NOMTO: Neural Operator-based symbolic Model approximaTion and discOvery

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.