DeSyR Framework Recovers Equations from Neural Approximations

Researchers have introduced DeSyR, a novel decoupled symbolic recovery framework designed to extract compact explicit solutions from neural approximations of differential equations. This framework addresses the challenge of imperfect teacher data by separating the process into two main stages: a physics-informed neural network (PINN) first guides the search for potential symbolic topologies, proposing candidate equations with provisional constants. Once a suitable topology is identified, DeSyR refines its coefficients exclusively using the governing physical equations and constraints, rather than relying on the potentially noisy teacher data. This physics-only refinement process significantly reduces error, achieving median relative L2 errors as low as 2.31x10^-14. The framework demonstrates robust performance across a wide range of differential equation problems, proving that approximate neural teachers can effectively guide topology discovery without propagating their inherent error into the final recovered coefficients.