An optimization method and system based on low-rank regression of historical iterative data

Abstract

The present invention provides an optimization method and system based on low-rank regression of historical iteration data, which belongs to the field of computer technology. The method comprises: obtaining historical iteration data, including change data of physical parameters to be optimized and result deviation data obtained by simulation through a forward model; based on the change data of physical parameters to be optimized and the result deviation data, continuously iteratively updating matrix coefficients and physical parameters to be optimized by means of low-rank linear regression and evaluating the updated physical parameters to be optimized until the iteration stop condition is met. In the second half of the iteration, the change data of physical parameters to be optimized and the result deviation data in the historical iteration are used to construct a low-rank matrix approximation that characterizes the small signal linear relationship between the two, and the updated physical parameters to be optimized are obtained accordingly, without the need to gradually reverse solve the forward model, effectively reducing the computational complexity of the optimization process and improving the computational efficiency of the optimization process.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology, and more specifically, relates to an optimization method and system based on low-rank regression of historical iterative data. Background Art

[0002] In many fields such as intelligent manufacturing, digital twins, optoelectronic technology, and industrial engineering, optimization problems of specific physical parameters frequently occur. For example, in computational lithography, a key technology of intelligent manufacturing, optical proximity correction (OPC) is to achieve resolution enhancement by optimizing the design of masks, thereby promoting the advancement of technology nodes. In this process, the efficiency of mask optimization is extremely high. In addition, in complex optimization problems such as simulation and solution calculation of fluids, calibration of digital twin models of intelligent manufacturing equipment or production lines, the requirements for computing efficiency are also getting higher and higher.

[0003] The mainstream optimization methods in the prior art, including various global optimization methods and local optimization methods, for the optimization methods of physical parameters in industrial production and manufacturing, all need to repeatedly solve the physical parameters to be optimized according to the output deviation of the forward model during the optimization process. For complex processes such as the above-mentioned computational lithography mask optimization and solution of fluid simulation diffusion equations, the calculation process of the forward model is relatively complicated, and the process of gradually reversing the solution is even more cumbersome and time-consuming. Each iteration of the optimization process requires calling the forward model, and according to the deviation of its output, the forward model is gradually reversed to calculate the updated value of the physical parameter to be optimized. The computational consumption of the reverse solution process occupies most of the time in the optimization process. How to improve the computational efficiency of the optimization process is a technical problem that needs to be solved urgently in the industry. Summary of the invention

[0004] In view of the defects of the prior art, the purpose of the present invention is to improve the computational efficiency of the optimization process, aiming to solve the problem of low efficiency of the optimization method in the prior art.

[0005] To achieve the above objectives, in a first aspect, the present invention provides an optimization method based on low-rank regression of historical iterative data, comprising:

[0006] Acquire historical iteration data, wherein the historical iteration data includes physical parameter change data to be optimized and result deviation data obtained by simulation through a forward model;

[0007] Based on the physical parameter change data to be optimized and the result deviation data, continuously iteratively updating the matrix coefficients and the physical parameters to be optimized by means of low-rank linear regression and evaluating the updated physical parameters to be optimized until an iteration stop condition is met;

[0008] Among them, the matrix coefficients are used to characterize the linear relationship between the change data of the physical parameter to be optimized and the result deviation data, and the updated value of the physical parameter to be optimized is determined based on the matrix coefficients of the current round of iteration and the simulation result deviation value of the previous round of iteration.

[0009] Optionally, iteratively updating the matrix coefficients and the physical parameters to be optimized by means of low-rank linear regression and evaluating the updated physical parameters to be optimized include:

[0010] Based on the physical parameter change data to be optimized and the result deviation data, estimation is performed through low-rank linear regression to update the matrix coefficients;

[0011] Based on the updated matrix coefficients and the deviation value of the simulation result of the previous iteration, the physical parameter to be optimized is updated;

[0012] Based on the updated physical parameters to be optimized, a simulation is performed through a forward model to determine a simulation result deviation value of the current round of iteration;

[0013] Based on the current number of iterations and the deviation value of the simulation result of the current iteration, it is determined whether to execute the next iteration or stop the iteration.

