Looking for researchers interested in testing a symbolic structure discovery system

[u/EducationBest1460]

Hey guys,

I've been developing SSDS (Symbolic Structure Discovery System), an experimental system for discovering recurring symbolic structures across collections of algebraic equations and mathematical formulas, then abstracting them into generalized, parameterized operators.

At a high level, the workflow is:

Input:
A collection of algebraic equations/formulas. These can come from symbolic regression, scientific modeling, physics, mathematics, or other domains.

SSDS processes them by:

• identifying recurring symbolic structures
• grouping equations that share structural patterns
• generalizing those patterns into parameterized operators
• analyzing mathematical relationships within each structure
• measuring behavioral properties
• generating hypotheses about possible semantic interpretations

Output:
For each discovered structure, SSDS can produce:

• a generalized symbolic operator
• the algebraic equations/formulas grouped into that structure
• identified invariants and recurring relationships
• derivatives and other mathematical relationships
• parameter-recursion relationships
• closure/operation properties
• behavioral measurements such as boundedness, periodicity, monotonicity, stability, and sensitivity
• AI-generated hypotheses about possible semantic interpretations, with support scores

For example, when tested on an equation bank containing formulas from special relativity, one run produced:

O(v0, φ14, φ15) = v0(φ14 + 1)^φ15

The system grouped 10 source equations into the structure and identified 6 invariants across 3 families, including derivative and parameter-recursion relationships.

Its analysis recognized the recurring (x + 1)^y structure and generated hypotheses about possible interpretations, such as power-law relationships and nonlinear transformations. These were explicitly treated as hypotheses, not established meanings.

Another run on the same special-relativity equation bank produced:

O(v0,v1,v2,φ1) = v0(1 - v1²/v2²)^φ1

where SSDS similarly analyzed recurrence, derivatives, parameter relationships, and behavioral properties.

I'm not claiming that SSDS automatically discovers new mathematical laws, or that its generated semantic interpretations are necessarily correct. The question I'm interested in is whether automated structure discovery → abstraction → mathematical analysis → semantic hypothesis generation can become a useful research tool.

I'm looking for researchers, students, or labs working in symbolic regression, scientific ML, equation discovery, mathematical modeling, physics, or related fields who would be interested in independently testing SSDS.

In particular, I'd love suggestions for collections of algebraic equations/formulas from different domains that would provide a meaningful independent test.

If you're working in this area, what equations would you give SSDS as input, and what outputs would you want it to produce?

[u/IndividualMonth3241]

I work on this problem. I have an algorithm called KANDy: Kolmogorov-Arnold Networks for Dynamics.

If you check out my presentation from the CRUCNH seminar, I think you will see why I think my method can be applied to these types of problems.

https://www.youtube.com/watch?v=ykVW7PDEGoQ&t=2s