2208.11853
Data-driven Discovery of Chemotactic Migration of Bacteria via Machine Learning
Yorgos M. Psarellis, Seungjoon Lee, Tapomoy Bhattacharjee, Sujit S. Datta, Juan M. Bello-Rivas, Ioannis G. Kevrekidis
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper demonstrates partial-information PDE learning and a c-observer empirically, motivating the approach via Takens/Whitney embeddings, but it does not provide a rigorous existence/uniqueness argument for the learned closures. The model’s solution supplies a mathematically coherent existence proof (via Tietze/McShane extensions) under explicit identifiability assumptions (delay embedding and an injective jet map), thereby filling the theoretical gap. These assumptions are stronger than what the paper states, but under them the model’s argument is correct.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript convincingly demonstrates data-driven PDE discovery and closure/observer learning (including a challenging partial-information setting) on chemotaxis data. The empirical methodology is well executed. To aid readers, the assumptions underpinning the Takens/Whitney motivation (finite-dimensional attractor, generic observables) and the handling of boundary conditions under learned closures should be made explicit, but these are clarifications rather than substantive changes.