[0014] Optionally, the estimating based on the physical parameter change data to be optimized and the result deviation data and updating the matrix coefficients by low-rank linear regression specifically includes updating the matrix coefficients by the following formula:

[0015]

[0016] in, represents the estimated value of the matrix coefficient, |y i > <x i | uses Dirac symbols, |.> represents the right arrow, <.| represents the left arrow, λ represents the weight, i represents the iteration number, x represents the left arrow, i represents the change value of the physical parameter to be optimized in the i-th iteration, y i It represents the result deviation value of the i-th iteration, k represents the number corresponding to the current iteration, r represents the number of iterations corresponding to the historical iteration data, r is less than k, and r and k increase as the number of iterations increases.

[0017] Optionally, singular value decomposition can be applied to compute the estimate Here all x' vectors are orthogonal to each other, r'≤r.

[0018] Optionally, before updating the physical parameter to be optimized based on the updated matrix coefficients and the deviation value of the simulation result of the previous iteration, the method further includes determining the Hermitian conjugate of the matrix coefficients by the following formula:

[0019]

[0020] in, represents the estimate of the Hermitian conjugate of the matrix coefficients, λ i * Represents λ i The complex conjugate of .

[0021] Optionally, updating the physical parameter to be optimized includes selecting an optimization algorithm to calculate the reference value direction and reference value of the parameter to be optimized in this iteration. It is worth noting that the present invention is not limited to the optimization algorithm, and the least squares method, conjugate gradient method, regularization, convex optimization and other methods can be used for solution.

[0022] Optionally, the optimization algorithm selected includes adopting the least squares method: Substitute the estimated values ​​of the matrix coefficients and the estimated values ​​of their Hermitian conjugates into x + A + Ax calculates all the items needed.

[0023] Optionally, the performing simulation based on the updated physical parameter to be optimized by a forward model to determine the simulation result deviation value of the current round of iteration includes:

[0024] The updated physical parameter to be optimized is used as a simulation condition, and a simulation is performed through a forward model to obtain a simulation result value;

[0025] Based on the reference target value and the simulation result value, the simulation result deviation value of the current iteration is determined through difference analysis.

[0026] Optionally, determining to execute the next round of iteration or to stop the iteration based on the current number of iterations and the deviation value of the simulation result of the current round of iterations includes:

[0027] If it is determined that the current number of iterations reaches the maximum number of iterations or the simulation result deviation value is less than the preset deviation value, it is determined to stop the iteration; otherwise, it is determined to execute the next round of iterations.

[0028] Optionally, before executing the next iteration, the following steps are also included:

[0029] The historical iteration data is updated based on the change value of the physical parameter to be optimized and the deviation value of the simulation result in the current iteration.

[0030] In a second aspect, the present invention further provides an optimization system based on low-rank regression of historical iterative data, comprising:

[0031] A historical data acquisition module is used to acquire historical iteration data, wherein the historical iteration data includes the change data of the physical parameter to be optimized and the result deviation data obtained by simulation through the forward model;

[0032] An iteration module, for iteratively updating the matrix coefficients and the physical parameters to be optimized by low-rank linear regression based on the physical parameter change data to be optimized and the result deviation data, and evaluating the updated physical parameters to be optimized until an iteration stop condition is met;

[0033] Among them, the matrix coefficients are used to characterize the linear relationship between the change data of the physical parameter to be optimized and the result deviation data, and the updated value of the physical parameter to be optimized is determined based on the matrix coefficients of the current round of iteration and the simulation result deviation value of the previous round of iteration.

