reviews: 
Comments: The paper introduces a new method to apply strict physical rules in mixture-of-experts (MoE) for intricate dynamic systems. The authors believe that when training neural networks, using well-known physical rules, like conservation laws, can enhance results and speed up learning processes. But, there's a drawback: this method can take up a lot of computing power and storage, especially with big systems.

To solve this, the authors suggest using MoE. Here, the data is split into sections, with each section having an "expert" to apply the rules. Every expert works on a specific part of the data, and a special network decides how much importance to give each expert's output. This method saves on computing power and storage but still gives accurate results.

They test their method on various physical problems, such as fluid movement and quantum mechanics. They compare their results with other top methods and find their method is just as good, if not better, and uses less resources. Plus, it can handle big systems. In conclusion, the paper offers a fresh and effective way to use MoE to apply strict physical rules, which could make neural networks better and faster at solving complex systems.
Strengths: 1. Novel approach: The paper presents a novel approach to enforcing hard physical constraints using a mixture of experts (MoE) that significantly reduces computational and memory costs while maintaining accuracy and convergence guarantees.

2. Scalability: The authors demonstrate that their approach scales well to large-scale systems, making it suitable for complex dynamical systems.

3. Comparative analysis: The paper provides a detailed comparative analysis of their approach with other state-of-the-art approaches, showing that it achieves comparable or better performance while being significantly more efficient.

4. Real-world applications: The authors demonstrate the effectiveness of their approach on several physical problems, including fluid dynamics, structural mechanics, and quantum mechanics, showing that it has real-world applications.

5. Clear presentation: The paper is well-written and clearly presents the approach, methodology, and results, making it easy to understand and follow.
Weaknesses: While the paper presents a novel and scalable approach to enforcing hard physical constraints using mixture-of-experts (MoE), there are some potential weaknesses that should be considered. 

Firstly, the paper lacks empirical evaluation of the approach on a wider range of physical problems. While the authors demonstrate the effectiveness of their approach on several physical problems, including fluid dynamics, structural mechanics, and quantum mechanics, it would have been beneficial to have more empirical evaluation of the approach on a wider range of physical problems. This would have helped to better understand the generalizability and limitations of the approach.

Secondly, the paper does not provide a detailed theoretical analysis of the approach. While the authors provide a detailed description of the approach, they do not provide a detailed theoretical analysis of the method. This could have helped to better understand the underlying principles and assumptions of the method, and to provide a more solid foundation for future research.

Thirdly, the paper does not discuss the limitations of the approach. While the authors discuss the advantages of their approach, they do not discuss the limitations of the method. For example, the assumptions made about the physical system or the potential impact of the choice of experts on the overall performance. This could limit the ability of readers to fully understand the applicability and limitations of the approach.
Recommendation: 6: marginally above the acceptance threshold
Reviewer confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 3 good
Clarity: 3 good