Symbolic regression embedding dimensionality analysis

Patent metadata

Field	Value
Publication number	US-10599766-B2
Application number	US-201715843118-A
Country	US
Kind code	B2
Filing date	Dec 15, 2017
Priority date	Dec 15, 2017
Publication date	Mar 24, 2020
Grant date	Mar 24, 2020

Abstract

A dimensionality analysis method, system, and computer program product, include defining a grammar that describes an admissible relationship between quantities in a data set, discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar, conducting a search that determines which valid expression in the data set satisfy the grammar, and selecting the expression that fits the dataset and minimizes a measure of a complexity of the expression.

First claim

What is claimed is:

1. A computer-implemented dimensionality analysis method, the method comprising:
defining a free-form grammar that describes an admissible relationship between quantities in a data set;
discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar;
conducting a search that determines which valid expressions in the data set satisfies the grammar and that determines a measure of a complexity of the expression; and
selecting the valid expressions that fits the dataset and minimizes the measure of the complexity of the expression.

2. The computer-implemented dimensionality analysis method of claim 1 , wherein the plurality of valid expressions are determined, and the valid expressions comprise a set of symbols representing viable operators, variables, and coefficients, along with grammatical rules that define a syntax of the valid expressions.

3. The computer-implemented dimensionality analysis method of claim 2 , wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

4. The computer-implemented dimensionality analysis method of claim 3 , wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

5. The computer-implemented dimensionality analysis method of claim 1 , wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

6. The computer-implemented dimensionality analysis method of claim 5 , wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationship between quantities.

7. The computer-implemented method of claim 1 , embodied in a cloud-computing environment.

8. A computer program product, the computer program product comprising a non-transitory computer-readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to perform:
defining a free-form grammar that describes an admissible relationship between quantities in a data set;
discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar;
conducting a search that determines which valid expressions in the data set satisfies the grammar and that determines a measure of a complexity of the expression; and
selecting the valid expressions that fits the dataset and minimizes the measure of the complexity of the expression.

9. The computer program product of claim 8 , wherein the valid expressions comprise a set of symbols representing viable operators, variables, and coefficients, along with grammatical rules that define a syntax of the valid expressions.

10. The computer program product of claim 9 , wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

11. The computer program product of claim 10 , wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationship between quantities.

12. The computer program product of claim 8 , wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

13. The computer program product of claim 12 , wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

14. A dimensionality analysis system, said system comprising:
a processor; and
a memory, the memory storing instructions to cause the processor to:
defining a free-form grammar that describes an admissible relationship between quantities in a data set;
discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar;
conducting a search that determines which valid expressions in the data set satisfies the grammar and that determines a measure of a complexity of the expression; and
selecting the valid expressions that fits the dataset and minimizes the measure of the complexity of the expression.

15. The system of claim 14 , wherein the valid expressions comprise a set of symbols representing viable operators, variables, and coefficients, along with grammatical rules that define a syntax of the valid expressions.

16. The system of claim 15 , wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between admissible relationships are allowed, depending on the corresponding attributes.

17. The system of claim 16 , wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

18. The system of claim 14 , wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between admissible relationship are allowed, depending on the corresponding attributes.

19. The system of claim 18 , wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

20. The system of claim 14 , embodied in a cloud-computing environment.

Assignees

• IBM

Inventors

• Gunawan Oki
• Horesh Lior
• Nannicini Giacomo
• Zhou Wang

Classifications

• G06F40/253 Primary

  Grammatical analysis; Style critique · CPC title

• G06F40/211 Primary

  Syntactic parsing, e.g. based on context-free grammar [CFG] or unification grammars · CPC title

• G06F16/3344

  using natural language analysis · CPC title

• G06F17/271

  Physics · mapped topic

• G06F17/274 Primary

  Physics · mapped topic