[0034] In a third aspect, the present invention provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory, wherein when the programs stored in the memory are executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0035] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0036] It can be understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0037] In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art:

[0038] In the second half of the iteration, the change data of the physical parameters to be optimized in the historical iterations and the result deviation data obtained by the forward model calculation are used to construct a low-rank matrix approximation that represents the small signal linear relationship between the two (small signal means that the change data of the physical parameters to be optimized is a small value and the result deviation data is also a small value), and the matrix coefficients are quickly regressed and estimated, and the updated physical parameters to be optimized are obtained accordingly. There is no need to gradually reverse solve the forward model, and the constructed linear relationship is used to replace the reverse solution of the complex forward model, which effectively reduces the computational complexity of the optimization process and improves the computational efficiency of the optimization solution. Moreover, by using linear approximation for local solution, analytical methods can be used for rapid solution, which is not easy to fall into oscillation and has a faster convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 It is one of the flow charts of the optimization method based on low-rank regression of historical iterative data provided by the present invention;

[0041] Figure 2 This is the second flow chart of the optimization method based on low-rank regression of historical iterative data provided by the present invention;

[0042] Figure 3 This is the third flow chart of the optimization method based on low-rank regression of historical iterative data provided by the present invention;

[0043] Figure 4 It is a structural schematic diagram of the optimization system based on low-rank regression of historical iterative data provided by the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0045] In the embodiments of the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present invention should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0046] In the description of the embodiments of the present invention, unless otherwise specified, “multiple” means two or more than two. For example, multiple processing units means two or more processing units, etc.; multiple elements means two or more elements, etc.

[0047] Next, the technical solution provided in the embodiments of the present invention is introduced.

[0048] Figure 1 This is one of the flow charts of the optimization method based on historical iterative data low-rank regression provided by the present invention, such as Figure 1 As shown, the execution subject of the method may be an electronic device, such as a server, etc. The method comprises: step S101 and step S102.

[0049] Step S101, obtaining historical iteration data, the historical iteration data including the change data of the physical parameters to be optimized and the result deviation data obtained by simulation through the forward model.

[0050] Specifically, the optimization method in the related art can be used to obtain and store historical iteration data of several iterations. The historical iteration data includes the change value x of the physical parameter to be optimized and the forward model output deviation y in each iteration, which respectively constitute the physical parameter change data set X to be optimized (that is, the physical parameter change data to be optimized) and the result deviation data set Y (that is, the result deviation data).

[0051] The physical parameter to be optimized may be a logic signal, such as a force signal, a position signal, a velocity signal, an acceleration signal, a light signal, a graphic image signal or an electrical signal.

[0052] The physical parameter to be optimized may be a digital signal, such as a time-discrete acquisition signal or a space-discrete acquisition signal.

[0053] Step S102, based on the physical parameter change data to be optimized and the result deviation data, continuously iteratively update the matrix coefficients and the physical parameters to be optimized by means of low-rank linear regression and evaluate the updated physical parameters to be optimized until the iteration stop condition is met;

[0054] Among them, the matrix coefficients are used to characterize the linear relationship between the change data of the physical parameters to be optimized and the result deviation data. The update value of the physical parameters to be optimized is determined based on the matrix coefficients of the current round of iteration and the simulation result deviation value of the previous round of iteration.

[0055] It is understandable that in the process of optimizing the physical parameters to be optimized, especially when an optimization algorithm has found a neighborhood near the optimal solution, where the objective function to be optimized can be approximately expressed as a quadratic function of multiple variables, continuing to use global optimization or other nonlinear optimization algorithms can easily cause the iterative process to fall into oscillation and converge very slowly.

[0056] The optimization solution process for the physical parameters to be optimized can be divided into the first half of the iteration and the second half of the iteration. The first half of the iteration can adopt the optimization methods in the relevant technology (various global optimization methods and local optimization methods) to accumulate historical iteration data for use in this method. In the second half of the iteration, each iteration can iteratively update the matrix coefficients and the physical parameters to be optimized and evaluate the updated physical parameters to be optimized by low-rank linear regression. The evaluation result can indicate that the iteration stop condition is met or that the iteration stop condition is not met. Using the change value x of the physical parameter to be optimized in each iteration of the historical iteration and the result deviation value y obtained by forward model calculation, a low-rank matrix approximation representing the small signal linear relationship Ax=y between the two is constructed, and the matrix coefficient A is quickly regressed and estimated by low-rank regression to update the estimated value of the matrix coefficient A for each iteration.

[0057] Write x and y in vector form, x∈R n , y∈R m , matrix coefficients A∈R m×n The estimated value of the matrix coefficient A can be calculated by selecting a total of r iteration data from the history according to the rank r and calculating the estimated value of A.

