Can We Formally Verify Neural PDE Surrogates? SMT Compilation of Small Fourier Neural Operators

ArXi:2605.08938v1 Announce Type: new Fourier Neural Operators (FNOs) can greatly accelerate PDE simulation, but they are often used without formal guarantees that they preserve basic physical structure. We show that, once the trained weights and grid are fixed, the spectral convolution in an FNO is a linear map. As a result, the full forward pass is piecewise-linear and can be represented exactly in Z3's linear real arithmetic. We study two encodings. The exact encoding compiles the spectral convolution into a dense matrix multiplication, which is sound for both proofs and counterexamples.