21 results about "Approximation function" patented technology

Calculation time is reduced without degrading approximation accuracy in calculation of a complicated function through secure computation. A secret batch approximation system calculates a concealed text [z] of an approximate value z for a function value y satisfying yj=f(xj) by using a concealed text [x] of a value x as input. g is defined as a polynomial for approximating each section of m sections into which the function f is divided. A parameter acquisition unit acquires a concealed text [a] of a parameter a corresponding to the value x for each integer j that is not less than 1 and not more than n, where aj is defined as a parameter pi corresponding to a section Ri including a value xj. A polynomial calculation unit calculates a polynomial g([x], [a]) by using the concealed text [x] of the value x as input based on the concealed text [a].

To accurately predict a bidding curve without difficult-to-obtain information such as power supply configuration information on all power supply facilities that may affect market prices or information on bidding policies of all market participants.SOLUTION: A prediction system, for each pair of a division section number candidate and an approximation function, approximates a portion of a bidding curve to the approximation function, for each division section obtained by division according to the division section number candidate, calculates an approximation evaluation index for the pair, selects a pair of the approximation function and the division section number candidate with the best approximation evaluation index, constructs a parameter model based on a parameter extraction result according to the pair and a factor value for each factor, and predicts the bidding curve using a parameter value predicted using the model and the approximation function in the pair.SELECTED DRAWING: Figure 3

Function approximation includes receiving a number value to be input to a function. The number value includes a first and second plurality of bits. A first approximation value of a function is determined using the first plurality of bits as an index to a first lookup table including a plurality of candidate first approximation values. A first correction coefficient is determined using the first plurality of bits as an index to a second lookup table including a plurality of candidate first correction coefficients. A second correction coefficient is determined by using the first plurality of bits as an index to a third lookup table including a plurality of candidate second correction coefficients. A second approximation value of the function is determined based on the first approximation value, the first correction coefficient, and the second plurality of bits.

This specification provides a method and device for determining a seismic reflection coefficient. Based on this method, after constructing a first objective function for the seismic reflection coefficient of a target area based on post-stack seismic data and a seismic wavelet convolution model, a dual approximate function corresponding to the first objective function can be constructed as a second objective function, thereby converting the problem of directly solving the optimal value of the first objective function into a corresponding dual problem, avoiding the direct solution of the first objective function; then, the second objective function is processed by adopting a preset processing method based on semidefinite programming theory to determine the reflection time. This eliminates the need to discretize the sparse domain of the reflection coefficient, effectively avoids the problem of basis mismatch, and thus accurately inverts the reflection coefficient to obtain a higher-precision reflection coefficient, solving the technical problems of large errors and low precision in the determined reflection coefficient in existing methods.

The invention relates to a computer-implemented method for training a convolutional neural network, the convolutional neural network comprising nodes arranged in layers and a prune mask, the method comprising the steps of:-providing at least one marked training data set (S10); -initializing the convolutional neural network (S12); -passing the training data through the convolutional neural network (S14); -calculating a loss function (S16) and comparing the loss function with the labels of the training data; and-minimizing the loss function by back propagation (S18), including determining a gradient of the loss function; wherein passing the training data through the delete mask comprises multiplying the structure si of the input of the delete mask by a delete parameter Mi, the delete parameter Mi for the structure si being 0 or 1; wherein the mask is approximately pruned by an approximation function during back propagation.

An auto calibration method according to at least one example embodiment may include receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design, generating at least one approximation function based on the input data and the hardware data, determining at least one loss function based on the generated at least one approximation function, determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that a value of the loss function is 0, and selectively adjusting the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.

The invention relates to a method carried out by at least one device, the method comprising: - Obtaining measurement data that yields the value of a Zernike coefficient Z i Specify the path length y along a scan direction of a photolithography process for different distances; - Defining an approximation function a(y) that reproduces the obtained measurement data. The task of specifying a method with which a Zernike coefficient function can be approximated with increased accuracy is solved by making the approximation function a(y) at least piecewise a spline interpolation s(y) of the measurement data.

The invention provides a method and system for calculating a Cole-Cole model by using a rational fraction approximation method, a medium and a product, and relates to the field of electric digital data processing. An error expression between a Cole-Cole target model and a rational fraction approximation function before solving is multiplied by a denominator polynomial of the approximation function, and a denominator coefficient to be solved is moved to a linear expression from a denominator position, so that a linearized error function is obtained. Then, on the basis of the linearization error, discrete sampling points are selected in the full frequency band, and a target function with the purpose of minimizing the sum of errors is established. A nonlinear problem which needs to be solved through complex iteration originally is converted into an optimization problem which can be solved in a one-time and deterministic mode through a standard linear solving algorithm. The high efficiency of the solving process and the stability of the result are ensured, the effect and the accuracy of the induced polarization effect are improved, and meanwhile the cost is reduced.

