Learning Compositional Koopman Operators for Model-Based Control
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have proposed to use deep neural networks as a more expressive class of basis functions for calculating the Koopman operators. These approaches, however, assume a fixed dimensional state space; they are therefore not applicable to scenarios with a variable number of objects. In this paper, we propose to learn compositional Koopman operators, using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The learned dynamics can quickly adapt to new environments of unknown physical parameters and produce control signals to achieve a specified goal. Our experiments on manipulating ropes and controlling soft robots show that the proposed method has better efficiency and generalization ability than existing baselines.
This paper proposes to learn compositional Koopman operators using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The combination of deep Koopman operator with graph neural nets is very novel and interesting. The experiments are also well designed and the results shown in the paper also indicate the effectiveness and efficiency of the algorithm in both simulation and control. In conclusion, I think this work can inspire more wok into modeling larger and more complex systems by integrating the power of the Koopman theory and the expressiveness of neural networks.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Compositional Koopman Operators for Model-Based Control
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have proposed to use deep neural networks as a more expressive class of basis functions for calculating the Koopman operators. These approaches, however, assume a fixed dimensional state space; they are therefore not applicable to scenarios with a variable number of objects. In this paper, we propose to learn compositional Koopman operators, using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The learned dynamics can quickly adapt to new environments of unknown physical parameters and produce control signals to achieve a specified goal. Our experiments on manipulating ropes and controlling soft robots show that the proposed method has better efficiency and generalization ability than existing baselines.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper proposes to learn compositional Koopman operators using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The combination of deep Koopman operator with graph neural nets is very novel and interesting. The experiments are also well designed and the results shown in the paper also indicate the effectiveness and efficiency of the algorithm in both simulation and control. In conclusion, I think this work can inspire more wok into modeling larger and more complex systems by integrating the power of the Koopman theory and the expressiveness of neural networks.
assistant
This paper proposes to learn compositional Koopman operators using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The combination of deep Koopman operator with graph neural nets is very novel and interesting. The experiments are also well designed and the results shown in the paper also indicate the effectiveness and efficiency of the algorithm in both simulation and control. In conclusion, I think this work can inspire more wok into modeling larger and more complex systems by integrating the power of the Koopman theory and the expressiveness of neural networks.