SINDybrid: automatic generation of hybrid models for dynamic systems

The paper formulates the identification problem with an L1 loss and a per-column sparsity regularizer (P1, their Eq. (8)), and then gives a Mixed-Integer Linear Programming reformulation (P2, their Eq. (9)) using slack variables Y,Z for absolute values and an auxiliary integer s with constraint Σj δj − s ≤ 0 and a positive penalty on s; this is the standard linearization and is correct in intent, though no proof is provided in the paper text . The candidate solution supplies the missing optimality argument that at an optimum y = |XLΞ − hexp|, z = |Ξ|, and s = Σj δj, so the P2 objective reduces exactly to P1. The candidate further proves an exact-support recovery statement under noiseless realizability and a full-column-rank condition on XL (an additional assumption not claimed by the paper), which is coherent and mathematically sound as an extension. Overall: the paper’s reformulation is correct but informal; the model gives a correct, explicit proof and adds a reasonable uniqueness result under extra hypotheses.