Multi-objective SINDy for parameterized model discovery from single transient trajectory data

The paper states and implements the weighted multi-objective SINDy formulation, shows its stacking equivalence, motivates the α→0 and α→∞ limits (linking the latter to a constrained formulation and the dimension condition nr ≤ nd − p), and explains why column normalization keeps λ from depending on α; these claims are accurate but given at a high level. The candidate model provides rigorous proofs of A–D, including a careful α-limit analysis and a spectral conditioning study that the paper only motivates qualitatively. Thus, the two are consistent; the model supplies detailed proofs aligned with the paper’s claims.