Venue: ICLR 2023 TinyPapers

Reviews:

final_score: rating: Needs Clarification (NC): a submission which does not meet the reviewing criteria and needs clarification for its described problem or solution
review_content: summary_of_contributions: The paper proposes an extension of an older ICLR 2022 article “D-CODE: Discovering closed form ODEs from closed trajectories”, that proposes a symbolic regression framework that approximates  time derivatives from time-series data variationally. The present paper proposes an extension of the framework to systems with higher order derivatives by considering higher order derivatives of the test functions employed in the variational formulation.
strengths_and_weaknesses: strengths:
+ Interesting problem, that might be nevertheless challenging to solve adequately due to the difficulty to estimate the order of the observed system (to my understanding).

+ Clearly formulated aim of the project.


weaknesses:
- Several typos (e.g., section 2 first sentence)

- Inconsistencies between proposed formalism and claims/numerical experiments (see suggested changes)

- No literature review

suggested_changes: -I am a little bit confused with the assumptions of the method, so I think they require some clarification. In particular, in section 2 third line, the authors mention that $\mathcal{F}$ (the observed system) is a linear combination of up to n-th derivatives of $x(t)$. What I understand from this is assumed that the observed system is a linear system of n-th order. However the numerical experiments of the proposed method are applied to nonlinear systems. Here it needs some clarification if the assumption about linearity of $\mathcal{F}$ was indeed what the authors assume, and if the numerical experiment on purpose deviates from their assumption to test the capabilities and robustness of the approach. If yes I would think that another simpler example that follows the initial assumptions is also required to establish some baseline performance. Otherwise one of these two points have to be changed to resolve the inconsistency.

-No discussion or reference to previous literature excluding D-CODE paper. However there is limited space to do so, but I would suggest adding a section in an appendix.

-Not clear to me how one can know/infer the order of the observed system from the observations. Or is there the assumption that if one includes more orders in the estimation, the corresponding terms will be identified as almost zero?

-Line 9 section 2: “as in the paper”. You might want to mention the citation here.

-Typos at the beginning of section 2.
review_title: null

final_score: rating: Clear, Correct, and Reproducible (CCR): a submission which meets the reviewing criteria
review_content: summary_of_contributions: This tiny paper extends a previous work of symbolic regression for discovering ODE (D-CODE) to a setting which works for discovering higher order ODEs. Proofs and numerical results were provided to illustrate the application of the proposed method.  
strengths_and_weaknesses: Strengths:
1. The paper is well-written, concise and has a strong motivation for the work presented.
2. Numerical results are provided along with proofs of the proposed method
3. The paper also mets the formatting requirements.

Weaknesses:
1. While I appreciate the conciseness, some additional references and introduction would have improved the paper for readers not familiar with the previous work. 
2. Additional results comparing the proposed method to the previous method would have made the results more compelling.
3. Some typos
suggested_changes: 1. There seems to be some formatting and typos in the paper. For example, the first sentence in Section 2 is not capitalized and potentially had repeated phrases. Section 3. also refers to Table A3 twice.

2. I understand that in general, it might be challenging to provide comparisons as a benchmark to the proposed algorithm. However, it would make the lack of comparisons more compelling if the authors could explain why their method couldn't at least be benchmarked against the original method (D-CODE) in terms of the timing and the ODE discovered?

3. I believe that the paper's readability could be improved if the authors could also cite several seminal papers relevant to the field, in case the readers are not familiar and would like to get a better background on the work. 

All the best!
review_title: null

Meta-review: metareview: This concise paper tackles an interesting problem. While minor errors and inconsistencies present in the manuscript, it provides both theoretical arguments and experimental results to demonstrate the effectiveness of the proposed framework.
confidence: 3: The area chair is somewhat confident
Decision: Invite to revise