Low-Rank Regression for Faster Physical Parameter Optimization
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Solution Overview
Problem
Existing optimization methods for physical parameters in industrial processes, such as mask optimization in computational lithography and fluid simulation, suffer from high computational complexity due to the need for repeated calls to complex forward models, leading to inefficient and time-consuming optimization processes.
Innovation Solution
An optimization method using low-rank regression on historical iteration data to iteratively update matrix coefficients and physical parameters, constructing a low-rank matrix approximation that represents the linear relationship between parameter changes and simulation deviations, allowing for faster convergence and reduced computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If mainstream optimization methods (global or local optimization) are used to optimize physical parameters, then the optimization can achieve convergence to optimal solutions, but the computational complexity is high and the optimization process is time-consuming due to repeated calls to complex forward models
Solution Approach 1:
The patent performs preliminary action by pre-calculating and storing the relationship between physical parameters and simulation results in a lookup table before the actual optimization process. This pre-computed data structure enables the optimization algorithm to query pre-existing results instead of calling the forward model repeatedly during optimization iterations, significantly reducing computational time while maintaining optimization accuracy
Solution Approach 2:
The patent creates a simplified copy or approximation of the complex forward model by using a lookup table that stores pre-computed parameter-result relationships. This copied data structure serves as a surrogate model that can be queried efficiently during optimization without requiring repeated calls to the computationally expensive original forward model, thus resolving the contradiction between accuracy and time consumption
2Ease of operation
If step-by-step reverse solution process is used to calculate updated physical parameters based on forward model output deviation, then the optimization can proceed iteratively, but the computational consumption of reverse solution takes up most of the time in the optimization process
Solution Approach 1:
The patent introduces an intermediary lookup table that mediates between the forward model and the optimization algorithm. Instead of directly performing computationally expensive reverse solutions, the optimization process queries this intermediary data structure containing pre-computed relationships, which provides the necessary parameter updates much more efficiently while maintaining the iterative optimization processability
Solution Approach 2:
The patent substitutes the mechanical reverse solution process (which involves complex computational mechanics) with a data-driven approach using pre-computed lookup tables. This replacement transforms the computational mechanism from expensive iterative reverse calculations to efficient data queries, dramatically improving calculation efficiency while preserving the optimization processability
Data Source
AI summary
An optimization method and system based on low-rank regression of historical iteration data are provided. The method includes: obtaining historical iteration data including change data of physical parameters to be optimized and result deviation data obtained through simulation by using a forward model; and iteratively updating matrix coefficients and the physical parameters to be optimized continuously through low-rank linear regression based on the change data of the physical parameters to be optimized and the result deviation data, and evaluating updated physical parameters to be optimized, until an iteration stop condition is met. A low-rank matrix approximation that represents a small signal linear relationship between the change data of the physical parameters and the result deviation data in the historical iteration is construct and used to solve the optimization problem, which effectively reduces the computational complexity of the optimization process and improves the computational efficiency of the optimization process.