Learning Partially Observed PDE Dynamics with Neural Networks
Spatio-Temporal processes bear a central importance in many applied scientific fields. Generally, differential equations are used to describe these processes. In this work, we address the problem of learning spatio-temporal dynamics with neural networks when only partial information on the system*s state is available. Taking inspiration from the dynamical system approach, we outline a general framework in which complex dynamics generated by families of differential equations can be learned in a principled way. Two models are derived from this framework. We demonstrate how they can be applied in practice by considering the problem of forecasting fluid flows. We show how the underlying equations fit into our formalism and evaluate our method by comparing with standard baselines.
 + An interesting idea to learn the hidden state evolution and the state-observation mapping jointly + The experiments on Euler*s equation are slightly better than ResNet for 30 steps ahead forecasting in terms of MSE + The paper is clearly written and well-explained - The model is not new: ResNet for state evolution and Conv-Deconv for state-observation mapping - The difference between ResNet and the proposed framework is not significant, ResNet is even better in Figure 2 - Missing an important experiment: test whether the model can generalize, that is to forecast on different initial conditions than the training dataset - How does the model compare with GANs (Y. Xie* , E. Franz* and M. Chu* and N. Thuereyy, “tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow”)?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Partially Observed PDE Dynamics with Neural Networks
Spatio-Temporal processes bear a central importance in many applied scientific fields. Generally, differential equations are used to describe these processes. In this work, we address the problem of learning spatio-temporal dynamics with neural networks when only partial information on the system*s state is available. Taking inspiration from the dynamical system approach, we outline a general framework in which complex dynamics generated by families of differential equations can be learned in a principled way. Two models are derived from this framework. We demonstrate how they can be applied in practice by considering the problem of forecasting fluid flows. We show how the underlying equations fit into our formalism and evaluate our method by comparing with standard 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>



 + An interesting idea to learn the hidden state evolution and the state-observation mapping jointly + The experiments on Euler*s equation are slightly better than ResNet for 30 steps ahead forecasting in terms of MSE + The paper is clearly written and well-explained - The model is not new: ResNet for state evolution and Conv-Deconv for state-observation mapping - The difference between ResNet and the proposed framework is not significant, ResNet is even better in Figure 2 - Missing an important experiment: test whether the model can generalize, that is to forecast on different initial conditions than the training dataset - How does the model compare with GANs (Y. Xie* , E. Franz* and M. Chu* and N. Thuereyy, “tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow”)?
assistant
 + An interesting idea to learn the hidden state evolution and the state-observation mapping jointly + The experiments on Euler*s equation are slightly better than ResNet for 30 steps ahead forecasting in terms of MSE + The paper is clearly written and well-explained - The model is not new: ResNet for state evolution and Conv-Deconv for state-observation mapping - The difference between ResNet and the proposed framework is not significant, ResNet is even better in Figure 2 - Missing an important experiment: test whether the model can generalize, that is to forecast on different initial conditions than the training dataset - How does the model compare with GANs (Y. Xie* , E. Franz* and M. Chu* and N. Thuereyy, “tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow”)?