Efficient Interdependent Systems Recovery Modeling with DeepONets

Somayajulu L. N. Dhulipala, Ryan C. Hruska

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper correctly formulates SoS recovery via a Markov-renewal Volterra equation, derives F(t)=I^T R(t) F, and informally matches it to the DeepONet template and architecture; however, it provides no rigorous well-posedness proof and loosely identifies the integrand mapping. The model solution gives a precise change-of-variables identification to the DeepONet form, supplies standard continuity/uniqueness conditions for the Volterra equation, and correctly notes that in the symmetric 4-system/16-state case with functionality vector {0, 0.25×4, 0.5×6, 0.75×4, 1}, the SoS functionality equals the average of the individual recovery probabilities. Aside from the paper’s minor mislabeling of the Markov-renewal equation as ‘nonlinear’, both accounts align; the model adds rigor and detail beyond the paper’s WIP exposition.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

Promising application and empirical results support the main claim that DeepONet can accelerate SoS recovery prediction. However, the theoretical exposition is informal: the Volterra equation is mislabeled as nonlinear, the DeepONet mapping is only sketched without an explicit change of variables or an explicit definition of the inner operator, and no minimal assumptions for well-posedness are stated. These gaps can be addressed with concise additions and clarifications, improving rigor without altering the main narrative.