Estimating Varying Parameters in Dynamical Systems: A Modular Framework Using Switch Detection, Optimization, and Sparse Regression

The paper introduces a modular framework for estimating time‑varying parameters via switch detection (binseg) with hyperparameters σ and s_g, segment‑wise optimization with numerical integration, and an optional sparse‑regression stage for continuous p(t). It defines the problem, metrics, and a complexity expression m·O(fSD(N)) + N̂s·O(N·fopt(N,np)), arguing O(N^2) in typical worst cases, and notes that global optimality of all substeps would be required but does not present a formal correctness proof (their Remark 3) . The candidate solution reproduces the same modular pipeline, matches the complexity claim, and provides consistent guidance on σ and s_g; additionally, it supplies a conditional noiseless‑correctness argument under explicit identifiability and perfect detection assumptions that the paper does not formalize. Hence both are consistent and correct in scope: the paper is methodological and empirical; the model adds a compatible, idealized correctness argument.