NOMTO: Neural Operator-based symbolic Model approximaTion and discOvery

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Hauptverfasser: Garmaev, Sergei, Mishra, Siddhartha, Fink, Olga
Format: Preprint
Veröffentlicht: 2025
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author Garmaev, Sergei
Mishra, Siddhartha
Fink, Olga
author_facet Garmaev, Sergei
Mishra, Siddhartha
Fink, Olga
contents While many physical and engineering processes are most effectively described by non-linear symbolic models, existing non-linear symbolic regression (SR) methods are restricted to a limited set of continuous algebraic functions, thereby limiting their applicability to discover higher order non-linear differential relations. In this work, we introduce the Neural Operator-based symbolic Model approximaTion and discOvery (NOMTO) method, a novel approach to symbolic model discovery that leverages Neural Operators to encompass a broad range of symbolic operations. We demonstrate that NOMTO can successfully identify symbolic expressions containing elementary functions with singularities, special functions, and derivatives. Additionally, our experiments demonstrate that NOMTO can accurately rediscover second-order non-linear partial differential equations. By broadening the set of symbolic operations available for discovery, NOMTO significantly advances the capabilities of existing SR methods. It provides a powerful and flexible tool for model discovery, capable of capturing complex relations in a variety of physical systems.
format Preprint
id arxiv_https___arxiv_org_abs_2501_08086
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle NOMTO: Neural Operator-based symbolic Model approximaTion and discOvery
Garmaev, Sergei
Mishra, Siddhartha
Fink, Olga
Artificial Intelligence
Symbolic Computation
While many physical and engineering processes are most effectively described by non-linear symbolic models, existing non-linear symbolic regression (SR) methods are restricted to a limited set of continuous algebraic functions, thereby limiting their applicability to discover higher order non-linear differential relations. In this work, we introduce the Neural Operator-based symbolic Model approximaTion and discOvery (NOMTO) method, a novel approach to symbolic model discovery that leverages Neural Operators to encompass a broad range of symbolic operations. We demonstrate that NOMTO can successfully identify symbolic expressions containing elementary functions with singularities, special functions, and derivatives. Additionally, our experiments demonstrate that NOMTO can accurately rediscover second-order non-linear partial differential equations. By broadening the set of symbolic operations available for discovery, NOMTO significantly advances the capabilities of existing SR methods. It provides a powerful and flexible tool for model discovery, capable of capturing complex relations in a variety of physical systems.
title NOMTO: Neural Operator-based symbolic Model approximaTion and discOvery
topic Artificial Intelligence
Symbolic Computation
url https://arxiv.org/abs/2501.08086