Symbolic Regression Dimensionality Analysis via Grammar Constraints
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Solution Overview
Problem
Conventional dimensionality analysis techniques fail to ensure consistency in unit dimensions of physical entities, leading to inconsistent and meaningless expressions, especially when dealing with large datasets where fixed-form solutions are not generalized and difficult to interpret.
Innovation Solution
A computer-implemented method that defines a grammar to describe admissible relationships between quantities, discovers symbolic expressions that account for dimensionality analysis, and conducts a search to select expressions that fit the dataset while minimizing complexity, using a dimensional attribute tree to ensure valid and meaningful interpretations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional fixed-form dimensionality analysis techniques are used, then the analysis process is simple, but the expressions become inconsistent and meaningless when dealing with large datasets
Solution Approach 1:
The patent transforms the rigid fixed-form approach into a flexible parameter-based system where dimensional attributes are represented as changeable parameters. The symbolic regression engine dynamically adjusts dimensional parameters to maintain consistency across diverse datasets, resolving the contradiction between reliability and complexity by making the system adaptive rather than static.
Solution Approach 2:
The patent introduces a grammar-based intermediary layer that mediates between raw data and dimensionality analysis results. This grammar acts as a mediator that enforces dimensional consistency rules while allowing flexible expression forms, thereby ensuring reliability without requiring complex ad-hoc analysis for each dataset.
2Adaptability or versatility
If free-form symbolic expressions are used to improve generalization, then the interpretability and meaning of expressions becomes difficult
Solution Approach 1:
The patent implements feedback mechanisms where the symbolic regression engine continuously evaluates expressions against dimensional grammar rules. This feedback loop ensures that while expressions can take free-form structures for better generalization, they must satisfy dimensional consistency constraints that maintain interpretability and physical meaning.
Solution Approach 2:
The patent segments the expression validation process into distinct grammatical rules for different dimensional attributes. By breaking down complex expressions into segmentable components that can be individually validated against dimensional grammar, the system maintains interpretability while allowing overall expression flexibility for generalization.
3Measurement precision
If a large amount of data is used to cover the space between points, then the accuracy improves, but the complexity and computational cost increases significantly
Solution Approach 1:
The patent performs preliminary action by pre-defining dimensional grammar rules and attribute hierarchies before analyzing datasets. This preliminary structuring of dimensional knowledge allows the system to efficiently evaluate expressions without requiring exhaustive computational exploration, thereby maintaining accuracy while improving productivity.
Solution Approach 2:
The patent creates a universal dimensional grammar framework that can handle multiple dimensional attributes and expression types through a single unified system. This multi-functional grammar structure eliminates the need for separate analysis procedures for different data scenarios, reducing computational overhead while maintaining precision across diverse datasets.
Data Source
AI summary
A dimensionality analysis method, system, and computer program product, include conducting a search that determines which valid expressions in a data set satisfies a defined free-form grammar that describes the data set.