order order and the convergence rate. This invention solves the problems of imbalance between robustness and smoothness and weak time-delay adaptability in existing technologies, significantly improving control accuracy and reliability.

This application belongs to the field of light field display technology, specifically disclosing a rigorous scalar light field calculation and solution method and system. It includes: obtaining the complex amplitude distribution on the source plane; and calculating the rigorous scalar light field distribution on the observation plane based on rigorous scalar diffraction theory and the complex amplitude distribution on the source plane. Based on scalar diffraction theory, this application constructs a light field propagation model for arbitrary propagation distances, avoids approximation errors in geometric correction methods through a rigorous scalar light field propagation method, overcomes the propagation distance constraints of the scalable angular spectrum propagation model, and achieves Abbe diffraction-limited resolution through a phase retrieval algorithm.

The invention provides an actor-commentator training method and system based on Hamiltonian error wavelet filtering, and relates to the technical field of artificial intelligence and automatic control. The invention aims to solve the problems of slow training and low precision caused by noise contained in Hamiltonian-Jacobi-Bellman approximation errors. The method comprises the following steps: calculating an approximate error signal of a Hamiltonian-Jacobi-Bellman equation; filtering the signal and extracting main components for training; updating parameters of the actor network and the commentator network based on the filtered error signals; the invention further discloses a corresponding system. By filtering the core error signal updated by the driving network, the training mechanism is improved, and the loss function is smoother, so that the convergence speed is accelerated, and the control precision and robustness are improved.

This invention belongs to the field of numerical simulation in computational electromagnetics, specifically a non-uniform conformal FDTD method based on submesh technology. This invention introduces non-uniform conformal geometric corrections within the submesh to achieve high-precision fitting of curved surface boundaries, reducing step approximation errors and improving the accuracy of field calculations near the boundaries. At the master-submesh interface, a bidirectional coupling transfer is established that simultaneously satisfies line integral conservation and flux conservation, avoiding disruption of the conservation relationships required by the non-uniform conformal FDTD method. This effectively suppresses numerical reflections at the interface, reduces energy non-physical errors, and improves long-term stability. Furthermore, by using fine meshes only in the neighborhood of local microstructures and coordinating with time sub-cycle progression, global mesh refinement and the global time step being limited by the smallest unit are avoided, significantly reducing storage and computation time overhead while maintaining accuracy. This invention balances geometric modeling accuracy, interface stability, and computational efficiency, and has high engineering application value.

The application discloses a federated data valuation method based on influence pruning sampling, belongs to the field of federated data valuation, adopts a Shapley value calculation scheme based on marginal contribution, and designs a Shapley value approximation algorithm based on influence pruning sampling, so that combinations of clients with low influence are pruned and combinations with high influence are sampled. Given the number of clients n and the total sampling round number γ, the average time of one federated learning is τ, and the time complexity of the method is O(γτ), which can effectively reduce the time overhead. Assuming that the average data amount of the client in the federated learning is t, the approximate error limit of the method is in the general federated scenario, the data amount t of the client is usually large, and therefore even in the case that k * the approximate error of the method is small.