Paper:
Published as a conference paper at ICLR 2018 DEEP LEARNING FOR PHYSICAL PROCESSES: INCORPORATING PRIOR SCIENTIFIC KNOWLEDGE
We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge more traditional approaches elaborated over the years in fields like maths or physics. However, despite considerable successes in a variety of application domains, the machine learning field is not yet ready to handle the level of complexity required by such problems. Using an example application, namely Sea Surface Temperature Prediction, we show how general background knowledge gained from the physics could be used as a guideline for designing efficient Deep Learning models. In order to motivate the approach and to assess its generality we demonstrate a formal link between the solution of a class of differential equations underlying a large family of physical phenomena and the proposed model. Experiments and comparison with series of baselines including a state of the art numerical approach is then provided.

Review:
The paper ‘Deep learning for Physical Process: incorporating prior physical knowledge’ proposes
to question the use of data-intensive strategies such as deep learning in solving physical 
inverse problems that are traditionally solved through assimilation strategies. They notably show
how physical priors on a given phenomenon can be incorporated in the learning process and propose 
an application on the problem of estimating sea surface temperature directly from a given 
collection of satellite images.
All in all the paper is very clear and interesting. The results obtained on the considered problem
are clearly of great interest, especially when compared to state-of-the-art assimilation strategies
such as the one of Béréziat. While the learning architecture is not original in itself, it is 
shown that a proper physical regularization greatly improves the performance. For these reasons I 
believe the paper has sufficient merits to be published at ICLR. That being said, I believe that 
some discussions could strengthen the paper:
 - Most classical variational assimilation schemes are stochastic in nature, notably by incorporating
uncertainties in the observation or physical evolution models. It is still unclear how those uncertainties 
can be integrated in the model;
 - Assimilation methods are usually independent of the type of data at hand. It is not clear how the model
learnt on one particular type of data transpose to other data sequences. Notably, the question of transfer
and generalization is of high relevance here. Does the learnt model performs well on other dataset (for instance,
acquired on a different region or at a distant time). I believe this type of issue has to be examinated 
for this type of approach to be widely use in inverse physical problems.