Year: 2024
Type: preprint
Abstract: In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. Instead, most differential equation discovery algorithms try to recover the coefficients for a known structure. In this paper, we describe an algorithm that allows the discovery of unknown equations using automatically or manually extracted background knowledge. Instead of imposing rigid constraints, we modify the structure space so that certain terms are likely to appear within the crossover and mutation operators. In this way, we mimic expertly chosen terms while preserving the possibility of obtaining any equation form. The paper shows that the extraction and use of knowledge allows it to outperform the SINDy algorithm in terms of search stability and robustness. Synthetic examples are given for Burgers, wave, and Korteweg--De Vries equations.
Source: arXiv (Cornell University)
Authors: Ivanchik, Elizaveta, Hvatov, Alexander
Institution: ITMO University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2928192979, G3977144709, G6485016510
OpenAlex ID: W4406031422