NOMTO: Neural Operator-based symbolic Model approximaTion and discOvery

TL;DR

NOMTO introduces a neural operator-based approach for symbolic model discovery, enabling the identification of complex non-linear relations and differential equations beyond the limitations of traditional symbolic regression methods.

Contribution

It presents a novel neural operator framework that broadens the scope of symbolic operations for discovering complex models in physical systems.

Findings

Successfully identifies symbolic expressions with singularities and special functions.

Accurately rediscoveres second-order non-linear PDEs.

Significantly enhances the capabilities of existing symbolic regression methods.

Abstract

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.