Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper proposes a solution called 'Neural Hybrid Automata' to model real world dynamical systems with multiple modes of operation and stochastic switching between modes. Such problems are plentiful in a variety of engineering domains. The authors address this using three modules: Dynamics model, Latent model to select the mode and Event model to predict the scitching.
main_review: This paper relies heavily on recent work around the use of Neuro-ODE, Hamiltonian and Lagrangian dynamics. From that perspective this is quite timely and relevant. The maths look good to me. I consider this very interesting, but there are a couple of things that can be improved.

- The first 2 modules of the work are quite solid. However, the last module that focuses on the switching is not as convincing, It is unclear how well it can capture stochasticity for example in a stock price as it reacts to market moving events. This is an area that has been well explored and there exists plentiful literature. Since not enough experiments have been conducted, it is unclear how this extends the state of the are as far as usefulness goes.

- Related to the above, the paper doesn't conduct enough experimentation for real world problems and that in my mind is a limitation. The experiments that are shown with synthetic data are not convincing enough.

- I would also like to see how it compares against known state of the art solutions.
limitations_and_societal_impact: Some limitations have already been mentioned in the paper. Please see the main review for additional ones.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This paper considers a modeling class (NHA) based on stochastic hybrid systems that can represent continuous-time processes with discrete events. They discuss the foundations of these models of the dynamics model, discrete latent selector, and event module to select events, and proposed a self-supervised mode recovery and supervision for events and jumps. NHA excel in diverse experimental settings on Reno TCP, mode mixing in switching systems, and behavioral control of wheeled robots. 
main_review: I like the paper! The foundations are reasonable and the experiments are well-investigated, analyzed, and documented for the community. 
S5.4 provides a nice overview of their insights and observations, and Fig 7 shows a nice visualization of the learned mode classification boundaries. 

My biggest question about this paper is on the experimental comparisons to neural ODE-based methods --- could NHAs be applied in many of the same settings where NODEs are already being used? The experiments presented in the paper have the feeling of new tasks that haven't been as considered before, which are interesting for the community to think about, but it would also be insightful if these methods could improve upon NODE-based modeling in the existing settings too.
limitations_and_societal_impact: The authors discuss some limitations and insights in S5.4 but otherwise did not have an extensive discussion in this space.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper introduces a complete pipeline for controlling with multi-modal transition and event handling. The method shown in the paper is based on normalizing flow and neural differential equations. In the experiments, the paper shows the efficacy in a few controlling cases. The method first segments the trajectory into multiple partitions, then performs the reconstruction using normalizing flow.
main_review: The problem formulation and presentation are fine. The figures (especially figure 2) are not really informative enough. The figures and captions should deliver straightforward ideas without ambiguities. The arrows are lack notations or explanations. It will be good to improve them.

The cross-reference in lines 254 and 259 are broken. The citation format is not uniform. They are not technical problems but it will be helpful to fix them.

My main reservation is the robustness of the proposed method. Does it perform constantly well against noises? A few quantitative results will help the reader understanding it.
limitations_and_societal_impact: Yes
review_title: null

Meta-review: After clarifications made by the authors in their rebuttal, all reviewers agreed about the merits of this work, and recommended acceptance. In the final version, please incorporate the feedback given in the reviews, and add the important clarifications of the rebuttal.
Decision: Accept (Poster)