[0058] Optionally, to ensure the applicability of the linear relationship, when selecting historical iteration data, the first several iterations should be excluded to avoid the situation where the local linear approximation is not applicable due to the larger step size of the first several iterations.

[0059] Optionally, as the number of iterations increases, the selected rank r also increases.

[0060] According to the updated matrix coefficient A, the updated reference data of the physical parameters to be optimized are obtained to update the physical parameters to be optimized. There is no need to perform a step-by-step reverse solution of the forward model. Instead, the constructed linear relationship is used to replace the reverse solution of the complex forward model, which effectively reduces the computational complexity of the optimization process and improves the computational efficiency of the optimization solution. Moreover, by using a linear approximate local solution, an analytical method can be used for rapid solution, which is not easy to fall into oscillation and has a faster convergence speed.

[0061] Figure 2 This is the second flow chart of the optimization method based on historical iterative data low-rank regression provided by the present invention, such as Figure 2 As shown, the method includes the following steps S201, step S202, step S203, step S204, step S205 and step S206.

[0062] Step S201, obtaining and storing several times of historical iteration data.

[0063] The optimization method in the related art can be used to obtain and store the historical data of several iterations. The historical data is the change value x of the physical parameter to be optimized and the output deviation y of the forward model in each iteration, which respectively constitute the physical parameter change data set X to be optimized and the result deviation data set Y.

[0064] Step S202, calculate the estimated value of the matrix coefficient, that is, based on the physical parameter change data to be optimized and the result deviation data, estimate through low-rank linear regression and update the matrix coefficient.

[0065] The estimated values ​​of the matrix coefficients can be calculated using the iterative historical data obtained in step S201. The estimated values ​​can be used to update the matrix coefficients.

[0066] in, represents the estimated value of the matrix coefficient, |y i > <x i | uses Dirac symbols, |.> represents the right arrow, <.| represents the left arrow, λ represents the weight, i represents the iteration number, x represents the left arrow, i represents the change value of the physical parameter to be optimized in the i-th iteration, y i It represents the result deviation value of the i-th iteration, and r represents the number of iterations corresponding to the historical iteration data.

[0067] Singular value decomposition can be applied to calculate estimates of the matrix coefficients Use this estimate to update the matrix coefficients A.

[0068] Optionally, compute estimates of the Hermitian conjugates of the matrix coefficients if needed

[0069]

[0070] in, represents the estimate of the Hermitian conjugate of the matrix coefficients, λ i * Represents λ i The complex conjugate of .

[0071] It is understandable that in the process of updating the physical parameters to be optimized based on the updated matrix coefficients and the deviation value of the simulation results of the previous iteration, optimization algorithms such as least squares method, conjugate gradient method, regularization, convex optimization and other algorithms can be used. If the Hermitian conjugate of the matrix coefficients needs to be calculated when calling these optimization algorithms, the method for fast regression estimation of the matrix coefficients proposed in the present invention can also be used to quickly estimate the Hermitian conjugate of the matrix coefficients. The estimated value of the Hermitian conjugate of the matrix coefficients can be Approximated as the Hermitian conjugate of the matrix coefficients.

[0072] Step S203, selecting an optimization algorithm, using the forward model output data and matrix coefficient estimates of the previous iterative calculation, and calculating and solving the reference values ​​for updating the parameters to be optimized in this iteration.

[0073] An optimization algorithm is selected, and the reference value direction and reference value x of the physical parameter to be optimized in this iteration are calculated based on the estimated values ​​of the matrix coefficients obtained in step S202 and the output deviation value calculated by the forward model after the previous iteration. It is worth noting that the present invention is not limited to the optimization algorithm, and the least squares method, conjugate gradient method, regularization or convex optimization method can be used for solution.

[0074] Alternatively, the least squares method can be used: Substitute the estimated value of the matrix coefficient calculated in step S202 and the estimated value of its Hermitian conjugate into x + A + Ax calculates all the items needed.

[0075] Step S204, adjust and update the parameters to be optimized, call the forward model, calculate the output value, and determine whether the iteration stop condition is met.