An approximate function calculation apparatus includes: a first error upper bound calculating unit which obtains an upper bound of a first error of an approximation of a function f(x) by the function gb(x) in a section [x0, b]; an expansion position calculating unit which obtains an expansion position b′ that represents a maximum b at which the upper bound of the first error; a second error upper bound calculating unit which obtains an upper bound of a second error of an approximation of the function f(x) by a function gb′(x) in a section [b′, x2]; a right end position calculating unit which calculates a right end position x2′ that represents a maximum x2 at which the upper bound of the second error; and a control unit which repeats processing of the respective units with a section [x2′, x1] as the section D.

The application discloses a data-driven optimal switching control method of a switching system. The application firstly determines an optimal control strategy to minimize the cost of the switching system in an infinite time domain; then deduces an optimal solution based on a finite time domain HJB equation, which starts from a positive definite function, obtains an approximation formula of a value function according to a partial derivative, and introduces an approximate function in the form of a multiplication of a base function and a weight to replace unknown quantities in the approximation formula; the weight of the approximate function in the approximation formula can be estimated by using a state data matrix; finally, the weight estimation value is continuously updated until an approximate optimal weight is obtained, and then the optimal cost and the optimal switching control strategy are calculated by substituting the approximate optimal weight into the infinite time domain HJB equation. The method only needs state data, does not need subsystem models, can realize the optimal switching control of the switching system, does not depend on system models, and is suitable for the case that the subsystem models of the switching system are unknown.

A computer-implemented method for generating input polynomial coefficients for use by a signal generator in a quantum control system. The signal generator is configured to generate an output signal which approximates a desired signal using fixed-point arithmetic and the input polynomial coefficients. The desired signal is segmented into a plurality of segments, the desired signal having one or more signal values in each segment. The method comprises, for each segment of the plurality of segments, obtaining one or more initial trial polynomial coefficients, and providing the one or more initial trial polynomial coefficients to an optimisation algorithm to generate the input polynomial coefficients. The optimisation algorithm comprises minimising a difference between the one or more signal values of the desired signal and one or more approximated signal values generated using an approximation function. The approximation function approximates the one or more signal values of the desired signal using the one or more initial trial polynomial coefficients and the fixed-point arithmetic used by the signal generator.

The application provides a multi-point approximation method based on an approximate Hessian matrix for structure optimization, comprising the following steps: step 1, establishing a finite element model of a spacecraft based on an initial design of a spacecraft structure; step 2, performing mechanical prediction of the spacecraft, and the analysis mode comprises static analysis, modal analysis, buckling analysis and transient response; step 3, establishing a structure optimization mathematical model, namely, defining an optimization target, a constraint function and a design variable; step 4, establishing a sequence approximation problem considering second-order information to approximate the original problem; step 5, estimating the Hessian matrix of the multi-point approximation function by using a quasi-Newton method; step 6, selecting known points by using a neighborhood selection strategy based on the Euclidean distance; step 7, establishing convergence discrimination and an automatic optimization system; step 8, method comparison, analysis and iteration explicitness; and setting an optimization example to illustrate the flow from spacecraft design to analysis and then to optimization, and the effectiveness is verified by comparing the results of the optimization method with those of a commercial software.

The invention discloses a concrete full-curve mechanical response-oriented numerical model parameter optimization method, which is applied to the technical field of phase field model solution parameter optimization calibration. Comprising the following steps: obtaining a simulation output result under a set phase field model solving parameter combination, and recording solving efficiency; calculating to obtain the fitting degree between each group of numerical simulation results and the test reference model and the corresponding solving efficiency; constructing a regression model by taking the model precision and the solving efficiency as target variables and taking each model solving parameter as an explanatory variable to obtain an approximate function expression of the fitting degree and the solving efficiency; and the global mechanical response curve is optimized and solved step by step according to the sequence of the fitting degrees. According to the method, on the basis of the fitting precision index, the solving efficiency is further introduced as a new optimization target, meanwhile, the optimization sequence is determined by combining the precision of the stress-strain behavior full-curve segmentation model, and system optimization of the concrete fracture phase field model solving parameters is achieved layer by layer and target by target.

The invention belongs to the technical field of artificial intelligence, and discloses a Diffusion Transform acceleration method, system and device based on incremental caching and a medium, and the method comprises the steps: obtaining a task demand, and constructing a target generation model; the task requirement is input into the target generation model, a cache data structure is constructed, and the cache data structure is input and output of each linear layer in the target generation model at any time step and is used for skipping redundancy calculation; constructing a low-rank approximation function to approximate the weight of each linear layer in the target generation model to obtain a correction parameter; and correcting and optimizing the cache data structure in a reverse process of the target generation model based on the correction parameters, and after calculation of each time step is completed, outputting a generation result corresponding to the task demand. According to the method, error accumulation can be effectively reduced, and the generation quality and the calculation complexity can be better balanced.

