11 results about "Approximation function" patented technology

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.

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.

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.