[0076] According to the reference direction and reference value of the physical parameter to be optimized obtained in step S203, the physical parameter to be optimized is adjusted and updated (that is, based on the updated matrix coefficient and the simulation result deviation value of the previous iteration, the physical parameter to be optimized is updated, the reference direction and reference value of the physical parameter to be optimized are determined, and then the physical parameter to be optimized is adjusted and updated accordingly), and then the updated physical parameter to be optimized (the updated physical parameter to be optimized is used as the simulation condition), the forward model is called for simulation, the output value (that is, the simulation result value) is calculated, and the output value of the forward model is compared with the reference target value (for example, the difference is calculated) to obtain the output deviation value (that is, the simulation result deviation value), and it is determined whether the iteration stop condition is met. If the stop condition is met, jump to step S205; if not, jump to step S206. The iteration stop condition can be adopted but is not limited to: the number of iterations reaches the maximum number of iterations limit; the model output deviation value is less than the specified value or the preset deviation value, etc.

[0077] Step S205, stop iteration and output the current optimization result.

[0078] Stop the iteration and output the current optimization result (the updated value of the physical parameter to be optimized obtained in the last iteration) as the final optimization result.

[0079] Step S206, record the data of this iteration (the change value of the physical parameter to be optimized and the deviation value of the simulation result of this iteration) into the historical iteration data and enter the next round of iteration.

[0080] The current iteration data, i.e., the change value of the physical parameter to be optimized in the current iteration (the change value of the physical parameter to be optimized in the current iteration can be determined based on the reference direction and reference value of the change of the physical parameter to be optimized obtained in step S203) and the forward model output deviation value are recorded in the historical iteration data to enter the next round of iteration.

[0081] The optimization method proposed in the present invention is illustrated below by taking calculation of photolithography mask optimization as an example. Figure 3 This is a flow chart of the third optimization method based on low-rank regression of historical iterative data provided by the present invention. The optimization method based on low-rank regression of historical iterative data provided by the present invention is used to perform computational lithography mask optimization. The specific implementation steps are as follows: Figure 3 As shown, the following steps are included:

[0082] Step S301, set the starting number of iterations k and rank r, and the maximum number of iterations K, all of which are positive integers and satisfy r<k≤K, that is, in the mask optimization process, the method proposed in the present invention is adopted starting from the kth iteration, and the historical iteration data used is the data of r iterations from the krth to the k-1th.

[0083] Step S302, using other (related technology) mask optimization methods, performing k-1 iterations, and storing each iteration data shown in P1 into the iteration history data set P2. The iteration history data set, for each iteration recorded for backup, includes a mask edge movement data set X consisting of the movement direction and length of each mask edge, and an edge position error (EPE) data set Y obtained by mask simulation exposure after movement.

[0084] It is worth noting that, for EPE, its data set Y may be, but is not limited to, a critical dimension error (CD error) set, an EPE set of each edge segment, or a photoresist contour error (contour error) set.

[0085] Step S303: extracting a total of r optimization iteration data from the krth to the k-1th from the historical data set P2.

[0086] Step S304, using the r groups of historical iteration data obtained in step S303, calculate the estimated value of the matrix coefficient A: and its Hermitian conjugate A + Estimated value: Where i represents the i-th iteration.

[0087] k represents the number corresponding to the current iteration, r represents the number of iterations corresponding to the historical iteration data, r is less than k, and r and k increase as the number of iterations increases. For example, after the current iteration ends and before entering the next iteration, the number of iterations k = k + 1 and the rank r = r + 1 are set.

[0088] Step S305, using the least squares method, the y calculated in the previous iteration k-1 The matrix coefficient estimate obtained in step S304 Calculate and solve x for this iteration k value: And store it into the iterative history data set P2, where ||.||2 represents the 2-norm. It is worth noting that the present invention does not limit the optimization solution method, and the least squares method, conjugate gradient method, regularization or convex optimization method can be used for solution.

[0089] Step S306: adjusting and updating the mask according to the mask edge movement data obtained in step S305.

[0090] Step S307: Using the mask from step S306, calling the forward model to simulate exposure, and calculating the x k The corresponding EPE value y k , and store it in the iteration history dataset P2.

