Analytic System Eliminating Unneeded Partial Derivatives
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Solution Overview
Problem
Existing methods for generating analytical derivatives in nonlinear models produce numerous unneeded partial derivatives, leading to significant waste of computer resources and reduced data processing throughput.
Innovation Solution
A method that identifies and eliminates unneeded partial derivatives by defining a symmetric matrix to indicate direct and indirect dependencies, allowing for the removal of unnecessary equations and reducing computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all partial derivatives are computed in nonlinear models, then complete derivative information is obtained, but computer resources and execution time are significantly wasted
Solution Approach 1:
The patent extracts and identifies only the necessary partial derivatives needed for the specific computation task by building a dependency graph and performing topological sorting. Unnecessary derivatives are excluded from computation, thereby reducing computer resource waste while maintaining the completeness of required derivative information.
Solution Approach 2:
The patent performs preliminary analysis by constructing a dependency graph of all equations and variables before actual computation. This preliminary action identifies which partial derivatives are actually needed based on the computational goal, allowing the system to avoid computing unnecessary derivatives and thus reduce energy consumption.
2Measurement precision
If all partial derivatives are computed in nonlinear models, then complete derivative information is obtained, but data processing throughput is reduced
Solution Approach 1:
The patent extracts only the essential partial derivatives required for the computation by analyzing the dependency structure of the system. By excluding unnecessary derivatives from the computation set, the data processing throughput is improved while still obtaining all necessary derivative information for the analytical model.
Solution Approach 2:
The patent performs preliminary dependency analysis and topological sorting before computation to identify the minimal set of required partial derivatives. This preliminary action enables the system to process data more efficiently by avoiding computations for derivatives that will not be used, thereby increasing productivity.
3Loss of time
If a symmetric matrix is defined to track all direct and indirect dependencies, then unneeded computations are accurately identified, but the complexity of the system increases
Solution Approach 1:
The patent introduces a symmetric matrix as an intermediary data structure to systematically track direct and indirect dependencies between equations and variables. This intermediary enables accurate identification of unnecessary computations through automated graph analysis, outweighing the additional complexity introduced by the matrix structure.
Solution Approach 2:
The patent segments the dependency analysis into distinct computational stages: building the dependency graph, populating the symmetric matrix with direct dependencies, performing transitive closure to identify indirect dependencies, and finally identifying removable equations. This segmentation makes the complex system more manageable and systematic.
4Productivity
If unnecessary partial derivative equations are removed, then computational efficiency is improved, but the risk of removing needed equations increases
Solution Approach 1:
The patent implements a feedback mechanism through the symmetric matrix that continuously tracks which equations depend on which variables, both directly and indirectly. This feedback system ensures that before removing any equation, the system verifies that no other required computation depends on it, thereby maintaining reliability while improving efficiency.
Solution Approach 2:
The patent performs preliminary dependency analysis using the symmetric matrix to identify equations that can be safely removed. By conducting this analysis before actual computation, the system ensures that only truly unnecessary equations are eliminated, preserving the accuracy of derivative computation while enhancing computational efficiency.
Data Source
AI summary
A computing device identifies and eliminates unneeded computations from an analytic computation. A symmetric matrix includes a row and a column for each of a set of partial derivative equations where each cell includes an indicator of whether or not a direct dependency exists and is updated to include an indicator of whether or not an indirect dependency exists. A solution row is identified from the symmetric matrix that includes a requested partial derivative. A cell is identified of the identified solution row that does not include the indicator that the direct or indirect dependency exists. The column is identified from the symmetric matrix that includes the identified cell. The partial derivative equation associated with the identified column is removed from the defined set of partial derivative equations to reduce a computer processing time to compute a derivative value for the requested partial derivative.