Structure-preserving generalized transferable neural networks for the Cahn-Hilliard equation

What the math gives to ML

The paper's most transferable machinery is a fixed-feature neural representation in which all nonlinear hidden parameters are sampled once and only a linear output layer is recomputed at each time step. This converts repeated nonlinear optimization into a constant-design-matrix least-squares solve, making the representation cheap to update and naturally reusable across time, domains, or related tasks. Its stronger contribution is an explicit post-solve projection onto a linear invariant, which can be generalized from Cahn-Hilliard mass conservation to exact conservation of token counts, graph mass, probability normalization, or other known linear constraints in neural outputs.