[0091] Step S308, determine the iteration stop condition, that is, whether the iterator of the current optimization process has reached the maximum number of iterations, that is, k>K, or determine whether the EPE obtained in step S307 satisfies the iteration stop condition |EPE|<ε. The iteration stop judgment condition is not limited to the above two cases. If the judgment result is "yes", jump to step S309; ​​if it is "no", jump to step S310.

[0092] Step S309, stop iteration and output the current result as the mask optimization result.

[0093] Step S310, set the number of iterations k=k+1, the rank r=r+1, and enter a new round of iterations.

[0094] The optimization system based on low-rank regression of historical iterative data provided by the present invention is described below. The optimization system based on low-rank regression of historical iterative data described below and the optimization method based on low-rank regression of historical iterative data described above can be referenced to each other.

[0095] Figure 4 : is a schematic diagram of the structure of the optimization system based on low-rank regression of historical iterative data provided by the present invention, such as Figure 4 As shown, the system includes: a historical data acquisition module 10 and an iteration module 20. Among them:

[0096] A historical data acquisition module 10 is used to acquire historical iteration data, wherein the historical iteration data includes the change data of the physical parameters to be optimized and the result deviation data obtained by simulation through the forward model;

[0097] An iteration module 20, for iteratively updating the matrix coefficients and the physical parameters to be optimized by low-rank linear regression based on the physical parameter change data to be optimized and the result deviation data, and evaluating the updated physical parameters to be optimized until the iteration stop condition is met;

[0098] Among them, the matrix coefficients are used to characterize the linear relationship between the change data of the physical parameters to be optimized and the result deviation data. The update value of the physical parameters to be optimized is determined based on the matrix coefficients of the current round of iteration and the simulation result deviation value of the previous round of iteration.

[0099] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method, which will not be repeated here.

[0100] Based on the method in the above embodiment, an embodiment of the present invention provides an electronic device. The device may include: at least one memory for storing programs and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the above embodiment.

[0101] Based on the method in the above embodiment, an embodiment of the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0102] Based on the method in the above embodiment, an embodiment of the present invention provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0103] It is understandable that the processor in the embodiment of the present invention may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0104] The method steps in the embodiments of the present invention can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0105] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid state disk (SSD)), etc.

[0106] It should be understood that the various numerical numbers involved in the embodiments of the present invention are only used for the convenience of description and are not used to limit the scope of the embodiments of the present invention.

[0107] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An optimization method based on low-rank regression of historical iterative data, characterized in that: include: Acquire historical iteration data, wherein the historical iteration data includes physical parameter change data to be optimized and result deviation data obtained by simulation through a forward model, wherein the physical parameter to be optimized is a photolithography mask, the physical parameter change data to be optimized is a mask edge movement data set, and the result deviation data is an edge position error data set; Based on the physical parameter change data to be optimized and the result deviation data, continuously iteratively updating the matrix coefficients and the physical parameters to be optimized by means of low-rank linear regression and evaluating the updated physical parameters to be optimized until an iteration stop condition is met; The matrix coefficients are used to characterize the linear relationship between the physical parameter change data to be optimized and the result deviation data, and the update value of the physical parameter to be optimized is determined based on the matrix coefficients of the current iteration and the simulation result deviation value of the previous iteration; The iterative updating of matrix coefficients and physical parameters to be optimized by low-rank linear regression and evaluating the updated physical parameters to be optimized include: Based on the physical parameter change data to be optimized and the result deviation data, estimation is performed through low-rank linear regression to update the matrix coefficients; Based on the updated matrix coefficients and the deviation value of the simulation result of the previous iteration, the physical parameter to be optimized is updated; Based on the updated physical parameters to be optimized, a simulation is performed through a forward model to determine a simulation result deviation value of the current round of iteration; Based on the current number of iterations and the deviation value of the simulation result of the current iteration, determine to execute the next iteration or stop the iteration; The updating of the matrix coefficients by estimating based on the physical parameter change data to be optimized and the result deviation data through low-rank linear regression specifically includes updating the matrix coefficients through the following formula: ； in, represents the estimated values ​​of the matrix coefficients, Using Dirac symbols, |.> represents the right arrow, <.| represents the left arrow, λ represents the weight, represents the iteration number, Indicates The change value of the physical parameter to be optimized in the iteration, Indicates The result deviation value of the iteration is Indicates the number corresponding to the current iteration. Indicates the number of iterations corresponding to the historical iteration data, Less than , and It increases as the number of iterations increases.

