Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning

Hector Vargas Alvarez, Dimitrios G. Patsatzis, Lucia Russo, Ioannis Kevrekidis, Constantinos Siettos

correcthigh confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:57 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper states and proves that POD-based reconstruction preserves the column-sum (mass) when data columns are normalized, using centering H = I - (1/nt)11^T, the fact that 1^T_nc X̄ = 0, that left singular vectors of X̄ are orthogonal to 1_nc, and that adding back the mean yields 1^T_nc X(I - H) = 1^T_nt; hence 1^T_nc X̃ = 1^T_nt (Proposition 1 and its proof) . The candidate solution follows the same chain of equalities and explicitly notes the σ_j>0 condition for retained modes, matching the paper’s logic.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The proof that POD reconstruction preserves mass is correct and important for physically faithful ROMs of crowd densities. The contribution integrates this guarantee into a practical latent-space forecasting pipeline. Minor clarifications about the precise rank reference (X vs. X̄) and the nonzero-singular-value condition for retained modes would improve precision.