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Title: Adaptive Self-Design Algorithm

Sep 2026 · Zenodo (CERN European Organization for Nuclear Research)

Abstract

Adaptive Self-Design Algorithm is a novel algorithmic framework designed to automate the design and optimization of mathematical formulas, particularly within complex non-standard and nonlinear equation systems. This approach leverages a probabilistic search algorithm, incorporating reinforcement learning and genetic algorithms, to iteratively refine formula parameters and capture the intricate structure of the formula. The algorithm's key innovation lies in the development of a "probability search" mechanism, coupled with graph neural networks to enhance formula complexity understanding. This represents a significant advancement over existing automated formula design methods, which often rely on predefined rules and limited flexibility. The proposed algorithm demonstrates the potential to overcome human limitations in formula creation, offering a robust and adaptable solution for a diverse range of mathematical challenges.

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