A Neural Operator-Based Approach to Symbolic Discovery of PDEs

Discovering governing equations from data remains challenging when the underlying dynamics involve nonlocal differential operators, field interactions governed by auxiliary equations, or temporal memory effects. We propose Neural Operator-based symbolic Model approximaTion and discOvery (NOMTO), a framework that extends Equation Learner-type symbolic architectures by incorporating pretrained neural operators as nodes in the symbolic network. NOMTO represents candidate equations as sparse differentiable computational graphs that combine algebraic operations with fixed neural operator surrogates pretrained to approximate nonlinear operators. We evaluate the method on model-discovery problems involving nonlocal spatial operators, couplings mediated by auxiliary field equations, and temporal integral terms representing memory effects. The results show that NOMTO can recover compact governing equations containing nonlocal operator terms, thereby extending symbolic model discovery beyond libraries restricted to local derivatives and point-wise algebraic combinations.