The application discloses a time series-based weighted probability density processing method and related equipment, and the method comprises the following steps: obtaining an approximate function of a first time series and a second time series respectively based on a linear interpolation method; obtaining a time point at each interval boundary based on the approximate function of the first time series; dividing the approximate function of the first time series and the approximate function of the second time series into time series segments based on the time point; obtaining the time series segments, and assigning a weight of the time series segment to a corresponding interval to obtain a weighted probability density. The application obtains a time point of an approximate function of a variable at each interval boundary, divides the approximate function of the variable into time series segments according to the obtained time point, and assigns a weight to the interval, so that the calculation of the weighted probability density of the variable is closer to the true value than the result calculated by a weighted histogram without interpolation, and the result along the change range of the variable is very small.

The application discloses a method and system for supporting brain-like simulation model learning, and the method comprises the following steps: managing all parameters in the brain-like simulation model, and classifying the parameters into fixed parameters, variable parameters, non-differentiable parameters and learnable parameters according to calculation characteristics; designing an approximate function operator library for the non-differentiable parameters, and integrating the library into the system; designing usage rules of the approximate functions, so that the original calculation function of the non-differentiable parameters is used in the forward calculation process of the model, and the approximate function of the non-differentiable parameters is called to perform differential calculation in the gradient solving stage of the back propagation; designing an approximate function calling interface of the brain-like simulation model, replacing the non-differentiable calculation part in the model; and constructing a learnable brain-like simulation model network to perform task learning and training. Through the fine parameter management and the approximate function simulation gradient calculation, the application realizes efficient learning and training of the brain-like simulation model, and is successfully applied to complex classification tasks.

To provide a prediction method for predicting dynamic performance of a tire in a short time.SOLUTION: A prediction method includes: a first step S1 of acquiring design parameter information; a second step s2 for acquiring an actual measurement value of a response to a measurement condition that changes with time; a third step S3 for preparing an approximation function showing a relationship between a measurement condition and a response; a fourth step S4 for identifying a coefficient of an approximation function by regression analysis on the basis of an actual measurement value; a fifth step S5 for generating a learning model with design parameter information in the first step as an input layer and the coefficient in the fourth step as an output layer; a sixth step S6 that inputs design parameter information of a predicted tire to a learning model and calculating a coefficient of an approximation function for a predicted tire; and a seventh step S7 for predicting dynamic performance by using an approximation function including the coefficient in the sixth step S6.SELECTED DRAWING: Figure 2

The present disclosure relates to a neural network including at least one neural network layer and a specific type of activation function connected to the output of the at least one neural network layer, where the activation function is implemented as an approximation function of a mathematically defined real-valued nonlinear activation function, the approximation function allowing processing only integers of a fixed-point representation of the input values ​​of the approximation function.

A secret share value [ft(x)−f′t(x)] of ft(x)−f′t(x) is obtained through secure computation using a secret share value [x] of a real number x, and a secret share value [ft(x)−f′t(x)]r of (ft(x)−f′t(x))r obtained by right-shifting ft(x)−f′t(x) by the predetermined number of bits is obtained through secure computation using the secret share value [ft(x)−f′t(x)]. Here, [μ] is a secret share value of μ, n is an integer equal to or greater than 1, t=0, . . . , n−1, u=1, . . . , n−1, ft(x) is a function of the real number x, f′t(x) is an approximation function of the function ft(x), a secret share value [f′0(x)] of an approximation function f′0(x) is [f′0(x)]=c0,0+c0,1[x], a secret share value [f′u(x)] of an approximation function f′u(x) is [f′u(x)]=cu,0+cu,1[x]+cu,2[f0(x)]+ . . . +cu,u+1[fu−1(x)], ct,0 is a public value, and ct,1, . . . , ct,n+1 are coefficients.

The invention discloses an air conditioner compressor sliding vane sound control method based on multi-parameter collaborative optimization, and the method comprises the steps: carrying out the multi-parameter collaborative optimization of a sliding vane and a sliding vane groove in a compressor, and a spring connected with the sliding vane, and constructing an approximate function relation between an optimization target and an optimization variable through a Kriging model method, according to the method, training sample points are selected through an optimal Latin hypercube sampling method, and optimal design parameters of optimization variables are obtained by adopting a genetic algorithm, so that normal contact force between the sliding vane and the piston is improved, periodic separation and collision between the sliding vane and the piston are avoided, and the sliding vane sound of the air conditioner compressor is reduced.

A system and method of designing an integrated circuit for calculating an approximation of a target function over a predetermined interval may include employing an approximation algorithm, to calculate a first approximation function, which approximates the target function. Embodiments may construct an objective function based on the first approximation function. Based on the objective function, embodiments may calculate a first set of outcome coefficient values, which define an outcome approximation function, and generate, based on the outcome approximation function, an approximation schematic. The approximation schematic may represent an electrical approximation circuit, adapted to (i) receive an input value within the predetermined interval, and (ii) produce an estimation of the mathematical function at the input value, according to the outcome approximation function.