A Neural Operator-Based Approach to Symbolic Discovery of PDEs

The article introduces NOMTO (Neural Operator-based symbolic Model approximaTion and discOvery), a framework that enhances symbolic equation discovery by integrating pretrained neural operators into symbolic networks. This approach allows for the representation of candidate equations as sparse differentiable computational graphs, effectively handling nonlocal differential operators and temporal memory effects. The method demonstrates its capability to recover complex governing equations, significantly broadening the scope of symbolic model discovery beyond traditional local derivative constraints, which is crucial for practitioners working with diverse dynamical systems in AI applications.