2. The optimization method based on low-rank regression of historical iterative data according to claim 1, characterized in that: Before updating the physical parameter to be optimized based on the updated matrix coefficients and the deviation value of the simulation result of the previous iteration, the method further includes determining the Hermitian conjugate of the matrix coefficients by the following formula: ； in, represents an estimate of the Hermitian conjugate of the matrix coefficients, express The complex conjugate of .

3. The optimization method based on low-rank regression of historical iterative data according to claim 1, characterized in that: The method of performing simulation based on the updated physical parameter to be optimized by using a forward model to determine the deviation value of the simulation result of the current round of iteration includes: The updated physical parameter to be optimized is used as a simulation condition, and a simulation is performed through a forward model to obtain a simulation result value; Based on the reference target value and the simulation result value, the simulation result deviation value of the current iteration is determined through difference analysis.

4. The optimization method based on low-rank regression of historical iterative data according to claim 1, characterized in that: The step of determining to execute the next round of iteration or to stop the iteration based on the current number of iterations and the deviation value of the simulation result of the current round of iterations comprises: If it is determined that the current number of iterations reaches the maximum number of iterations or the simulation result deviation value is less than the preset deviation value, it is determined to stop the iteration; otherwise, it is determined to execute the next round of iterations.

5. The optimization method based on low-rank regression of historical iterative data according to claim 4 is characterized in that: Before executing the next iteration, it also includes: The historical iteration data is updated based on the change value of the physical parameter to be optimized and the deviation value of the simulation result in the current iteration.

6. An optimization system based on low-rank regression of historical iterative data, characterized in that: include: A historical data acquisition module, used to acquire historical iteration data, wherein the historical iteration data includes physical parameter change data to be optimized and result deviation data obtained by simulation through a forward model, wherein the physical parameter to be optimized is a photolithography mask, the physical parameter change data to be optimized is a mask edge movement data set, and the result deviation data is an edge position error data set; An iteration module, for iteratively updating the matrix coefficients and the physical parameters to be optimized by low-rank linear regression based on the physical parameter change data to be optimized and the result deviation data, and evaluating the updated physical parameters to be optimized until an iteration stop condition is met; The matrix coefficients are used to characterize the linear relationship between the physical parameter change data to be optimized and the result deviation data, and the update value of the physical parameter to be optimized is determined based on the matrix coefficients of the current iteration and the simulation result deviation value of the previous iteration; The iterative updating of matrix coefficients and physical parameters to be optimized by low-rank linear regression and evaluating the updated physical parameters to be optimized include: Based on the physical parameter change data to be optimized and the result deviation data, estimation is performed through low-rank linear regression to update the matrix coefficients; Based on the updated matrix coefficients and the deviation value of the simulation result of the previous iteration, the physical parameter to be optimized is updated; Based on the updated physical parameters to be optimized, a simulation is performed through a forward model to determine a simulation result deviation value of the current round of iteration; Based on the current number of iterations and the deviation value of the simulation result of the current iteration, determine to execute the next iteration or stop the iteration; The updating of the matrix coefficients by estimating based on the physical parameter change data to be optimized and the result deviation data through low-rank linear regression specifically includes updating the matrix coefficients through the following formula: ； in, represents the estimated values ​​of the matrix coefficients, Using Dirac symbols, |.> represents the right arrow, <.| represents the left arrow, λ represents the weight, represents the iteration number, Indicates The change value of the physical parameter to be optimized in the iteration, Indicates The result deviation value of the iteration is Indicates the number corresponding to the current iteration. Indicates the number of iterations corresponding to the historical iteration data, Less than , and It increases as the number of iterations increases.

7. An electronic device, characterized in that: include: at least one memory for storing a program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium storing a computer program, characterized in that: When the computer program runs on a processor, the processor is caused to execute the method according to any one of claims 1 to 5.

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