Multi evolutional deep neural networks (Multi-EDNN)

The paper’s methodology defines solution and flux corrections that (i) make the assembled solution continuous across interfaces and (ii) enforce common interface-normal fluxes, with the auxiliary variable equal to the gradient of the corrected solution; it also introduces 1D monomial correction functions and states the C-EDNN cost reduction. The candidate solution re-derives these results with explicit proofs (e.g., differentiating under the boundary integral and showing interface-flux matching and global conservation), and verifies properties of the monomial family and the complexity scaling. Aside from a minor boundary-condition typo in the paper’s 1D cardinality statement, the two are consistent, with the model offering a more formal treatment. Key steps, definitions, and formulas align with the paper’s equations for correction, flux splitting, and complexity claims.